THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 

GIFT  OF 
Bift  U.C.  Librait 


We  keep  on  sale  the  largest  stock  of 
FINE  SHOES  in  the  city. 

Making  to  Measure,  for  Ladies,  Gents, 
and  Children,  a  specialty. 


Sea-faring  men  and  their  families  will  receive  special 
attention.  Any  orders  they  may  favor  us  with  will  be 
promptly  and  carefully  filled. 

Kast's 


Fashionable 


Nos.  2,  4  and  6 
DUPONT  ST. 


SAN  FRANCISCO 
CAL. 


Corner  of  Market  and  Dupont  Streets. 
PIONEER   SHIRT  .FACTORY, 

No.  233  Kearny  Street. 


FOR  THE  BEST  FITTING  SHIRT 


GO    TO 


233  KEARNY  STREET,  BET.  BUSH  AND  SUTTER. 

A  FINE  ASSORTMEMT  OF 


SHIRTS  MADE  TO  ORDER,  A  SPECIALTY. 

Special  Attention  given  to  Afasters  and  Officers 

of  Ships, 


W.W.  MONTAGUE  &  CO. 


IMPORTERS  OF 


Metals,  Stoves 

.       RANGES  |  CABOOSES, 

SHEET  AND  BOLT  COPPER, 

SHEET    IRON, 


WIRE, 

Rivets,Lead,Tin  Plate 

RUBBER  HOSE, 
SIIDEI   ILIEOIKTS,  IETO- 


MANUFACTURERS  OF 


COPPER,  SHEET  IRON  I  TIN  WARE 


PROMPT  ATTENTION  GIVEN  TO 


SHIP    WORK    OF    ALL    KINDS. 
1 10,  1 12,  1 14,  1 1 6  &  1 1 8  Battery  Street 

SAN   FRANCISCO. 
/        it 


T.    LUNDY, 

Importer  and  Jobber  of 

AMERICAN     AND     FOREIGN 

Clocks,  Jewelry 


AND 


OPTICAL   GOODS, 

9 


CORNER  OF  MARKET 

SAN    FRANCISCO. 


SILBERSTEIN'S 

SHIRT  FACTORY 

Nos.  950  and  952  Market  Street, 

UNDER  THE  BALDWIN, 
(Formerly  of  506  Kearny  Street,)  SAN  FRANCISCO,  CAL. 

IMPORTER  OF 

Meris  Fine  Furnishing  Goods, 

HOSIERY,    ETC.,    ETC. 
SPECIALTY— SHIRTS   TO   ORDER. 

Sea   Captains   and    Officers   will   do   well   to   inspect  our  goods   before 
purchasing  else  were  their  outfits. 


W.  S.  RAY. 


W.  R.  ANDERSON. 


db  CO. 

12  and   14  Market  St.  9  and   11   Sacramento  St. 

SAN  FRANCISCO,  CAL. 
Manufacture  and  keep  constantly  on  hand,          , 

SHIPS'  STOVES 

Nos.  0, 1,  2,  3,  4,  5,  6  and  7. 

SUITABLE  FOR  VESSELS  OF  FROM  20  TO  2000  TONS. 
MISSISSIPPI  STOVES  (Sheet  Iron)  FOR  S  TEA  MS  II  //V>' 

Also  Manufacture  and  keep  an  assortment  of  the  following  on  hand: 

Sidelights,  Lanterns,  Binnacle  Lamps,  Ships' Water  Closets 

Tin,  Copper,  Sheet  Iron  Ware,  Store  Linings  of  all  kinds,  Extra  Castings  and 

Brick  for  all  kinds  of  Ships'  Stoves,  Extra  Basing  and  all  Repairs  for 

Water  Closets,  also  Head  Pumps;  Red,  Greeii  and  Round 

Fresual  Glasses  for  all  styles  Sidelights  and  Lanterns. 

REPAIRS  EXECUTED  IN  THE  BEST  POSSIBLE  MANNER  AT  REASONABLE  RATKS. 

Pottery;  Antioch,  Cal,     Foundry;  228  Main  St.,  S,  F. 
Special  Attention  to  Masters  and  Officers  of  Ships. 

UNIFORM    CAPS    MADE    TO    ORDER. 


SAN  FRANCISCO. 

BRANCH,  910  MARKET  STREET,  ABOVE  STOCKTON. 

THE  FINEST  GOODS  !       THE  LARGEST  STOCK !       THE  LOWEST  PRICES  ! 


Merchant  Tailor, 

203  MONTGOMERY  ST.,  AND  103  THIRD  ST.,  SAN  FRANCISCO 
THE  BEST  FIT,  LOWEST  PRICES  AND  FINEST  GOODS  IN  THE  WORLD. 


The  Great  Artist  and  Cutter, 

FROM  NEW  YORK. 

303  MONTGOMERY  ST.,  AND  103  THIRD  ST.,  SAN  FRANCISCO 


LORENTZ  FOARD, 

Dealer  in  New  and  Second-Hand 

SHIP  MATERIAL 

The  Highest  Cash  Price  paid  for  Copper,  Metal, 
Zinc*  Lead,  Sails,  Rope,  Etc. 

3  I  5  STEUART  STREET, 

NEAR    MARKET,  SAN     FRANCISCO. 

All   kinds  of  Blocks  and   Flags,  old  and   new,  always  on   hand. 
SAILS  RENTED  OUT  BY  THE  DAY,  WEEK  OR  MONTH 

IMPORTANT  NOTICE  TO  OWNERS  AND  MASTERS  OF  VESSELS. 


METALINE  BUSHING 

FOR    BLOCKS. 


CAN  BE  RUN  AT  QUICK  SPEED  WITHOUT  OIL. 

A  new  improvement  in  the  Bushing  of  Blocks,  which  acting  as  its  own  lubricator,  overcomes  all 

friction,  at  the  same  lime  allowing  a  heavier  strain  and  workng  easier  than  any  other  Hushing 

ever  introduced  in  the  market.     For  all  places  where  a  heavy  strain  and  quick 

hoisting  is  required,  it  far  excels  all  other  kinds  of  Bushing. 

It  is  Admirably  Adapted  for   Wheel  Blocks  on  Account  of  its  Durability. 

WE  ALSO  HAVE  ALL  KINDS  OF  BLOCKS  AND  LlGNUM-vriVK  WoRK  FOR  SlUp'sUsE 

And  we  would  be  pleased  to  receive  a  call  from  you.     Our  Goods  can  be  found  at 

No.  18  Market  St. ,  San  Francisco,  Cal. 
BAGNALL  &  LOUD,  BOSTON,  MASS.     JOSEPH  CHESSMAN,  AGENT. 


Established  in  1852. 


(FROM  LONDON.) 

418  BATTERY  STREET, 

Between  Washington  and  Merchant.  SAN   FRANCISCO,  CALIFORNIA 

A  LARGE  ASSORTMENT  OF  CHARTS 


PUBLISHED    BY 


The  U.  S.  Hydrographic  Office          The    British   Admiralty 

The  U.  S.  Coast  Survey  Messrs.    Inray   &   Sons,  Etc.,  Etc. 

SAILING  DIRECTIONS, 

McNEVIN'S  PRACTICAL  NAVIGATION, 
SHIPPING  LAWS, 

WORKS  ON  NAVIGATION, 

LOG  BOOKS  AND  SLATES 

MARINE§OPERA  GLASSES 

TELIES  COPIES, 

Sextants,  Octants,  and    Quadrants, 
MESSRS.  JOHN  BLISS  &  GO'S  PATENT  TAFFRAIL  LOG 

AND 

MCNEVIN'S  LEE  WAY  INDICATOR. 

AGENT  FOR 

MASSEY'S  AND  WALKER'S  PATENT  LOGS 

AN  ASSORTMENT  OF 

Chronometers  by  approved  makers  for  sale  or  to  hire. 

CHRONOMETERS    REPAIRED,  CLEANED    AND    RATED    BY 
TRANSIT  OBSERVATIONS. 

Watches  of  all  descriptions  Carefully  Cleaned  and  li*1  paired. 


ANDERSON  &  RANDOLPH, 


MANUFACTURING 


Jewelers  and  Silversmiths 

101  &  103  MONTGOMERY  ST. 


CORNER  OF  SUTTER, 


E 


CO 

tf 
W 


w 

HH 

H 

hJ 
H- I 

U 

t— I 

O 


SAN     FRANCISCO,    CAL. 


n 
w 
z 

H 


en 

O 

a 

H 


> 

D 

O 
H 


o 

i— i 

^ 
»— i 

n 


THE  LARGEST  STOCK  IN  THE  CITY 

OF 

Gold  and  Silver  Watches,  Diamonds,  Jewelry  and  Silverware 

AT    MANUFACTURERS'    PRICES. 


SPECIAL  ATTENTION  PAID  TO  THE  REPAIRING  AND  REGULATING  OF 
FINE     WATCHES,    ETC. 


PLAZA      STORES 

OF 

C.  P.  Yan  Schaack  &  Co 

Nos.  706  TO  716  KEARNY  STREET, 

OPPOISTE    THE    PLAZA,  SAN  FRANCISCO,    CAL. 

Importers,  Wholesale  and  Retail  Dealers  in 

FURNISHING  GOODS, 

oiiOTimsro, 
HATS,  CAPS,  ETC.,  ETC. 


Captains  and  Officers   of  Ships   would   do  well   to  call  before  making 

their   purchases. 

SLOP-CHESTS  FITTED  UP  ON  REASONABLE  TERMS. 
EXCELLENT   OILSKINS,  ETC.,  ETC. 


DR.  SPINNEY  &  CO. 

No.  ii  KEARNY  STREET, 

TREAT  ALL  CHRONIC  AND  SPECIAL  DISEASES. 

YOUNG    MEN 

Who  may  be  suffering  from  the  effect  of  youthful  follies  or  indiscretion,  will  do  well  to 
avail  themselves  of  this,  the  greatest  boon  ever  laid  at  the  alter  of  suffering  humanity. 

DR.    SPINNEY 

will  guarantee  to  forfeit  $5°°  f°r  every  case  of  seminal  weakness,  or  private  disease 
of  any  kind  or  character  which  he  undertakes  and  fails  to  cure. 

MIDDLE-AGED     MEN. 

There  are  men  of  the  age  of  thirty  to  sixty  years  who  are  troubled  with  too 
frequent  evacuation  of  the  bladder,  often  accompanied  by  a  slight  smarting  sensation 
and  a  weakening  of  the  system  in  a  manner  the  patient  cannot  account  for.  On 
examining  the  urinary  deposits  a  ropy  sediment  will  often  be  found,  and  sometimes 
small  particles  of  albumen  will  appear,  or  the  color  be  of  a  thin  and  milkish  hue, 
again  changing  to  a  dark  and  torpid  appearance.  There  are  many  men  who  die  of 
this  difficulty,  ignorant  of  the  cause,  which  is  the  second  stage  of  seminal  weakness. 
Dr.  S.  &  Co.  will  guarantee  a  perfect  cure  in  all  such  cases,  and  a  healthy  restoration 
of  the  genito-urinary  organs. 

Medicine  Chests  fitted  up  on  reasonable  terms. 

OFFICE  HOURS:— 10  to  4  and  6  to  8.  Sundays  from  10  to  u  a.  m. 
Consultation  free.  Thorough  examination  and  advice,  $5.  Call  or  address. 

DR.  SPINNEY  &  CO. 

No.  1 1  Kearny  Street,  San  Francisco 


THIS 


H  A  M  M  A  M 

FINEST  BATH  HOUSE  IN  THE  WORLD. 

Improved  Turkish, 

Imperial  Russian, 
Medicated 


AND 


Electric 

BATHS  S  ALL  KINDS. 

NO  CHARGE  FOR  MEDICAL  SERVICES. 

Single  Baths,  $  1.50 

Ten  Tickets,  10.00 

A.  M.  LORYEA,  M.  D. 

PROPRIETOR. 


SAN    FRANCISCO,   CALIFORNIA. 


A.  L.  BANCROFT  &  CO. 

PRINTERS  AND   PUBLISHERS. 


Manufacturing  and  Publishing  of  Books  for  Authors. 


In  addition  to  a  large  number  of  law-books,  school-books,  and  pam- 
phlets that  we  have  published  during  the  last  year  or  so,  the  following  are 
among  those  which  were  published  more  particularly  for  authors,  for 
which  we  will  be  pleased  to  receive  orders: 

A  La  California.     Sketches  of  Life  in  the  Golden  State.     By  Col.  Albert 

S.  Evans.     379  pages.     8vo.     Cloth. 

Almond-Eyed.    A  Story  of  the  Day.    By  Atwell  Whitney.    With  17  full- 

page  illustrations.     170  pages,     izmo.     Paper.     1878.     50  cts. 

Behind  the  Arras.     By  C.  M.  Neville.     251  pages.     8vo.    Paper.     1877. 

$1.00. 

Birthday  Ode  to  Her  Most  Gracious  Majesty  Queen  Victoria  of  England. 

By  Mrs.  Theresa  Corlett.     8  pages.     8vo.     1877.     50  cts. 

Caxton's  Book.     A  Collection  of  Essays,  Poems,  Tales  and  Sketches.    By 

the  late  W.  H.  Rhodes.     Edited  by  Daniel  O'Connell.     300  pages.    Large  i2mo.    Cloth.    $3.00. 

Checkered  Life;  in  the  Old  and  New  World.    By  Rev.  J.  L.  Ver  Mehr. 

476  pages.     Svo.     Cloth.     1877.     $3.00. 

Fidelite.     By  Edna  Verne.     125  pages.  .    i2mo.     Paper.     1877.     50  cts. 
Ho!  for  Elf-Land.     By  Alice  Kingsbury.    136  pages.    Small  square  410. 

9  full-page  illustrations.     1877.     $1.50. 

Journal  of  Army  Life.  By  R.  Glisan.    511  pages.  Svo.  Illustrated.  $3.00. 
Madame  Jane  Junk  and  Joe.     By  Oraquill.     539  pages.     Large  i2mo. 

Cloth.     $3.00. 

Semi-Tropical  California.    By  Major  Ben.  C.  Truman.    204  pages.    8vo. 

Cloth.     Si. 50. 

Silver  Shimmer.     By  William  Darwin  Crabb.    92  pages.     i6mo.    Cloth, 

$1.00.     Paper,  50  cts. 

The  New  Penelope,   and  other  Stories  and  Poems.     By  Frances  Fuller 

Victor.     349  pages.     Small  Svo.     Cloth.     1877.     $2.00. 

The  Coal  Mines  of  the  Western  Coast  of  the  United  States.     By  W.  A. 

Goodyear.     153  pages.     Large  i2mo.     1877.     $2.50. 

The  Log  of  an  Ancient  Mariner.     Being   the  Life  and  Adventures  of 

Captain  Edgar  Wakeman.     378  pages.     Svo.     Cloth.     Illustrated.     1878.     $3.00. 

The  Poison  Fountain,  or  Anti-Parental  Education.    By  Zach.  Montgomery. 

189  pages.    Svo.    Cloth.     1878.    $1.50. 

[JUST    PUBLISHED.] 

A  Guide  to  Practical  Navigation.     Containing  the  rules  and  methods  of 

solving  problems  in  the  most  practical  manner;  the  simplest  and  most  complete  method  of  find- 
ing a  ship's  position  at  sea,  as  well  as  a  thoroughly  approved  method  of  finding  the  latitude  and 
longitude  at  the  same  instant  of  time  by  double  altitudes.  By  Capt.  E.  McNevin.  348  pages. 
Svo.  Cloth.  1878.  $4.00. 

Any  of  the  above  sent  by  mail,  post  paid,  on  receipt  of  advertised  price. 

[IN  PRESS.] 
History  of  San  Francisco,  and  Incidentally  of  California.     By  John  S. 

Hittell.     Svo.     Cloth.     $5.00. 

Apache-Land.     By  Chas.  D.  Poston.    i2mo.    Cloth.     150  pages.    $2.00. 

A.  L.  BANCROFT  &  CO. 

721  Market  Street,  San  Francisco,  Cal. 


A  GUIDE 


TO 


THE   RULES  AND  METHODS  OF  SOLVING  PROBLEMS  IN  THE  MOST  PRACTICAL  MAN- 
NER J    THE  SIMPLEST  AND  MOST  COMPLETE  METHOD  FOR  FINDING  A  SHIP'S 
POSITION  AT  SEA,  AS  WELL  AS  A  THOROUGHLY  APPROVED  METHOD 
OF  FINDING   THE  LATITUDE  AND  LONGITUDE  AT  THE  SAME 
INSTANT    OF    TIME.    BY    DOUBLE    ALTITUDES. 


BY 

CAPTAIN  E.  McNEVIK 


SAN   FRANCISCO: 

A.  L.  BANCROFT  &  COMPANY,  PRINTERS, 

721  MABKKT  STREET. 
1878. 


Copyright,  18/7,  T>y 
CAPTAIN  E.  McNEVIX. 


THE  RIGHT   OF  TRANSLATION  RESERVED  BY  THE  AUTHOR. 


.55  S" 


PREFACE. 


THIS  treatise  Las  been  written,  not  for  scientists  but  for  seamen; 
to  enable  the  navigator  to  find  at  any  time  quickly  and  accurately, 
his  position  at  sea.  By  carefully  studying  the  rules,  and  solving 
the  problems  herein  given,  he  will  assuredly  be  able  to  do  so.  The 
problems  are  solved  in  the  simplest  manner,  and  are  only  such  as  an 
experience  of  twenty  years  in  the  mercantile  service  has  shown  me 
to  be  necessary. 

This  book  is  therefore  not  encumbered  with  matter  and  tables  sel- 
dom or  never  used,  at  least  by  those  in  command  of  merchant  vessels; 
all  extra  methods  of  determining  latitude  and  longitude,  either 
difficult  in  themselves  or  of  doubtful  accuracy,  (such  as  lunar  and 
stellar  observations)  being  wholly  omitted.  This  book,  it  is  hoped 
will  enable  a  seaman  of  ordinary  education  to  instruct  himself  in 
all  that  is  really  necessary  for  him  to  know,  while  at  the  same  time 
it  will  aid  rather  than  repel  (as  many  works  have  done)  those  de- 
sirous of  subsequently  attaining  in  this  fine  science  a  higher  degree 
of  skill  than  is  needed  for  ordinary  navigation. 

To  polar-star  observations  for  finding  latitude,  (of  which  some  ex- 
amples are  given)  I  do  not  attach  much  importance,  as  the  pole  star 
is  too  dim  for  observation,  demanding,  (what  is  seldom  to  be  had,)  a 
well  defined  horizon,  and  is  besides,  available  only  in  the  Northern 
hemisphere.  As  to  lunars,  aside  from  the  expense  of  the  requisite 
tables,  and  the  fact  that  they  would  not  be  understood  by  more  than 
one  out  of  twenty,  they  are  rendered  still  less  necessary  since  the 
perfecting  of  chronometers.  In  my  long  career  I  have  met  but  few 
men  who  could  take,  accurately,  distances  by  lunar  observations; 
though  every  master,  when  questioned  as  to  his  ability  in  this  re- 
spect, can  do  so  to  perfection.  There  are  a  number  of  lunar  tables 
published,  but  to  those  wanting  such  I  would  recommend  Thomp- 
son's as  being  both  simple  and  accurate. 

I  have  given  Napier's  logarithmic  tables  of  natural  numbers,  being 
indispensable  for  accuracy  in  nautical  calculations.  These  tables, 
Captain  Thorn,  in  his  treatise,  not  only  omits,  but  repudiates,  telling 
us,  forsooth,  that  they  "  are  never  used  at  sea  ! "  He  might  almost 


565323 


PREFACE. 

as  well  have  said  that  the  compass  had  been  rendered  obsolete  by 
some  ' '  method  "  of  his  for  finding  the  north.  I  mention  this  that 
no  one  may  be  led  astray  by  statements  so  absurd.  Moreover,  we 
should  never  rely  (as  does  this  author)  upon  the  crude  approxima- 
tions of  inspection.  The  necessary  rules,  however,  for  working  by 
this  method,  are  given  for  those  who  wish  to  employ  them. 

For  finding  latitude  by  stellar  altitudes  (which  circumstances  not 
infrequently  render  desirable  at  sea)  I  have  referred  to  the  American 
Ephemeris  for  the  declination  of  the  fixed  stars  instead  of  to  the 
English  tables;  and  have  also  followed  the  star-notation  of  the  for- 
mer. I  have  used  a  portion  of  the  latter  only  in  the  problems  foi 
exercise  in  this  work. 

I  would  call  the  student's  special  attention  to  the  system  of  finding 
simultaneously  latitude  and  longitude  by  double  altitude;  a  system 
not  to  be  found  in  any  American  work  that  I  have  seen,  and  one 
upon  which  too  much  stress  can  scarcely  be  laid. 

In  this  work  I  would  also  call  attention  to  a  leeway  indicator, 
(of  .which  a  diagram  is  given)  and  which  I  have  long  used  with  great 
satisfaction  at  sea.  This  it  is  believed  will  be  found  highly  useful  to 
the  mariner. 

In  conclusion  I  would  say,  that  as  I  have  had  in  the  preparation 
of  this  work  only  the  needs  and  interests  of  sea-faring  men  in  view, 
I  trust  that  it  will  fulfill  its  mission  and  be  thought  worthy  of  their 
patronage. 

EDMUND  McNEVIX. 


CONTENTS. 


PREFACE :t 

DEFINITIONS   5 

TABLE  OF  ANGLES 9 

MULTIPLICATION  BY  LOGARITHMS   10 

DIVISION  BY  LOGARITHMS 11 

REDUCTION 12 

COMPOUND  ADDITION 13 

COMPOUND  SUBTRACTION 1& 

LATITUDES 14 

TRAVERSE  SAILING 18 

PARALLEL  SAILING ...  19 

MIDDLE  LATITUDE  SAILING 20 

MERCATOR'S  SAILING 30* 

DEVIATION  OF  THE  COMPASS 39 

VARIATION  OF  THE  COMPASS 41 

LEEWAY 4& 

DAY'S  WORK 49 

TIME    •. 55 

AMPLITUDE 58 

CORRECTION  OF  THE  COMPASS  BY  AN  AZIMUTH  62 

LATITUDE  BY  MEUIDIAN  ALTITUDE  OF  SUN 65 

LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN 68 

LATITUDE  BY  STAR'S  MERIDIAN  ALTITUDE 71 

LONGITUDE  BY  CHRONOMETER 73 

RULES  FOR  FINDING  THE  LONGITUDE 75 

EXAMINATION  PAPERS  AS  WORKED  OUT  FOR  THE  BOARD  OF  TRADE  ...  81 

LATITUDE  AND  LONGITUDE  BY  DOUBLE  ALTITUDES 94 

LATITUDE  BY  POLE  STAR 104 

To  FIND  THE  TIME   OF  A  STAR'S   PASSING  THE   MERIDIAN,    ALSO,   ITS 

APPROXIMATE  ALTITUDE 106 

FINDING  THE  TIME  AT  A  GIVEN  MERIDIAN 108 

To  FIND  THE  ERROR  OF  A  WATCH  OR  CHRONOMETER  BY  EQUAL  ALTI- 
TUDES OF  THE  SUN Ill 

EQUATIONS  OF  EQUAL  ALTITUDES 112. 

To   FIND  THE   SHIP'S    POSITION   FROM   TWO   BEARINGS   OF   THE    SAMI: 

OBJECT 115. 

TABLE  FOR  SAME 117. 

EXPLANATION  OF  THE  TABLES 118 

TABLES  .                                                                                                  .....  127. 


CONTENTS. 

CONTENTS   OF   THE  TABLES. 

PAGE 

I.  LOGARITHMS  OF  NUMBERS 127 

II.  LOGARITHMIC  SINES,  TANGENTS,  SECANTS,  ETC 143 

III.  DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  POINTS  .  .  .  188 

IV.  DIFFERENCE  OF  'LATITUDE  AND  DEPARTURE  FOR  DEGREES.  .  204 
V.  MERIDIONAL  PARTS 249 

VI.  REFRACTION 257 

VII.  DIP  OF  THE  HORIZON 257 

VIII.   SUN'S  PARALLAX 257 

IX.   To  REDUCE   THE  EQUATION   OF  TIME  TO   ANY  TIME  UNDER 

THE  MERIDIAN  OF  GREENWICH 258 

X.  To    OBTAIN   THE  PROPORTIONAL   PART  OF  THE   RATE  OF   A 
CHRONOMETER   FROM   NOON,    TO   ANT   GIVEN  HOUR  AT 

GREENWICH 258 

XI.  TURNING  DEGREES  INTO  TIME,  AND  VICE  VERSA 259 

XII.  To  REDUCE  THE  SUN'S  DECLINATION  AT  ANY  MERIDIAN.  .  .  .   26Q 

XIII.  CORRECTION  FOR  APPARENT  ALTITUDE  OF  SUN  OR  STAR  .  .  .    262 

XIV.  NATURAL  SINES  AND  COSINES 265 

XV.  FOR  FINDING  THE   DISTANCE   OF   TERRESTRIAL   OBJECTS   AT 

SEA 274 

XVI.  LOGS  A  AND  B  FOR  COMPUTING  THE   EQUATION  OF   EQUAL 

ALTITUDES 276 

XVII.  LoG-RisiNfl%  FOR  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN.    277 
XVIII.  LOGARITHMS  FOR  FINDING  THE  APPARENT  TIME  OR  HORARY 

ANGLE 285 

XIX.  LATITUDE  BY  ALTITUDE  OF  POLE  STAR 294 

XX.  AMPLITUDE 295 

XXI.   NAUTICAL  ALMANAC  FOR  1878 '  298 

XXII.   LATITUDES  AND  LONGITUDES  OF  THE  PRINCIPAL  PORTS,  HAR- 
BORS, CAPES,  ETC.,  IN  THE  WORLD 322 


DEFINITIONS. 


1.  The  Equator  is  a  circle  passing  round  the  Earth,  equally  dis- 
tant from  the  poles,  dividing  the  globe  into  the  northern  and  south- 
ern hemispheres. 

2.  The  Poles  are  the  extremities  of  the  earth's  axis. 

3.  A  Meridian  is  a  great  circle  passing  through  both  poles,  cross- 
ing the  equator  at  right  angles,  and  dividing  the  globe  into  two 
parts,  called  eastern  and  western  hemispheres. 

4.  The  Ecliptic  is  the  apparent  annual  path  of  the  sun  in  the 
heavens. 

5.  The  Tropics  are  that  portion  of  the  earth  between  23i°  N,  and 
23i°  S. 

G.  Latitude  is  the  number  of  degrees  N.  or  S.  of  the  equator. 

7.  Parallels  of  Latitude  are  circles  parallel  to  the  equator. 

8.  Longitude  is  the  number  of  degrees  E.  or  AV.  of  Greenwich. 

9.  The  Visible  Horizon  is  the  circle  that  bounds  the  observer's 
view  at  sea. 

10.  The  Sensible  Horizon  is  the  circle  that  passes  through  the  eye 
of  an  observer  whose  poles  are  in  the  zenith  and  Nadir. 

11.  The  Rational  Horizon  is  the  circle  parallel  to  the  sensible 
horizon,  whose  plane  passes  through  the  center  of  the  earth. 

12.  The  True  Course  of  a  ship  is  the  compass. course  corrected  for 
deviation,  lee-way  and  variation. 

13.  A  Magnetic  Course  is  a  compass  course  corrected  for  lee-way 
and  deviation. 

14.  A  Compass  Course  is  the  course  steered  by  a  compass. 

15.  Variation  of  the  compass  is  the  angle  between  the  true  north 
and  the  magnetic  north. 

1G.  Deviation  of  the  compass  is  the  angle  between  the  magnetic 
north  and  the  compass  north. 

17.  The  Error  of  the  compass  is  the  sum  of  the  deviation  and 
variation. 

18.  Lee-way  is  the  angle  between  the  ship's  course  by  compass 
and  her  path  through  the  water. 


DEFINITIONS. 

19.  The  Meridian  Altitude  of  a  celestial  object  is  tlie  highest  alti- 
tude it  attains,  or  its  altitude  when  on  the  observer's  meridian. 

20.  Azimuth  is  the  angular  distance  of  a  body  from  the  meridian, 
measured  on  the  horizon. 

21.  Amplitude  is  the  complement  of  azimuth,  or  the  true  bearing 
of  an  object,  east  or  west,  on  the  horizon. 

22.  Declination  is  the  number  of  degrees  any  celestial  "object  is 
north  or  south  of  the  equator;  similar  to  latitude. 

23.  Polar  Distance  is  the  number  of  degrees  an  object  is  from 
the  elevated  pole. 

24.  Eight  Ascension  is  the  distance  of  a  celestial  object  from  the 
first  point  of  Aries,  measured  in  time  eastward  on  the  equinoctial. 

25.  The  Dip  or  Depression  of  the  horizon  is  the  angle  contained 
between  the  sensible  and  the  visible  horizon. 

26.  Refraction,  is  the  difference  between  the  real  and  the  apparent 
place  of  a  heavenly  body,  produced  by  the  passage  of  the  rays  of 
light  through  the  atmosphere. 

27.  Parallax  is  the  difference  between  an  altitude  of  a  celestial 
body  observed  at  the  center  of  the  earth  and  on  the  surface  of  the 
earth.     Semi-diameter  is  half  the  angle  under  which  the  heavenly 
bodies  appear  to  an  observer  on  the  earth. 

28.  An  Observed  Altitude  is  the  height  of  the  sun,  moon,  planet 
or  star  above  the  horizon,  as  measured  by  a  quadrant  or  sextant. 

29.  The  Apparent  Altitude  is  the  observed  altitude  corrected  for 
index  error  and  dip. 

30.  The  True  Altitude  is  the  apparent  altitude  corrected  for  re- 
fraction and  parallax. 

31.  Zenith  Distance  is  the  distance  of  a  heavenly  body  from  the 
•zenith,  or  point  of  the  heavens  over  our  heads. 

32.  Vertical  Circles  are  great  circles  passing  through  the  zenith 
and  Nadir;  perpendicular  to  the  horizon. 

33.  The  Prime  Yertical  is  a  great  circle  passing  through  the  zenith 
and  Nadir,  cutting  the  horizon  in  the  east  and  west  points. 

34.  Civil  Time  begins  and  ends  at  midnight;  the  first  12  hours 
called  A.  M.  ;  the  last  12  hours  called  p.  M. 

35.  Astronomical  Time  is  the  time  between  two  successive  tran- 
sits of  the  sun's  mean  center  over  the  same  meridian,  which  always 
begins  at  noon,  and  is  reckoned  through  the  24  hours  to  noon  again. 

36.  Mean  Time  is  the  hour  angle  of  the  mean  sun  westward  of  the 
meridian. 

37.  Apparent  Time  is  the  interval  hetween  the  sun's  departure 
from  and  his  return  to  the  same  meridian;  or  time  shown  by  the  sun 
.according  to  his  altitude,  reckoned  westward  of  the  meridian. 

38.  Equation  of  Time  is  the  difference  between  mean  time  and 
apparent  time. 


DEFINITIONS. 

39.  The  Hour  Angle  of  a  celestial  object  is  an  arc  of  the  equator 
contained  between  the  meridian  of  the  place  and  that  of  the  object. 

40.  The  Complement  of  an  arc  or  angle  is  what  that  arc  or  angle 
is  short  of  being  90°. 

41.  The  Supplement  of  an  arc  or  angle  is  what  that  arc  or  angle 
requires  to  make  it  180°. 

42.  The  Co-latitude  is  the  difference  between  a  given  latitude  and 
90°.     Polar  distance  is  a  celestial  object's  distance  from  the  north 
pole. 

43.  The  difference  of  latitude  of  two  places  is  the  portion  of  the 
meridian  included  between  their  parallels. 

44.  The  difference  of  latitude  of  a  ship  is  the  distance  she  makes 
from  any  point,  north  or  south. 

45.  The  difference  of  longitude  of  two  places  is  the  portion  of  the 
equator  included  between  their  meridians. 

EIGHT- ANGLED   TRIANGLE. 

• 

46.  The  course  steered  is  the  angle  between  the  meridian  and  the 
ship's  head;  the  course  made  good  is  the  angle  between  the  mer- 
idian and  the  ship's  real  track  on  the  ocean. 

47.  The  course  is  reckoned  from  the  meridian  accordingly,  north 
or  south  towards  the  east  or  west,  if  less  than  eight  points,  or  90°. 

48.  The  course  is  measured  in  points  of  11°  15'  each. 

49.  The  rhumb  line  is  the  ship's  track  when  crossing  all  the  me- 
ridians at  the  same  angle. 

50.  The  distance  between  two  places,  or  the  distance  sailed  by 
the  ship  on  a  certain  course,  is  measured  in  nautical  miles  of  60  to 
the  degree  of  latitude,  each  containing  6082  feet. 

51.  Three  such  miles  make  a  league. 

52.  The  departure  is  the  distance  sailed  clue  east  or  west,  or  the 
•distance  from  the  ship's  first  meridian,  and  is  always  equal  to  the 
difference  of  latitude  in  miles.     It  is  also  called  easting  or  westing, 
and  is  always  expressed  in  miles.     When  a  ship  sails  due  east  or 
west  she  makes  no  difference  of  latitude. 

53.  The  difference  of  latitude  is  the  space  contained  between  two 
parallels  of  latitude,  and  is  counted  on  the  meridian.     When  a  ship 
sails  north  or  south  she  makes  no  departure. 

54.  Taking  a  departure  means  taking  the  bearing  of  any  object 
by  compass,  or  its  angle  with  the  meridian,  and  estimating-  its  dis- 
tance from  the  ship  on  leaving  the  land. 


GIVEN  THE  TRUE  COURSE,  TO  FIND 
THE  MAGNETIC  COURSE. 

Easterly  variation  allow  to  the  left 
hand. 

Easterly  deviation  allow  in  the  same 
way. 

Westerly  variation  allow'to  the  rigljt 
hand. 

Westerly  deviation  allow  in  the  same 
way. 

ALLOW  LEEWAY 


GIVEN  THE  MAGNETIC  COURSE,  TO 
FIND  THE  TRUE  COURSE. 

Easterly  variation  allow  to  the  right 
hand. 

Easterly  deviation  allow  in  the  same 

way- 
Westerly  variation  allow  to  the  left 

hand. 
Westerly  deviation  allow  in  the  same 

way. 

FROM  THE  WIND. 


PRACTICAL  NAVIGATION. 


A  TABLE  OF  THE  ANGLES 

Which  every  point  and  quarter  point  of  the  compass  makes  with  the  meridian. 


NORTH. 

POINTS. 

O        '       " 

POINTS. 

SOUTH. 

D.     M.     8. 

01 

2  48  45 

01 

o$ 

5  37  30 

o{ 

of 

8  2G  15 

Of 

NbE 

NbW 

11  15  00 

SbE 

SbW 

11 

14  03  45 

11 

4 

1G  52  30 

if 

19  41  15 

If 

NNE 

NNW 

£ 

22  30  00 

2 

SSE 

SSW 

21 

25  18  45 

2i 

24 

28  07  30 

2| 

2| 

30  56  15 

n 

NEbN 

NWbN 

3 

33  45  00 

3 

SEbS 

SWb  S 

31 

36  33  45 

31 

si 

39  22  30 

8| 

42  11  15 

sf 

NE 

NW 

4 

45  00  00 

4 

SE 

SW 

41 

47  48  45 

41 

50  37  30 

44 

4 

53  26  15 

4| 

NEbE 

NWbW 

5 

5G  15  00 

5 

SEbE 

SWbW 

51 

59  03  45 

51 

61  52  30 

5§ 

64  41  15 

5f 

ENE 

WNW 

G 

67  30  00 

6 

ESE 

WSW 

Gl 

70  18  45 

61 

6^ 

73  07  30 

6* 

Gj 

75  56  15 

6f 

EbN 

WbN 

7 

78  45  00 

7 

EbS 

WbS 

71 

81  33  45 

71 

7* 

84  22  30 

7rV 

87  11  15 

7} 

EAST 

WEST 

8 

90  00  00 

8 

EAST 

WEST 

PRACTICAL  NAVIGATION. 


MULTIPLICATION  BY  LOGAEITHMS. 

Place  the  numbers  one  under  the  other,  the  same  manner  as  if 
they  were  to  be  multiplied  by  common  multiplication. 

Give  to  each  number  its  own  index,  which  will  always  be  one  less 
than  the  figures  in  the  whole  number. 

Next,  in  Table  I  (logarithms  of  numbers),  find  the  log.  corres- 
ponding to  each  number,  and  place  as  in  the  worked  example  oppo- 
site; then  add  the  logarithms  andindexes  together,  and  the  index  now 
obtained  will  show  how  many  figures. are  wanted  in  the  answer, 
which  is  always  one  more  than  the  index. 

4 
Rule  for  getting  Five,  or  more  Figures  in  tlie  Answer. 

Find  the  Logarithm  next  less  to  the  given  log.  which  will  point 
out  the  first  four  figures  of  your  answer — three  on  the  left  side,  and 
the  other  at  the  head  of  the  column  you  find  the  next  less  in;  then 
take  the  next  less  log.  found  from  yours,  to  which  annex  as  many 
ciphers  as  there  are  figures  wanted  more  than  four,  divide  this  by 
the  difference,  which  is  found  in  the  column  on  the  right  hand  side, 
and  the  quotient  will  be  the  remaining  figures  required;  and  if  you 
want  to  turn  the  remainder  into  a  decimal,  annex  a  cipher  and  divide 
again  by  the  same  difference  as  before. 

Rule  for  taking  out  a  Logarithm  for  a  number  consisting  of  Five,  or 

more  figures. 

Take  out  a  log.  for  the  first  four  figures  and  set  it  out  to  one  side; 
then  multiply  the  figures  that  there  are  more  than  four  in  your  num- 
ber, by  the  difference  on  the  right  hand  side  of  Table  I.  Cut  off 
from  the  product  to  the  right  hand  as  many  as  you  had  over  four 
in  your  number,  and  what  remains  being  added  to  the  logarithm 


DIYISIOX  BY  LOGARITHMS. 


11 


taken  out  for  the  first  four  figures,  makes  the  logarithm  required  for 
the  whole  number. 

When  the  first  of  the  figures  pointed  off  is  five,  or  exceeds  five,  add 
one  to  the  figures  you  are  going  to  apply  to  the  log.  of  the  first  four 
figures. 

Multiply  7235  by  822,  by  Common  Logarithms. 

7  ' 


91487 


Add  in  Multiplication. 


Ans.  5947164  =  6.774310 

774298  nearest  less  log. 

Diff.  73)     12000    (164 
73 

470 
438 

320 
292 

28  Remainder. 


Multiply  7890     by  987,      by  Common  Logarithms. 
Multiply  4789      by  976,      by  Common  Logarithms. 
Multiply  5648     by  765,      by  Common  Logarithms. 
Multiply  6979      by  878,      by  Common  Logarithms. 
Multiply  7898      by  549,      by  Common  Logarithms. 
Multiply  348.25  by  71.25,  by  Common  Logarithms. 
Multiply  7298       by  3.475,  by  Common  Logarithms. 
Multiply  3650.0  by  208.0,  by  Common  Logarithms. 
Multiply  65703    by  475,      by  Common  Logarithms. 

Ans.      7787428 
Ans.      4674064 
Ans.      4320720 
Ans.      6127549 
Aus.      4336000 
Ans.     24812.8* 
Ans.  25360.58* 
Aus.        759200 
Ans.    31208920 

NOTE. — A  decimal  is  got  by  annexing  a  cipher  and  dividing  again.  '  Bead  explanation  of 
Table  I  carefully. 


DIVISION  BY  LOGARITHMS. 

Place  the  number  and  their  indexes  as  in  multiplication,  and  get 
out  the  Logarithms,  which  are  subtracted  iu  division. 

"When  dividing  for  the  figures  wanted  more  than  four,  remember 
you  do  not  use  more  than  one  cipher  at  a  time,  viz :  Suppose  the  dif- 
ference between  the  logs  is  15,  and  you  annex  three  ciphers  which 
make  15,000;  now,  if  this  is  to  be  divided  by  say,  160)15,000(0  is 
the  first  figure  because  it  will  not  go  in  150,  that  is,  taking  one  of  the 
ciphers  only  at  a  time;  and  should  it  not  go  with  another  cipher 
taken  in,  as  it  may  sometimes  occur,  then  the  second  figures  will 
also  be  0.  And  again,  should  the  logs,  when  looking  for  the  next 
less,  agree  exactly,  then,  where  they  agree,  it  gives  you  the  first 
four,  and  any  more  wanted  will  be  ciphers  annexed  to  make  the 
required  number;  for  example — the  index  is  8  and  the  first  four  got 
out  is  7799,  then  the  proper  answer  is  779900000. 


12 


PRACTICAL  NAVIGATION. 


Divide— 8756403  by  228  by  Common  Logarithms. 
Log.  of  1st  4  figures. 


Ans. 


Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 


8756403  =  6.942326- 
228  =  2.357935 


38405.3  =  4.584391 
584331 


-942306- 
20 

942326 


33  left  over  four. 
50  ditf. 


20. 150 


113)  600  (5.3 
565 

113)  350  (3 
339 


11  Remainder, 


5678465  by 
8789786  by 
4785895  by 
34650  by 
3876000  by 
8247877  by 
248.603  by 


425, 
540, 
487, 
185, 
.12, 
789, 
3910, 


8.50078  by  890.1, 
84361912  by  .0341, 


by  Common  Logarithms, 
by  Common  Logarithms, 
by  Common  Logarithms, 
by  Common  Logarithms, 
by  Common  Logarithms, 
by  Common  Logarithms, 
by  Common  Logarithms., 
by  Common  Logarithms, 
by  Common  Logarithms. 


Ans. 
Ans. 
Ans. 
Ans. 
Ans. 
Ans. 
Ans. 
Ans. 


13361. 

16277. 

9827. 

187.297. 

32300074. 

10453. 

.06358. 

.009550. 


Ans.     2473960227. 


REDUCTION. 

To  reduce  Degrees,  Minutes  and  Seconds  of  Arc,  to  Minutes  or 
Seconds  of  Arc. 

Multiply  the  degrees  by  60,  and  to  the  product  add  the  minutes. 
This  sura  is  the  whole  of  the  minutes. 

Again  multiply  this   sum  by  60,  and  to  the  product  add  the  sec- 
onds. 

This  last  sum  is  the  whole  of  the  seconds. 


Ex.  1.     Reduce  to  minutes. 

12°    27' 
x      60 

Ans.        747    miles. 


Ex.  2.     Reduce  to  seconds. 
35°    00' 2G" 
x      60 


2100 
x         CO 


Ans.        126026" 


To  reduce  Seconds  or  Minutes  of  Arc,  to  Degrees,  Minutes  and 

Seconds. 

Divide  the  seconds  by  60,  and  the  remainder,  if  there  be  any, 
will  be  the  odd  seconds. 

Again  divide  the  preceding  quotient  by  60,  and  the  remainder 
will  be  the  odd  minutes. 

And  the  last  quotient  will  be  the  degrees,  minutes  and  seconds. 


Ex.  1.     Reduce     046    minutes 
degrees  and  minutes. 

60)946' 

15°  46' 


COMPOUND    SUBTRACTION. 

to 


13 


Ex.  2.     Reduce    5674    seconds    to 
degrees,  miuutes  and  seconds. 
60)5674" 

60)94'  34" 
Ans.          1°  34'  34" 


COMPOUND  ADDITION. 

To  add  Degrees,  Minutes  and  Seconds  of  Arc. 

Place  degrees  under  degrees,  minutes  under  minutes,  and  seconds 
under  seconds. 

Add  the  seconds  together,  and  if  their  sum  be  GO  or  upwards,  re- 
duce it  to  minutes  and  seconds. 

Place  the  seconds  that  remain  under  the  other  seconds,  and  add 
the  minutes  to  the  other  minutes.  If  the  sum  of  the  minutes  equal 
60,  or  more,  reduce  it  to  degrees  and  minutes. 

Place  the  minutes  that  remain  under  the  other  minutes,  and  add 
the  degrees  to  the  other  degrees. 


Ex.  1. 

together. 


Add  49°  38'  and  22°  58' 

49°  38' 
22  58 


Ans.     72°  36' 


Ex.  2.     Add    105°    3¥    18"    and 
158°  02'  10". 

105°  32'  18" 
158  02   10 


Ans.      263°  34'  28" 


COMPOUND  SUBTRACTION. 

To  take  the  Difference  between  Degrees,  Minutes  and  Seconds  of  Arc. 

Place  the  quantities  as  in  addition. 

Begin  at  the  seconds  of  the  lesser  quantity,  and  subtract  them 
from  those  of  the  greater. 

If  the  seconds  of  the  lesser  quantity  be  more  than  those  of  the 
greater,  add  GO  to  those  of  the  greater,  and  subtract  those  of  the 
lesser  from  the  sum. 

In  the  same  manner  subtract  the  minutes  of  the  lesser  quantity 
from  those  of  the  greater. 

If  GO  has  been  added  to  the  minutes  of  the  lesser  quantity  before 
subtracting  them,  proceed  in  the  following  manner  with  the  degrees: 

15'  40"    from 


Ex.  1.     Subtract  4 
8°  22'  26'. 

8°  22'  26" 
4   15  40 


Ans.      4°  06'  4G" 


Ex.  2.    Subtract  30°  28'    54"  from 
80°  40'  20". 

80°  40' 20" 
30  2854 


Ans.      50°  11' 26" 


14 


PRACTICAL  NAVIGATION. 


LATITUDES. 

To  find  the  Difference  of  Latitude  between  Two  Places  whose  Latitude 

is  given. 

"When  both  latitudes  are  of  the  same  name,  that  is,  when  they  are 
both  north  or  both  south,  take  their  difference  by  subtracting  one 
from  the  other,  for  the  difference  of  latitude. 

"When  the  latitudes  are  of  different  names,  that  is,  when  one  is 
north  and  the  other  south,  take  their  sum  by  adding  both  latitudes 
together  for  the  difference  of  latitude. 

To  name  the  different  latitudes,  consider  whether  the  place 
bound  to  is  north  or  south  of  the  ship's  place,  and  mark  the  differ- 
ent latitude  north  or  south  accordingly. 

Ex.  1.  Given  Point  Bonita  in  lati- 
tude 37°  49'  N.  and  Cape Mendocino  in 
latitude  40"  26'  N.  Required  the  dif- 
ference of  latitude. 

Latitude  Point  Bonita  . . .  37° 
Latitude  Cape  Mendocino.  40 


49'  N. 
26    N. 


Difference  of  latitude  =2°    37' 
x60 


157  miles. 


Ex.  2.  Given  Point  Bonita  in  lati- 
tude 37°  49'  N.  and  Callao  in  latitude 
12°  04'  S.  Required  the  difference  of 
latitude. 

Latitude  Point  Bonita 37°    49' N. 

Latitude  Callao 12     04  S. 

Difference  of  latitude  =  49     53'  S. 
x  60 


2993  miles. 


Given  the  Latitude  Left  and  Difference  of  Latitude,  to  find  the  Lati- 
tude In. 

When  the  latitude  left  and  the  difference  of  latitude  are  of  the 
same  name,  add  them  together,  their  sum  is  the  latitude  in,  and  of 
the  same  name  as  the  latitude  left. 

"When  the  latitude  left  and  difference  of  latitude  are  of  different 
names,  subtract  the  lesser  from  the  greater,  and  their  difference  is 
the  latitude  in,  of  the  same  name  as  the  greater. 


Ex.  1.  Given  the  latitude  left  19°  06' 
X,  and  difference  of  latitude  2°  24'  N. 
Required  the  latitude  in. 

Latitude   left...  19°  06'     N. 
Difference   lat..     2    24      N. 


Latitude  iu    21°  30'     N. 


Ex.  2.  Given  the  latitude  left  8°  04' 
N.  and  difference  of  latitude  C°  05'  S. 
Required  the  latitude  in. 

Latitude  left...  8°  04'   N. 
Difference  lat...  6    05     S. 

Latitude  in    1°  59'    N. 


Having  the  Latitude  In,  and  Latitude  Left,  to  find  the  Middle  Latitude. 

Add  the  latitudes  together  and  divide  the  sum  by  2,  and  the  re- 
sult is  the  middle  latitude. 

"When  the  latitudes  are  of  different  names,  add  the  half  of  the 
greater  latitude  to  the  half  of  the  less  latitude,  and  take  their  half 
sum  for  the  middle  latitude. 

If  one  latitude  be  great  and  the  other  small,  take  the  half  of  the 
greater  latitude  for  the  middle  latitude. 


MERIDIONAL  DIFFERENCE  OF  LATITUDE. 


15 


Ex.  1.  Given  latitude  left  19;  O.V  X. 
and  latitude  in  G'  04'  N.  Required  the 
middle  latitude. 

Latitude  left..   19°  05'    N. 

Latitude   in...     6    04    N. 

2)25    09 
Ans.         12J34'mid.  lat. 


Ex.  2.  Given  latitude  left  32°  19'  S. 
and  latitude  in  57'  -4  !S.  Required  the 
middle  latitude. 

Latitude  left...   3'2'M9'    S. 

Latitude  in . .    .   57   24     S. 


2)89  43 
Ans.         44°  51'niid.  lat. 


Ex.  3.     Latitude  of  A.  40°  43'  N.— Half  of  A.  20°  21' 
Latitude  of  B.  34°  22'  S.— Half  of  13.  17°  11' 


2)37°  32' 
Middle  latitude,     18°  46' 

To  take  out  of  the  tables  the  Meridional  Parts  for  a  Given  Latitude. 

Look  for  the  number  of  degrees  of  latitude  at  the  top  of  the 
table,  and  for  the  number  of  the  minutes  of  latitude  in  the  column 
marked  miles.  Then  look  down  the  column  of  figures  under  the 
degrees,  until  it  meets  the  line  of  figures  opposite  the  minutes. 

Take  out  the  number  at  the  point  of  meeting,  which  will  be  the 
meridional  parts  for  the  given  latitude. 

Ex.  1.  Find  the  meridional  parts  of  36°  58' Ans.  2390. 

Ex.  2.  Find  the  meridional  parts  of  28"  10' Ans.  17<>2. 

Ex.  3.  Find  the  meridional  parts  of  46J  48' Ans.  3185. 

Ex.  4.  Find  the  meridional  parts  of  38°  59' Ans.  2544. 

Given  (he  Latitude  Left  and  Latitude  In,  to  find  the  Meridional  Dif- 
ference of  Latitude. 

Take  out  the  meridional  parts  for  both  latitudes. 

"When  both  latitudes  are  of  the  same  name,  take  the  difference 
of  the  meridional  parts  for  the  meridional  difference  of  latitude. 

"When  the  latitudes  are  of  different  names,  take  the  sum  of  the 
meridional  parts  for  the  meridional  difference  of  latitude. 

Ex.  2.     Given  latitude  left  4°  28' N. 
and  latitude  in  2"  58'  S.     Required  the 
meridional  difference  of  latitude. 
Lat.    left  4°  28' N.  mer.  parts  268. 
Lat.  in      2   58  S.  mer.  parts  178. 


Fx.  1.  Given  latitude  left  39°  44'  N. 
and  latitude  in 46J  24'  N.  Required  the 
meridional  difference  of  latitude. 


Lat,  left  39°  44'  N.  mer.  parts  2C02. 
Lat.  in    46   24  N.  mer.  parts  3150. 


6  40  Mer.  diff.  lat.   548  mis. 
x60 


400    miles. 


7   26   Mcr.  diff.  lat.  446  mis. 
x60 


446  miles. 


Given  the  latitude  left  in,  as  follows;  required  the  meridional 
difference  of  latitude: 


No. 

Lat.  left 

Lat.  in 

Ans. 

No. 

Lat.  left 

Lat.  in 

Ans. 

1 

28°  40'  X 

30°  31'  N 

127 

4 

2°  48'  s 

2°  52'  x 

340 

2 

19°  46'  S 

26°  30'  s 

440 

5 

4°  28'  N 

2°  58'  S 

446 

3 

22°  50'  X 

26°  22*  S 

3049 

C 

65°  27'  s 

1°  08'  S 

5175 

16 


PRACTICAL  NAVIGATION. 


Given  (he  Longitude  of  Two  Places,  to  find  their  Difference  of  Longi- 
tude. 

When  both  longitudes  are  of  the  same  name,  that  is,  both  east  or 
west,  take  their  difference  for  the  difference  of  longitude. 

"When  the  longitudes  are  of  different  names,  that  is,  one  east  and 
the  other  west,  take  their  sum  for  the  difference  of  longitude. 

When  the  difference  of  longitude  exceeds  180°  take  it  from  3GO° 
and  the  remainder  will  be  the  difference  of  longitude. 


Ex.  1.     Given  Nemen's    Island   in 
longitude  179° 07'  E.  and  Drummond's 
Island  in  longitude   174'J  53'  E.     Re- 
quired their  difference  in  longitude. 
Longitude  Nemen's  Is.  179°  07'  E. 
Longitude  Drum.  Is...  174   53  E. 

Difference  longitude. ..      4°  14'  E. 
x60 

254    miles. 


Ex.  2.     Given  Vonio  Island  in  long- 
itude  177°  14'  E.  and  the  Eddystone 
in  longitude  4°  16'  W.     Required  their 
difference  in  longitude. 
Longitude  Vonio  Is. . .  177°  14'  E. 
Longitude  Eddystone.       4    16  W. 

181   30 
360  00 


Difference  longitude.    178^30' 
x60 


10710    miles. 


Given  the  longitudes  of  two  places,  A  and  B,  as  follows;  required 
their  difference  in  longitude. 


No. 

Longitude. 

Ans. 

No. 

Longitude. 

Ans. 

A 

B 

A 

B 

1 

2 
3 

128°  32'  W 
66a  24'  E 
46°  28'  W 

138°  23'  E 
78°37'w 
523  46'  E 

93°  05' 
145°  01' 
99°  14' 

4 
5 
6 

113°42'E 
3°  10'  E 
0°  16'  W 

99°  26'  W 
4°  05'  E 
0°  32'  E 

146°  52' 
0°55' 
0°48' 

Given  the  Longitude  Left  and  Difference  of  Longitude,  to  find  the 

Longitude  In. 

When  the  longitude  left  and  difference  of  longitude  are  of  the 
same  name,  take  their  sum  for  the  longitude  in,  and  it  is  of  the  same 
name  as  the  longitude  left. 

When  the  sum  exceeds  180°,  take  it  from  360°,  and  the  remainder 
will  be  the  longitude  in,  of  contrary  name  to  the  longitude  left. 

AVhen  the  longitude  left  and  difference  of  longitude  are  of  con- 
trary names,  take  their  difference,  which  will  be  the  longitude  in, 
and  of  the  same  name  as  the  greater. 


Ex.  1.  Given  longitude  left  44°  16' 
W.,  and  difference  of  longitude  1°  20' 
W.  Required  the  longitude  in. 

Longitude  left 44°  16"  W. 

Difference  of  longitude     1  20    W. 

Longitude  in 45'  36'  W. 


Ex.  2.  Given  longitude  left  165°  18' 
W.,  and  difference  of  longitude  7°  46' 
W.  Required  the  longitude  in. 

Longitude  left 175°  18'  W. 

Difference  longitude.       7  46    W. 

183    04  W. 
360    00 


Longitude  in 170°  56'  E. 


MERIDIONAL  DIFFERENCE  OF  LATITUDE. 


17 


Given  longitude  left  and  difference  of  longitude,  as  follows;  re- 
quired tlie  longitude  in. 


No. 

Long,    left 

Diff.  long 

Ans. 

No. 

Long,  left 

Diff.  long 

Ans. 

1 

2 
3 

3°  40'  w 
12°  42'  E 
59J  16'  W 

2°  10'  E 
6y  20'  w 
3°  53'  E 

1°  30'  w 
6°  22'  E 
55°  23'  w 

4 
5 
6 

182°  00'  E 
14°22'E 
10°20'w 

53°  20'  E 
5°  00'  E 
0°35'\v 

124°  40'  w 
19°  22'  E 
10U  55'  w 

Given  the  Course  and  Distance  to  take  out  of  Table  III,  for  the  Differ- 
ence of  Latitude  and  Departure. 

If  the  course  does  not  exceed  4  points  or  45°,  look  for  it  at  the 
head  or  top  of  the  page;  but  if  it  exceed  4  points  or  45°,  look  for  it 
at  the  bottom  of  the  page. 

Find  the  distance  in  one  of  the  columns  marked  "Dist.,"  and 
take  out  of  the  two  adjoining  columns,  to  the  right  hand,  the  num- 
bers in  the  same  line  with  it. 

Observe  whether  the  course  is  found  at  the  top  or  bottom  of  the 
page,  and  mark  the  numbers  taken  out  according  as  they  are  marked 
at  the  part  of  the  page  the  course  is  found  in. 

Given  course  2f  points,  distance  28  miles;  to  find  difference  of 
latitude  and  departure.  (Table  III.)  Ans.  Difference  latitude 
24.0;  departure  14.4. 

Given  course  34°,  distance  253  miles;  to  find  difference  latitude 
aud  departure.  Ans.  Difference  latitude  209.7;  departure  141.5. 

Given  the  Difference  of  Latitude  and  Departure,  to  find  the  Course  and 
Distance  in  Table  IV. 

Look  in  Table  IV,  until  the  difference  latitude  and  departure,  or 
numbers  near  to  them  are  found  together;  take  out  the  course  and 
distance  corresponding  thereto. 

Given  difference  latitude  55.4,  departure  35.9;  to  find  the  course 
and  distance.  Ans.  Course  33°;  distance  66  miles. 

Given  difference  latitude  71.0,  departure  123.0;  to  find  the  course 
and  distance.  Ans.  Course  60°;  distance  142  miles. 

PBAO.  NAV.— 2 


18 


PRACTICAL  NAVIGATION. 


TRAVERSE  SAILING. 

Traverse  sailing  is  the  finding  of  a  single  course  or  distance,  such 
that  it  would  have  brought  a  ship  to  the  same  place  that  several 
courses  and  distances  have  done. 

Form  a  table  similar  to  the  one  annexed  to  the  first  example.  The 
fii*st  column  contains  the  several  courses,  the  second  contains  the 
distance  run  on  each  course,  the  third  and  fourth  are  headed  N. 
(for  north)  and  S.  (for  south),  and  the  fifth  and  sixth  are  headed  E. 
(for  east)  and  W.  (for  west).  Find  by  inspection,  the  difference  of 
latitude  and  departure  for  every  course  and  distance.  Proceed  in 
the  following  manner:  If  the  course  does  not  exceed  4  points,  or 
45°,  look  for  it  at  the  top  of  the  page;  but  if  it  exceeds  4  points,  or 
45°,  look  for  it  at  the  bottom  of  the  page.  (Table  III.) 

Find  the  distance  in  one  of  the  columns  (of  Table  III)  marked 
"Dist.,"  and  take  out  of  the  adjoining  columns,  to  the  right  hand, 
the  numbers  in  the  same  line  with  it. 

Observe  whether  the  course  is  found  at  the  top  or  bottom  of  the 
page,  and  mark  the  numbers  taken  out  according  as  they  are  marked 
at  the  part  of  the  page  the  course  is  found  in. 

Set  the  difference  .of  latitude  under  N.  or  S.,  according  as  the 
course  is  towards  the  north  or  south,  and  the  departure  xinder  E.  or 
W. ,  according  as  the  course  is  towards  the  east  or  west. 

Then  add  the  sums  up  carefully  of  the  columns  N.,  S.,E.  and  W. 
Take  the  difference  between  the  sums  of  N.  and  S.,  which  will  be 
the  difference  of  latitude  made  good,  of  the  same  name  as  the  greater. 
Then  as  before,  take  the  difference  between  the  sums  of  E.  and  W., 
which  will  be  the  departure  made  good,  and  to  be  named  the  same 
as  the  greater. 

"With  the  difference  of  latitude  and  departure  made  good,  find  the 
course  and  distance. 

Look  in  Table  IV,  until  the  difference  latitude  and  departure,  or 
numbers  near  to  them,  are  found  together;  take  out  the  course  and 
distance  corresponding  thereto. 

1.  A  ship  sails  E.  S.  E.  14  miles,  and  then  W.  N.  W.  28  miles; 
required  the  course  and  distance  made  good. 


Course. 

Dist, 

Diff.     Lat. 

N.        S. 

Den. 
E.       W. 

SCE 
NGW 

14 

28 

10.7 

5.4 

12.9 

'25.9 

(i 

5.4 

it 
ii 

ii 

12.9 

5.3 

13.0 

Difference  latitude  5.3,  depart- 
\uc  13.0,  give  Table  iu  IV.  Course 
GS'.  Distance  14'. 


PARALLEL   SAILING. 


19 


2.  A  ship  sails  N.  W.  30  miles,  N.  N.  E.  21  miles,  and  S.  E.  17 
miles;  required  the  course  and  distance  made  good. 


Course. 

Dist. 

Diff.    Lat. 

Dcp. 

N. 

S. 

E. 

W. 

N  4  W 
N  -2  K 
S  4E 

30 
21 
17 

21.2 
19.4 

12.0 

8.0 
12.0 

21.2 

40.6 
12.0 

12.0 

20.0 

21.2 

20.0 

" 

« 

28.6 

1.2 

Difference  latitude  28.6  N., 
departure  L 2  W.,  gives  the  course 
N.  2°  W.  Distance  29  miles. 


PARALLEL  SAILING. 

To  log.  secant  of  the  latitude  add  the  log.  of  the  departure,  their 
sum  less  10  from  the  index  is  the  log.  of  the  difference  of  longi- 
tude. 

1.  In  latitude  G6°  40'  north.  The  departure  made  good  was  387  miles.  Re- 
quired the  difference  of  longitude  by  Parallel  Sailing. 

Secant Latitude        66°  40'     =     10.402217        Table  II. 

Log Departure  387    =      2.587711        Table  I. 

Difference  of  longitude 


977.1 


2.989928        Table  I. 


2.  In  latitude  36°  17'  south.     The  departure  made  good  was  187  miles.     Re- 
quired the  .difference  of  longitude  by  parallel  sailing.     Ans.  232.0  miles. 

3.  In  latitude  63°  39'  N.     The  departure  made  good  \vas  8.25  miles.     Re- 
quired the  difference  of  longitude  by  parallel  sailing.     Ans.  18'.59. 

4.  In  latitude  53°  52'.     The  departure  made  good  was  C.75  miles.     Required 
the  difference  of  longitude  by  parallel  sailing.    Ans.  11'.  44* 

5.  In  latitude  54°  12'  N.     The  departure  made  good  was  596    miles.    Re- 
quired the  difference  of  longitude  by  parallel  sailing.     Ans.  1019'. 

6.  In  latitude  69°  11' S.     The  departure  made  good  was   64.75  miles.     Re- 
quired the  difference  of  longitude  by  parallel  sailing.     Ans.  182'. 2. 

7.  In  latitude  43°  35'  S.     The  departure  made  good  was  99  miles.     Required 
the  difference  of  longitude  by  parallel  sailing.    Ans.  136'. 7. 

8.  In  latitude  66°  40'  S.     The  departure  made  good  was  387  miles.     Required 
the  difference  of  longitude  by  parallel  sailing.     Ans.  977'.  1. 


20  PRACTICAL  NAVIGATION. 

MIDDLE  LATITUDE. 

SAILING. 

Middle  latitude  is  half  the  sura  of  the  two  latitudes  when  they 
are  of  the  same  name,  or  half  their  difference  if  of  contrary  names. 

Find  the  difference  of  latitude  by  subtracting  if  they  are  both  north 
or  both  south,  or  adding,  if  one  north  and  the  other  south. 

Then  reduce  this  difference  of  degrees  to  miles  by  multiply  ing  the 
degrees  by  sixty  (60)  and  call  it  proper  difference  of  latitude. 

Find  the  difference  of  longitude  thus: — if  both  east  or  both  west, 
subtract  them;  if  one  is  east  and  the  other  west,  add  them,  and  if 
their  sum  exceeds  180°  subtract  the  sum  from  360°,  and  the  re- 
mainder will  be  the  difference  of  longitude. 

Reduce  this  difference  of  degrees  to  miles  in  the  same  way  as  the 
latitude  and  call  it  difference  of  longitude. 

The  course  must  be  named  the  same  as  the  longitude  left,  when 
the  sum  of  the  longitudes  has  to  be  taken  from  3GO°. 

In  working,  proceed  as  per  example. 

NOTE. — The  tables  for  -working  out  all  prjblems  by  Midlle  Latitude,  Bailing,  are  Tables  I 
and  II. 

TO    FIND    THE    DEPARTURE. 

Find  the  logarithm  of  the  difference  of  longitude,  Table  I  of 
this  book,  call  the  index  one  less  than  the  number  of  figures  in 
the  difference  of  longitude;  find  the  first  thi'ee  figures  in  the  left 
hand  column,  and  opposite  to  them,  and  under  the  fourth  figure  at 
head  of  the  column  will  be  the  required  log.,  to  which  prefix  the 
index,  and  this  will  give  the  log.  required;  and  to  find  the  log. 
co-sine  of  middle  latitude,  enter  Table  II,  and  with  the  degrees  at 
the  top  or  bottom  of  the  page,  and  miles  in  the  column  of  miles, 
will  be  found  the  log.  wanted,  the  sum  of  these  logs.  Subtracting 
the  radius  will  give  the  log.  of  the  departure. 

The  index  of  radius  is  always  10. 

TO   FIND    THE    COURSE. 

Find  the  log.  of  the  difference  of  latitude  by  the  same  rule  as  the 
above,  also  the  log.  of  the  departure;  add  the  log.  of  departure  to 
the  radius,  and  subtract  the  log.  of  the  difference  of  latitude,  and 
this  will  give,  the  log. -tangent  of  the  course.  To  find  the  tangent 
look  in  the  column  marked  tangent  at  the  top  or  bottom  of  the  page, 
run  up  this  column  until  the  log.  nearest  to  the  given  one  is  found, 
which  will  be  the  tangent  of  the  course  in  degrees,  the  miles  will 
be  found  in  column  of  miles. 

Having  found  the  course,  name  it  north  or  south,  and  east  or 
west,  according  as  you  have  to  make  northing  or  southing,  easting 
or  westing,  to  arrive  at  the  place  hound  to. 


MIDDLE  LATITUDE — SAILING. 


21 


TO    FIND    THE   DISTANCE. 

A.ddthe  log.  of  the  difference  of  latitude  to  the  log.-secant  of  the 
course,  and  subtract  the  radius,  the  difference  will  give  the  log.  of 
the  distance  in  Table  I,  if  the  index  be  3,  the  answer  will  require  4 
figures.  Look  in  the  column  of  logs,  and  find  the  nearest  log.,  hav- 
ing done  so,  you  will  find  the  first  three  figures  in  the  left  hand  col- 
umn, and  the  fourth  figure  at  the  top  over  the  column  where  the  log. 
is  found. 

CASE  1. 

Ex.  1.  Required  the  course  and  distance  from  A.  to  B.  by  calculation  of  mid- 
dle latitude,  sailing  principle. 

The  latitude  of  A.  is  51°  01'  N.,  and  longitude  is  122°  27'  W.;  the  latitude  of 
B.  is  4°  22'  S.,  and  longitude  is  144°  W. 


A.  lat..  51°  01' N. 

B.  lat..  4  22   S. 


Dif.  lat..  55°  23 
60 


Dif.  lat.  miles.  3323 


51°  01' 
4  22 

2)46   39 
23°  19'  Mid.  lat. 


|Long..l22027'  W. 
'Long..  144  30  W. 

22  03 
60 


1323  Dif.  Ion.  mis. 


TO  FIND  THE  DEPABTUBE. 

Radius    10.000000 

TO  FIND   THE   COUBSE. 

Dif.  lat.  33'23  3.521530 

TO    FIND  THE   DISTANCE. 

R»ditis  Ifl.OOOfOO 

Dif  Ion"    1323                 3  121560 

Radius  10  000000 

Dif.  lat  3323                      3  5V15;"0 

Mid    lat.  23°  19'  Cos      9.962999 

Departure  1215  3084559 

Course  20°  05'  .  .    Sec    10  027°45 

13.084559 
10.000000 

3.084559 
3.6*158.1 

13.548775 
10.1'OOOCO 

Dep.  1215...                ,    3.034559 

C'rsesS.20°05  W'    tan.  9.5J3029 

Distance  3538  3.C48775 

Ex.  2.  Required  the  course  and  distance  from  A.  to  B.  by  calculation  on 
middle  latitude,  sailing  principle. 

The  latitude  of  A.  is  31°  01'  S.  and  its  longitude  162°  10'  W. ;  the  latitude  of 
B.  is  38°  55'  S.  and  its  longitude  152°  00'  E. 


Lat.  of  A..  31°  01'  S. 
Lat.  of  B..38  55  S. 

31°  01' 
33   55 

Long..  162°  10'  W. 
Long..  152  00   E. 

Dif.  lat  7  54 

2)69   56 

314   10 

00 

34°  58'  Alid   lat 

Dif.  lat.  miles...  474 

TO  FIND  THE  DEPARTURE. 

Radius                             10  000000 

TO  FIND  THE  COUBSE. 

Dif  lat  474   2.C75778 

45  50  Dif.  Ion. 
60 

2750  Dif.  Ion.  mis. 

TO  FIND  THE  DISTANCE. 

Radius  10.000COO 

Dif  long    2~50                  3.439333 

Radius      10.000000 

Dif.  lat.  474  2.C.75778 

Hid   lat.  34D58'  Cos..     9.9135il 

Dep.  2254  3.362^14 

Course  78°  07'....  tec.  10.086302 

13.352874 
10000000 

13.352874 
2.075778 

13.303(40 

10.000000 

Dep.  2254...                .     3.352874 

C'rse  8.  78°  07'  W.  tan.  10  C77096 

Distance  2302...        .    3.3C:ObO 

22 


PRACTICAL  NAVIGATION. 


Ex.  3.  Required  the  course  and  distance  from  a  place  in  the  latitude  of  36° 
53'  S.  and  longitude  of  20°  0'  E.,  to  another  place  in  the  latitude  of  32°  38'  S.  and 
longitude  of  8°  54'  W. 

Ans.  N.  79°  46'  W. ;  distance,  1447  miles;  departure,  1424'. 

Ex.  4.  Required  the  course  and  distance  from  a  place  in  the  latitude  of  37° 
55'  N.  and  longitude  of  54°  23'  W.,  to  another  place  in  the  latitude  of  32°  38'  N. 
and  longitude  of  17°  05'  W. 

Ans.  Course  S.  80°  03'  E.;  distance,  1854  miles;  departure,  1827'. 


CASE  II. 

The  Latitude,  Course,  and  Distance  being  given,  to  find  the  Departure, 
Latitude  and  Longitude. 

Ex.  1.  A  ship  from  latitude  29°  47'  N.  and  longitude  24°  36'  W.,  sails  S.  S.  W. 
3  W.  960  miles.  Required  the  departure,  difference  of  latitude  and  longitude. 
(From  compass  card,  S.  S.  W.  f  W.  is  30°  56'.) 


TO  FIND  THE  DIFFERENCE  OP  LATITUDE. 

As  radius 10.000000 

Is  to  distance  9GO 2.982271 

So  is  co-siiie  of  course  30°  56'    9  933369 


12.915640 
10.000000 


Istodif.  of  lat.  60)823 


2.915640 


13°  43' 


TO    FIND  THE  LATITUDE  IN. 

Dif.  of  lat.  823'. .  13°  43'  8. 
Latitude  left 29  47  N. 


Latitude  in 16  04  N. 


Lat.  left...  29°  47'  N. 
Lat.  in....  16  04    N. 


Sum  of  lat  2)  45  51 
Mid.  lat...  22°  55' 


TO    FIND   THE   DEPARTURE. 

As  radius 10.000000 

Is  t  J  distance  900 2.-./82271 

So  is  sine  of  course  30°  56'    9.710997 

12693268 
10.000000 


To  the  departure  493' ....    2.693268 


TO  FIND  THE  DIFFERENCE  OF  LONGITUDE 

As  co-sine  of  mid.  lat.  22°  55'    9.964294 

Is  to  the  departure  493 2.693268 

Sois  radius 10.000000 


12.693268 
9.964294 


To  dif .  of  long.  60)536 


2.728974 


8°  56" 


Lin.  left  24°  36'  W 
Dif.  long.    8   £6  W 


Long,  in   33°  32'  W 


Ex.  2.  A  ship  from  latitude  2°  5'  N.,  longitude  22°  30'  W.,  sails  W.  S.  W. 
256  leagues;  required  her  present  latitude  and  longitude. 
Ans.  Latitude  2°  49' S.;  longitude  34°  20'  W. 

Ex.  3.  A  ship  from  latitude  34°  35'  N.  and  longitude  45°  16'  W.;  course  S.  83° 
36    E.;  distance   101  miles.     Required  the  latitude  and  longitude  in. 
Ans.  Latitude  in  34°  24'  N.;  longitude  in  43°  15'  "W. 

Ex.  4.  A  ship  from  San  Francisco  in  latitude  37°  48' N;  longitude  122°  27' W., 
sails  S.  W.  200  miles.     Required  the  latitude  and  longitude  in. 
Ans.  Latitude  in  35°  27'  N.;  longitude  in  125°  23'  W. 


MIDDLE  LATITUDE — SAILING. 


23 


CASE  III. 

Both  Latitude  and  Departure  from  the  Meridian  being  given,  to  find 
the  Course,  Distance  and  Difference  of  Longitude. 

Ex.  1.  A  ship  in  latitude  56°  50'  N.,  and  longitude  20°  KX  W.,  sails  south-east- 
erly until  she  makes  '210  miles  departure,  and  her  latitude  in  is  49°  15'  N.  Re- 
quired the  course,  distance  and  longitude  in. 


Latitude  left 56°  50'  N. 

Latitude  in..         .49   15   N. 


Dif.  of  latitude ....     7  35 
60 


455  miles. 


56°  50' 
49   15 

Sum.    2)106  05 


TO  FIND  THE  COCESE.  TO  FIXD  THE  DISTANCE. 

Dif.  latitude  455 2.638011  j  Course  24°  47'  sine. . .     9.022409 

Radius lO.oudOOO  Dep.  210 2322219 

Dtp.  210 2.3J2219  Kadius 10.000000 


12.322219 
2.658011 


Courses.  24°  47' E.  tan.  9.G6420 


12.322219 
9.(i224  9 


Distance  501 2.C998K) 


53°  0?   Middle  latitude. 


TO  FIND    THE  DIF.  OF  LONG. 

Mtd.  lat.  53°  02  cos. . .     9.7791r8 

Hep.  210 2.322-19 

Kadius  10.0000CO 


Dif    long.  60)349 


12.322219 
9.77i>128 


2.543091 


5°  49' 


Long    sailed  from ..  20°  10'  W. 
Dif.  long 5  49      E. 

Longitude  in 14°  21'  W. 


Ex.  2.  A  ship  in  latitude  4°  57'  N.;  longitude  30°  10'  E.,  sails  south-westerly 
until  her  departure  is  740  miles,  and  her  latitude  in  2°  S.  Required  her  course, 
distance  and  longitude  in. 

Latitude  left 4°  57'  N.  4°  57'  N. 

Latitude  in 2          S. 


Dif.  of  latitude 6  57' 

60 


Difference  latitude,    417  miles. 


2)2  57 
1°  28'  Middle  latitude. 


TO  FIND  THE  COCnSE. 

Dif.1at417 2.G50130 

Radius 10.DOOOOO 

Departure  740 2.869.'3J 


12.8f.9232 
2.620136 


C'rse  S.  60°  06'  W.  tan.  10.249096 


TO  FIND  THE  DISTANCE. 

Course  00°  36'  sin 9.940125 

Departure  740 2.869232 

Kadius 10.000000 

12.869232 
0.940130 


Distance  849.... 


2.9l>'.'107 


TO  FIND  THE  DIF.  OF  LONGITUDE. 

Mid.  lat.  1°  28'  cos...     9.999358 

Dep.  740 2.809232 

Kadius  10  OOOi  CO 


19.80U2U 

9.SI99858 

Dif .  long.  60)  740 2 .801)374 

12°  20'  W. 

Long,  sailed  from  . .  80°  10'  E. 
Dif .  longitude 12  20  W. 

Longitude  in 17°  50'  E. 


Ex.  3.  A  ship  in  latitude  49°57'N.,  and  longitude  15°  1C' W.,  sails  south- 
westerly until  her  departure  is  789  miles,  and  latitude  in  is  39°  20'  N.  Re- 
quired course,  distance,  longitude  in. 

Ans.  Course  S.  51° 05'  W.;  distance  1014  miles;  longitude  in,  33°  45'  W. 


24 


PKACTICAL  NAVIGATION. 


CASE  IV. 

Both  Latitudes  and  Course  given,  to  find  the  Departure,  Distance  and 
Difference  of  Longitude. 

Ex.  1.  A  ship  from  latitude  49°  57'  N.  and  longitude  30°  00'  W.,  sails  S.  W.  J  S. 
and  after  sailing  several  days  finds  by  observation  that  her  latitude  is  45°  31'  N. 
Required  distance  sailed  and  longitude  in. 

Turn  the  given  course  into  degrees  by  Compass  Table,  find  tJie  departure,  distance, 
and  then  the  difference  of  longitude. 


Latitude  left 49°  57'  N. 

Latitude  in..        , .  45   31  N. 


4  26 
60 

2GG  miles. 


49°  57'  N. 
45  31  N. 


2)95  28 
47  44'  Middle  latitude. 


TO  FIND  THE  DEPARTURE. 
Radius  10.000COO 

TO  FIND  THE  DISTANCE. 

Course  39°  Cos  ...     9.890503 

TO  FIND  THE  DIF.  OF  LONGITrDE. 

Mid.  lat.  47°  44'  Cos..     9.827745 
Departure  215  4  .  .          "  :t33->.M 

Dil'.  lat.  260.   . 

2  4°488° 

Dif.  lat.  266  

.  .  .     2  424882 

.  .tan.    9.9083C9 

Radius  

.  ..  10.000000 

Radius    

.  lo  0>  '1)000 

Dep  215  4    ... 

Distance  342.3.... 

Dif.  Ion.  60)320 
5°  20' 
Dif.  Ion  

12.333251 
10.000000 

12.424882 
9.890503 

12.333251 
9.827745 

.   .  .     2  333251 

.  ..     2.534379 

2.505506 

5°  207  W. 
30  00    W. 

Long.  in... 

35=  20'  "W. 

Ex.  2.  A  ship  from  latitude  42°  25'  N,  and  longitude  15°  6'  W.,  sails  N.  E.  by 
E.  for  two  days  and  then  finds  by  observation  that  she  is  in  latitude  46°  20'  N. ; 
required  the  distance  she  has  made  and  the  longitude  in. 

Ans.  Departure,  351.7;  distance,  423  miles;  longitude  in  6°  54'  W. 

Ex.  3.  A  ship  from  Cape  Flattery  in  latitude  48°  23' N.,  longitude  124°  22'  W., 
sails  until  she  is  in  latitude  40°  10'  N, ;  her  course  is  S.  W.  ^  W. ;  find  longitude 
in  and  distance  made. 

Ans.  Longitude  in,  138"  21'  W. ;  distance,  777  miles. 

Ex.  4.  A  ship  from  Cape  Mendocino  in  latitude  40°  29'  N.,  longitude  124°  29' 
W.,  sails  S.  W.  by  W.  until  she  is  in  latitude  34°  18'  N.j  required  distance  and 
longitude  in. 

Ans.  Distance,  668;  longitude  in,  136°  08'  W. 


MIDDLE  LATITUDE — SAILING. 


25 


CASE  V. 

Both .  Latitudes  and  Distance  given,  to  find  the   Course  and  Differ- 
ence of  Longitude. 

Ex.  1.  A  ship  sails  from  latitude  G°  50'  N.,  south-easterly  800  miles,  when  she 
arrives  in  latitude  5°  00'  S.    Required  her  course  and  difference  of  longitude. 

Latitude  left G°  50'  N.  Half  3°  25 

Latitude  in 5  00    S.  Half  2  30 


11°  50' 
x    60 

710  miles. 

TO  FIKD  THE  COURSE. 

As  the  distance  800 2.903000 

Is  to  radius 10.000000 

So  is  dif .  of  lat.  710 2.8ol258 

12.8ol2o8 
2.903060 


To  co-sine  of  course  S.  27°  2G'  E 9.94S1G3 


2)5  55 
2J  57'  Middle  latitude. 


TO  FIND  THE  DIFFERENCE  OFLOXGITUEE. 

As  co-sine  mid.  lat.  23  57' 9.999424 

Is  to  taug.  of  course  27°  26' — 9.71.VJ42 

So  is  dif.  lat.  710 2.8ol258 

13JMMOO 

9.G091-J4 


Difference  of  longitude  3CU 2.56707 S 


Ex.  2.  A  ship  from  latitude  5G°  30'  N.  1ms  sailed  south-easterly  257  miles, 
when  she  arrives  in  latitude  54°  47'  N.  Required  the  course  and  difference  of 
longitude. 

Ans.   Course  S.  GG°  22'  E. ;  difference  of  longitude  417  miles. 

Ex.  3.  A  ship  sails  from  the  latitude  of  3°  20'  N.  and  longitude  29°  37'  W., 
960  miles  south-westerly,  and  then  by  observation  finds  that  her  latitude  is  10C 
40'  S.  Required  the  course  and  longitude  in. 

Ans.  Course  S.  29°  03'  \V. ;  longitude  in  37°  24'  W. 

Ex.  4.  A  ship  sails  from  Santa  Clara  in  latitude  3°  14'  S.  north-westerly  300 
miles,  until  it  is  found  by  observation  that  she  is  on  the  equator.  Required  the 
course  and  difference  of  longitude. 

Ans.  Course  N.  49°  43'  W.;  difference  of  longitude  3°  49'  W. 

CASE  VI. 
One  Latitude,  Course  and  Departure  given,  to  find  the  Distance  and 

Difference  of  Latitude  and  Difference  of  Longitude. 
Ex.  1.  A  ship  sails  E.  S.  E.  from  latitude  50°  10'  S.  and  longitude  30°  W  E. 
until  her  dcpariure  is  957  miles;  required  distance  sailed,  and  latitude  and  long- 
itude in. 

(Prom  Compass  Table  the  course  E.  S.  E.  is  C7°  30'.) 


FIRST:  TO  FIND  THE  DIF.  OF  LATITUDE. 
AH  sine  of  course  GTJ  30'  9.965fl5 
Is  t  >  departure  937  2.980912 

8ECO 

Lat. 
Dif. 

Lat. 

\D  :  TO  FIKD  LAT.  IN. 
left  50°10'S. 
of  lat  6  36  S. 

Lat.  left... 
Lat.  in.... 

Sum  

Miiiulelat. 

.       50°  10'  S. 
.       66  46   S. 

bo  id  co-siue  of  course  07°  30'  

To  dif.  of  latitude,       60)390.4.  .  .  . 
6=  3G' 

9.582840 

12.563752 
9.9G5615 

in.  .. 

.  .  .  5C°  4G'  S. 

.2)  106°  56' 
.      53°  28' 

2.598137 

THIRD:  TO  FIND  THE  DISTANCE. 

As  sine  of  courso  G73  30' 9.96."G15 

Is  to  the 'departure  957' 2.080912 

So  is  radius 10.000000 


To  the  distance  103C. 


12.980912 
9.9G5(.15 


3.015297 


FOURTH:  TO  FIKD  DIFFERENCE  or  LONGITUDE. 

As  co-sine  mid.  lat.  53°  28' 9774720 

Is  to  the  departure  957'  2.9801H2 

So  is  radius 10.000000 


To  dif .  of  lo.n,       60)1608 


3.20G183 


26°  4S'  E. 


Longitude  left 30°00'E. 

Difference  of  longitude 2G  48  E. 

Longitude  in 56°48'E. 


26 


PRACTICAL   NAVIGATION. 


Ex.  2.  A  ship  sails  S.  S.  W.  from  latitude  51°  15'N.,  and  longitude  9°  50"  W., 
until  her  departure  is  250  miles.  Required  the  distance  sailed  and  the  latitude 
and  longitude  in. 

Ans.  Latitude  in,  41°  12  N.;  longitude  in,  15°  51'  W. ;  distance,  G53.3 

Ex.  3.  A  ship  from  latitude  38°  40'  S.,  and  longitude,  1°  15'  W.,  sails  N.  E.  £ 
E.  until  her  departure  is  250  miles.     Required  the  latitude  and  longitude  in. 
Ans.  Latitude  in,  35°  14'  S.;  longitude  in,  3°  57'  E. ;  distance,  324  miles. 

Ex.  4.  A  ship  from  latitude  30°  15'  S.,  longitude,  178°  10'  E.,  sails  on  a  course 
N.  4  points  E.  until  her  departure  is  150  miles.  Required  the  distance  sailed 
aud  longitude  and  latitude  in. 

Ans.  Distance  sailed,  212  miles:  latitude  in,  27°  45'  S.,  and  longitude,  1783 
58'  W. 


CASE  VII. 

One  Latitude,  Distance,  and  Departure  given,  to  find  the  Course,  Dif- 
ference of  Latitude,  and  Difference  of  Longitude. 

Ex.  1.  A  ship  from  latitude  49°  30' N.  aud  longitude  25°  00' W.,  sails  south- 
easterly G45  miles  until  her  departure  is  500  miles.  Required  the  course  steered, 
and  her  latitude  and  longitude  in. 


FIKST:  TO  FIND  THE  CODBSE. 
As  di  Stan-  e  645  miles  2.809560 
Is  to  radius                              .  lOOOOnOO 

SECOND:  TO  FIND  DIF.  OF  LATITUDE. 
As  radius  lO.OOuOOO 
Is  to  distance  Gi5  2.8uy?(iO 

THIBD:  LAT.  ix  AND 

MID.  LAT. 

Lat.  left.  49°  30'  N. 

So  is  departure  500  2  GH8970 

bo  is  co-siue  of  c'rse  59D  49'    9.800J8J 

Oil',  of  lat  G  43    S. 

12.C98970 
'A8095oO 

12.G10142 
10.000000 

Lat.  in...  42  42    N. 
Sum..  i!)9'2  12 
Hid  lat   •iG     C 

To  Bine  of  c'rse  S.  50°  49'  E.    9.889410 

C°  48'  S. 

FOTJETH:  TO  FIND  DIFFEBENCE  OF  LONGITUDE. 

As  co-sine  mid.  lat.  40°  00 9.8J0985 

Is  to  departure  50u  miles 2.  98970 

So  is  radius 10.000000 


12.698970 
9.840985 


To  difference  of  longitude  60)  721 2.857985 

12°  01'  E. 


FIFTH:  TO  FIND  THE  LONGITUDE  IN. 

Longitude  left 15=00'  W. 

Difference  of  longitude 1201     E. 

Longitude  in 12°  C9'  W. 


Ex.  2.  A  ship  from  latitude  54°  N.  and  longitude  33°  20'  "W.,  sails  350  miles 
between  north  and  cast,  until  she  has  made  220  miles  of  departure.  Required 
the  course,  and  latitude  and  longitude  in. 

Ans.  Course,  N.  38° 57'  E. ;  latitude  hi,  58°  32'  N.;  and  longitude,  26°  44'  W. 

Ex.  3.  A  ship  from  latitude  23°  50'  N.;  longitude  23°  30'  W.,  sails  between  the 
south  and  west,  375  miles,  until  her  departure  is  200  miles.  Required  the 
course,  latitude  and  longitude  in. 

Ans.  Course,  S.  32°  14'  W.;  latitude  in,  18°  33'  K;  longitude  iu,  27°  05'  W. 


MIDDLE  LATITUDE — SAILING.  27 

CASE  VIII. 

One   Latitude,  Departure,  and  Difference  of  Longitude  given,  to  find 
Ike  other  Latitude,  Course  and  Distance. 

Ex.  1.  A  ship  from  latitude  37°  00'  N.,  sails  south-westerly  xintil  she  has 
made  483  miles  of  departure,  and  565  miles  difference  of  longitude.  Required 
her  present  latitude,  course  steered,  and  distance  run. 


TO  FISD  THE  MIDDLE  LATITUDE. 

Asdif.  of  longitude  505 2.752048 

I.s  to  radius ID  000000 

Bo  is  departure  483 2.G83U47 


12.CS3947 
2.752018 


Toco-sine  inid.  lat.  31°  15' 9.931899 

TO  FIND  THE  COUBSE. 

As  difference  of  latitude  C9J' 2.818S49 

1-itoru.dius  li).0ii!»0p 

So  is  departure  483  2.G3.1'J47 


Middle  latitude 31°  15' 


Double  middle  latitude C2  30 

Latitude  left .  37  00  X. 

Latitude  in..,  ..  25  CON. 


2.838849 
To  tang,  course  34°  59'. 9.845038 


Diff.  of  latitude 11°  30'  =690 


TO  FDfD   THE  DISTANCE. 

As  radiu« 10.000COO 

Id  to  difference  latitude  090 2.83*849 

So  is  B.C.  course  34°  &D' 10.U8G547 


12.925396 
10.000000 

To  the  distance  842. ..  . .  .2.9253U6 


Ex.  2.  A  ship  sails  from  latitude  49°  30'  N.,  south-easterly  until  her  departure 
is  1G7  miles,  and  difference  of  longiturc  is  252  miles.  Required  present  latitude, 
course  steered,  and  distance. 

Ans.  Latitude  in,  47°  30'  N. ;  course,  S.  54°  18'  E. ;  distance,  205  miles. 

Ex.  3.  A  chip  sails  horn  latitude  50°  10'  S.,  between  the  south  and  cast  until 
her  departure  is  ICO  miles,  and  her  difference  of  longi.ude  253  miles.  Required 
her  present  latitude,  course  and  distance. 

Ans.  Latitude  in,  51°  1C'  S.;  course,  E,  S.  E.;  distance,  175.2  miles. 

GENEHAL  RULES — TABLES  III  AND  IV. 
Solutions  of  the  different  cases  by  Inspection. 

If  seeking  a  course  which  is  under  45°  it  will  be  found  at  the  top 
of  the  pages,  but  if  it  is  over  45°  it  will  be  found  at  the  bottom  of 
the  pages.  If  the  departure,  or  difference  of  latitude,  or  distance, 
are  too  great  to  be  found  in  the  tables,  divide  them  by  10  or  by  100, 
and  then  multiply  the  quantities  found  (not  the  course  or  middle 
latitude)  by  the  same  number  you  used  in  dividing.  To  find  the 
difference  of  longitude,  use  either  of  these  two  methods.  (In  look- 
ing in  the  table  use  the  nearest  number  and  nearest  angle.)  With 
the  middle  latitude  as  a  course,  and  the  departure  in  the  latitude 
column,  the  difference  of  longitude  will  be  found  in  the  distance 
column.  Or  with  the  co-middle  latitude  (00°  lat.)  as  a  course,  and 
with  the  difference  of  latitude  in  its  own  column,  or  the  departure 
in  its  own  column,  will  be  found  the  difference  of  longitude  in  the 
distance  column. 

CASE  1.    Look  for  the  middle  latitude  23°  as  if  it  were  a  course. 


28  PEACTICAL   NAVIGATION. 

and  for  132.3  (one-tenth  the  difference  of  longitude)  in  the  distance 
column,  opposite  to  which  in  the  difference  of  latitude  column  -will 
be  found  121.5  which  being  multiplied  by  10,  gives  1215  the  depart- 
ure. "With  12.15  (one  hundredth  the  departure)  in  the  departure 
column  and  33.23  (one  hundredth  of  the  difference  of  latitude)  in 
the  latitude  column,  will  be  found  at  the  top  of  the  page  20°  the 
course;  and  35.00  in  the  distance  column,  which  being  multiplied 
by  100,  gives  3500  the  distance.  This  can  be  also  solved  by  taking 
the  co-middle  latitude  (90°  23')  G7°  as  a  course  and  the  difference  of 
longitude  in  the  distance  column  will  be  found  the  departure  in  the 
departure  column.  Then  proceed  as  before. 

CASE  2.  Look  for  the  course  31°  at  the  top  of  the  page,  and  96.0 
(one-tenth  the  distance)  in  its  column  opposite  to  the  distance,  in 
their  columns  will  be  the  difference  of  latitude  822  and  the  de- 
parture 494.  Then  with  the  middle  latitude  23°  as  a  course,  and 
the  departure  49.4  (one-tenth)  in  the  difference  of  latitude  column, 
will  be  found  54.0  in  the  distance  column;  this  multiplied  by  10, 
gives  the  difference  of  longitude,  540. 

CASE  3.  Look  in  the  departure  and  latitude  columns  until  they 
are  found  nearly  to  agree,  45.3  and  21.1;  the  course  is  found  at  the 
top  of  the  page,  it  is  25°.  The  distance,  50,  is  opposite  in  its  col- 
umn; this  multiplied  by  10,  gives  the  correct  distance,  500.  With 
the  middle  latitude  53°  as  a  course,  and  one-tenth  the  departure  in 
the  latitude  column,  35  is  found  in  the  distance  column;  this  multi- 
plied by  10,  gives  350,  the  difference  of  Jongitude. 

CASE  4.  With  the  course  39°,  and  one-tenth  the  difference  of  lati- 
tude, 2G.G  in  its  column,  in  the  departure  column  will  be  found  21.4, 
and  in  the  distance  column  34;  these  multiplied  by  10,  give  the  de- 
parture 214  and  the  distance  340.  Then  with  the  middle  latitude, 
48°  as  a  course,  and  with  21.4  in  the  latitude  column,  32  will  be 
found  in  the  distance  column ;  this  multiplied  by  10,  gives  320  for 
difference  of  longitude. 

CASE  5.  With  one-tenth  the  distance,  80,  and  one-tenth  the  dif- 
ference of  latitude,  71,  in  their  columns  at  the  top  of  the  page,  the 
course  27°  will  be  found.  Then  with  the  middle  latitude  1°  (nearly) 
as  a  course,  and  the  departure  36.3  in  the  latitude  column,  the  dif- 
ference of  longitude,  36.3,  (one-tenth)  will  be  opposite  in  the  dis- 
tance column. 

CASE  6.  Find  the  course  67°,  and  one-tenth  the  departure,  95.7 
in  its  column,  these  will  be  in  the  latitude  and  distance  columns, 
104  and  40.6,  but  as  this  course  is  67°  30',  take  half  the  sum  columns 
of  67°  and  those  of  68°;  this  will  give  the  correct  difference  of  lati- 


MIDDLE   LATITUDE — SAILING.  29 

tucle  39G,  (39. G  multiplied  by  10)  and  the  correct  distance  1035, 
(103.5  x  10),  then  with  the  middle  latitude  as  course,  and  depart- 
ure in  latitude  column,  the  difference  of  longitude  1590  will  be  found 
in  the  distance  column. 

CASE  7.  "With  one-tenth  the  distance  and  departure,  64.5;  50, 
agreeing  in  their  columns,  the  course,  51°,  will  be  found,  and  at  the 
same  time  the  difference  of  latitude  408  (40.8  x  10)  in  its  column. 
Then  with  the  middle  latitude  46°  as  a  course,  and  the  departure  50 
(one-tenth)  in  the  latitude  column,  one-tenth  of  the  difference  of 
longitude  will  be  found  in  the  distance  column  720,  (72  x  10). 

CASE  8.  "With  one-tenth  the  difference  of  longitude,  56.5  in  the 
distance  column,  and  one-tenth  the  departure,  48.3  in  the  latitude 
column  agreeing,  will  be  found  the  middle  latitude  31°,  at  the  top 
of  the  page.  Then  with  the  difference  of  latitude  in  its  column, 
and  the  departure  in  its  columns  will  be  found  the  course,  35°,  at 
the  top  of  the  page,  and  the  distance  850  in  the  distance  column. 


LOGAEITHMIC    SINES,    TANGENTS   AND    SECANTS. 

This  table  contains  the  logarithmic,  or,  the  artificial  sines,  tan- 
gents and  secants,  to  each  degree  and  minute  of  the  quadrant,  with 
their  complements  or  co-sines,  co-tangents  and  co-secants,  to  six 
places  of  figures,  besides  the  index;  but  it  may  be  observed,  as  of 
the  last  table,  that  five  places  being  generally  sufficient  in  the  com- 
mon practice  of  navigation,  when  the  sixth  is  omitted,  and  it  is  five 
or  above,  the  preceding  or  fifth  figure  is  to  be  increased  by  a  unit. 

To  find  the  Logarithmic  Sine,   Co-sine,  etc.,  of  any  given  Arc  in 
Degrees  and  Minutes. 

If  the  given  degrees  be  under  45°,  they  are  to  be  taken  from  the 
top,  and  the  minutes  from  the  left  side  column;  opposite  to  which, 
in  that  column  with  the  name  of  the  logarithm  at  top,  will  be  found 
the  required  logarithm. 

But  if  the  degrees  be  more  than  45°,  they  will  be  found  at  the 
bottom  of  the  page,  and  the  minutes  in  the  right-side  column;  like- 
wise the  name  of  the  logarithm  is  to  be  taken  from  the  bottom  of 
the  page. 

"When  the  given  degrees  exceed  90°,  they  are  to  be  subtracted  from 
180°  degrees,  and  the  logarithm  of  the  remainder  taken  out  as  be- 
fore, or  the  logarithmic  sine,  tangent,  etc.,  of  an  arc  more  than  90° is 
the  logarithmic  co-sine,  co-tangent,  etc.,  of  its  excess  above  90°. 


30 


PRACTICAL  NAVIGATION. 


To  find  the  Arc  in  Degrees  and  Minutes  nearest  corresponding  to  a 
given  Logarithmic  Sine,  Co-sine,  etc. 

Look  in  the  column  marked  at  the  top  or  bottom  with  the  name 
of  the  given  logarithm,  and,  when  the  nearest  to  it  is  found,  the 
corresponding  degrees  and  minutes  will  be  those  required;  observ- 
ing, that  when  the  name  is  at  the  top  of  the  column,  the  degrees 
are  to  be  taken  from  the  top,  and  the  minutes  from  the  left-side  col- 
umn; but,  if  the  name  be  at  the  bottom,  the  corresponding  degrees 
will  be  there  likewise,  and  the  minutes  in  the  right-side  column. 


MERCATOR'S  SAILING. 

CASE  1. 
To  find  the  Course  and  Distance  by  Mercator's  Sailing. 

To  this  sailing  apply  the  same  rules  as  in  middle  latitude  sail- 
ing, for  finding  difference  of  latitude  and  difference  of  longitude. 

To  get  the  meridional  difference  of  latitude  enter  Table  V,  with 
degrees  sought  at  top  of  column,  and  miles  in  the  left-hand  side 
marked  miles,  and  opposite  miles  and  under  degrees  will  be  found 
the  meridional  number  required. 

Having  taken  out  the  meridional  parts  for  both  latitudes,  add  or 
subtract  them  in  the  same  manner  as  adding  or  subtracting  to  find 
the  true"  difference  of  latitude,  and  the  sum  or  difference  will  give 
the  meridional  difference  of  latitude.  Then  proceed  as  per  ex- 
ample. 

NOTE. — Tables  required  for  working  Mercator's  Sailing. — Tables  I,  II,  and  V. 

The  Latitudes  and  Longitudes  of  Tico  Places  given-,  to  find  the  Course 
and  Distance  between  them. 

Ex.  1.  Required  the  course  and  distance  from  Buena  Vista  to  Rio 
Janeiro. 


Latitude  Buena  Vista  15U  57'  N. 
Latitude  Rio  Janeiro  22  54      S. 


Longitude  22°  53'  W. 
Longitude  43   16   W. 


Lat.  Buena  Vista  15°  57' N. 
Lat.  Ilio  Janeiro  22  54    S. 


Diff.  Latitude  38  51 
CO 


In  miles     2331 


Meridional  parts. .     970 
Meridional  parts. .   1412 


Mcr.  Diff.   Lat. . . .  2382 


Long.  Bucna  Vista  22°o3'W 
Long,  liio  Janeiro  43  1C  W 


Diff.  Lon; 


2023 
60 


In  miles.   1223 


TO   FIND   THE   COURSE. 

As  mer.  diff.  lat.  2382 3.376942 

Is  to  radius. 10.000000 

So  is  diff.   long.  1223 3.087426 


13.087426 

3.3761J42 


To  tang,  course  S  27°  11'  W      9.7104S4 


TO    FIND    THE   DISTANCE. 

As  radius 10.000CCO 

Is  to  prop.  diff.  lat.    2331 . ..     3.367542 
So  is  secant  course  27°  11'. .   10.050830 


13.418372 
10.000000 


To  distance  2620. 


MEBCATOR  3  SAILING. 


31 


Ex.  2.  Required  the  course  and  distance  from  A.  to  B. 


Lat.  of  A 50°  30'  S. 

Lat.   of  B 4S  20    S. 

2   10 
x      60 


In  miles        130 


Meridional  part 3521  i  Longitude ...   147°  50'  W. 


Meridional  part 3322 


Mer.  dif.  of  lat 199 


TO  FIND  THE  COURSE. 

As  mer.  dif.  of  lat,  199 2.298853 

Is  to  radius 10.000000 

So  is  dif.  of  long.  4392 3. 642662 


13.642662 
2.298853 


Longitude. . .   138  58    E. 

286  48 
360  90 

73   12 

x     60 

In  miles       4392 


TO  FIND  THE  DISTANCE. 

As  radius 10.000000 

Is  to  prop.  dif.  of  lat.  130.  . .     2. 1 13043 
So  is  secant  of  course.  87°  24'  11.34329S 


13.457241 
10.000000 


To  tang,  of  course  N  87°  24'  W  1 1. 343809   To  the  distance  2866 3.457241 

Ex.  3.  Required  the  course  (in  degrees  and  miles)  and  distance  from  A.  to  B. 

Latitude  of  A ....  55°  22'  N Longitude ....     7"  24'  \V. 

Latitude  of  B 49  40   N Longitude 53  54  W. 

Aiis.     CourseS.  78°  35'  W.j  distance  172S. 

Ex.  4.  Required  the  course  (in  degrees  and  miles)  and  distance  from  A.  to  B. 

Latitude  of  A 44°  44'  N Longitude 63°  36'  W. 

Latitude  of  B 33  07    S Longitude....   17   58    E. 

Ans.     CourseS.  43"  44'  E.;  distance  64G4. 

Ex.  5.  Required  the  course  (in  degrees  and  miles)  and  distance  from  C  to  D. 

Latitude  of  C 54°  32'  S Longitude 36J  12'  W. 

Latitude  of  D ....  38  54  S Longitude....  143  40  E. 

Ans.     Course  N.  82°  42'  E.;  distance  7382. 


CASE  II. 

One  Latitude,  Course  and  Distance  given,  to  find  the  difference  of  Lat- 
ilu.de  and  difference  of  Longitude. 

Ex.  1.  A  ship  from  latitude  52°  06'  N.  and  longitude  35°  06'  W.,  sails  N.  W. 
by  W.  (56°  15')  229  miles.     Required  the  latitude  and  longitude  in. 


TO  FIND  THE  DIFFERENCE  OF  LAT. 

As  radius 10.000000 

Is  to  distance  229 2. 359835 

So  is  co-siue  of  course  56°  15'    9.744739 

12. 104574 
10.000000 


To  dif.  of  lat.  60)127.2 2.104574 

2°  07 

TO  FIND  THE  DIFFERENCE  OF  LONG. 

As  radius 10.000000 

Is  to  mer.  dif.  of  lat.  212 2.32«;>36 

So  is  tang,  of  course    56°  15'  10.175107 


12.501443 
10.000000 


To  dif.  of  long.  60)317.3. ...     2.501443 
5 '  17' 


TO  FIND  THE  LATITUDE  IN. 

Lat.  left     52l  06'  N. . .  .Mer.  pts.  3675 
Dif.  of  lat    2     7   N. 


Lat.  in...  54°  13'  N....Mcr.  pts.  3S87 
Mer  dif  of  lat.  212 


TO  FIND  THE  LONGITUDE  IN. 

Longitude  left 35°  06'  W. 

Dif.  of  long..  5  17  W. 


Longitude  in . .  , .  40J  23'  W. 


32 


PRACTICAL  NAVIGATION. 


Ex.  2.  A  ship  from  latitude  42°  30'  N.  and  longitude  58°  51  W.,  sails  S.  W.  by 
S.  591  miles.     Required  the  latitude  and  longitude  in. 
Ans.     Latitude  34°  19'  N. ;  longitude  65°  51'  W. 


CASE  III. 

Both  Latitudes  and  Departure  given,  to  find  the  Course,  Distance  and 
Difference  of  Longitude. 

A  ship  from  latitude  9°  10'  N.  and  longitude  19°  32'  W.,  sails  in  the  S.  E.  quar- 
ter until  she  has  made  415  miles  of  departure,  and  is  by  observation  in  latitude 
2°  19'  S.  Required  her  course,  steered,  distance  run,  and  longitude  in. 

NOTE. — Find  first  proper  difference  of  latitude,  meridional  difference  of  latitude,  course,  dis- 
tance, difference  of  longitude  and  longitude  in. 

Latitude  left 9°  10'  N Mer.  parts 552. 

Latitude  in 2   19    S Mer.  parts 139. 


11°  29' 
X  60 


In  miles 


G89 


Mer.  dif.  of  lat.      691. 


TO  FIND  THE  COUESE. 

As  dif.  of  lat.  689 2.838219 

Is  to  radius 10.000000 

So  is  departure  415 2.618048 


12.618048 
2.838219 


To  tan",  of  course  S.  31°  04'  E  9.779829 


TO  FIND  THE  DISTANCE. 

As  sine  of  course  31°  04' 9.712679 

Is  to  departure  415 2.C18048 

So  radius 10.000000 


12.618048 
9.712679 


To  the  distance  804. 2 . .  2. 905369 


TO  FIND  THE  DIFFERENCE  OF  LONG. 

As  radius 10.000000 

Is  to  mer.  clif.  of  lat.  691 ....     2.839478 
So  is  tang,  of  course  31°  04'..     9.779818 


12.619296 
10.000000 


To  dif.  of  long.  60)416.2  E.     2.619296 
6°  56'  E. 


TO  FIND  THE  LONGITUDE  IN. 

Longitude  left 19°  32'  W. 

Dif.  of  longitude  416' 656    E. 

Longitude  in 12°  3G'  W. 


Ex.  2.  A  ship  from  latitude  49°  57'  N.  and  longitude  15°  16'  W.,  sails  south- 
westerly until  her  departure  is  789  miles,  and  is  in  by  observation,  latitude  39° 
20'  N.  Required  her  course,  distance  and  longitude  in. 

Ans.     Course  S.  51°  05'  W. ;  longitude  in  33°  50'  W.;  distance  1014  miles. 

Ex.  3.  A  ship  from  latitude  49°  57' N.  and  longitude  5°  11'  W.,  sails  between 
the  sou tli  and  west  until  she  arrives  in  latitude  38°  27' N.,  and  finds  she  has 
made  440  miles  of  departure.  Required  the  course  she  has  steered,  distance 
run  and  longitude  the  ship  is  in. 

Ans.     Course  S.  323  31'  W.;  distance  818.5  miles;  longitude  in  15°  27'  W, 


MERCATOR'S  SAILING. 


33 


CASE  IV. 

Both  Latitudes  and  Course  given,  to  find  the  distance  and  Difference  of 

Longitude. 

Ex.  1.  A  ship  from  latitude  49°  57'  N.  and  longitude  30°  00'  W.,  sails  S.  W. 
*  S.  for  several  days,  and  then  finds  by  observation  that  she  is  in  latitude  45°  31' 
N.  Required  the  distance  she  has  made  and  her  present  longitude. 

NOTE. — First  find  proper  difference  of  latitude,  meridional  difference  of  latitude,  distance, 
difference  of  longitude  and  longitude  in. 


Latitude  left 49°  57'  N . 

Latitude  in . .         .  45  31  N . 


In  miles 


4°  26' 
60 

266 


TO  FIND  THE  DISTANCE. 

As  co-sine  of  course  39°  22' . .     9. 888237 

Is  to  dif.  of  lat.  266 2.424882 

So  is  radius 10.000000 

12.424882 

9.888237 


To  the  distance  344. 1 2.536645 


Mer.  parts 3470. 

Mer.  parts 3074. 

396 


TO  FIND  DIFFERENCE  OF  LONGITUDE. 

As  radius 10.000000 

Is  to  mer.  dif.  of  lat.  396 2.597695 

So  is  tang,  of  course  39°  22'. .     9. 914044 


12.511739 
10.000000 

To  dif.  of  long.    60)324.9. . . .     2.511739 
5°  24' 

Longitude  left 30°  00'    W. 

Difference  of  longitude 5  24     W. 

Longitude  in 35U24'    W. 


Ex.  2.  A  ship  from  latitude  42°  40'  N.  and  longitude  16°  20' W.,  sails  N.  E., 
and  then  finds  by  observation  that  she  is  in  latitude  50°  50'  N.  Required  the 
distance  sailed,  and  present  longitude. 

Ans.     Distance,  693  miles;  longitude  in,  4°  23'  W. 

Ex.  3.  A  ship  from  latitude  30°  IV  N.  and  longitude  5°  10'  E.,  sails  S.  by  E., 
and  then  finds  by  sun's  observation  that  she  is  in  latitude  42°  25'  S.  Required 
the  distance  sailed  and  longitude  in. 

Ans.     Distance,  1440  miles;  longitude  in,  20°  48'  E. 

Ex.  4.  A  ship  from  latitude  42°  25'  N.  and  longitude  15°  06' W.,  sails  N.  E. 
'by  E.,  and  finds  by  observation  that  she  is  in  latitude  46°  20'  N.  Required  the 
distance  sailed,  and  longitude  in. 

Ans.     Distance,  423  miles;  longitude  in,  6°  54'  W. 


PKAC.  NAV. — 3 


PRACTICAL   NAVIGATION. 


CASE  V. 

Both  Latitudes  and  Distance  given,  to  find  the  Course  and  Difference 

of  Longitude. 

Ex.  1.  A  ship  from  latitude  50°  30'  N.  has  sailed  south-easterly  300  miles, 
when  she  arrives  at  latitude  45°  40'  N.  Required  her  course  steered,  and  differ- 
ence of  longitude. 

NOTE. — First  find  proper  difference  of  latitude,  meridional  difference  of  latitude,  course,  and 
difference  of  longitude. 


Latitude  left 50&  30'  N. 

Latitude  in 45  40  N. 

4°  50' 
x  60 

In  miles..  290 


Meridional  parts 3521 

Meridional  parts 3087 

Mer.  diff.  of  lat..  434 


TO  FIND  THE  COURSE. 

As  the  distance,  300 2.477121 

Is  to  radius 10.000000 

.  So  is  dif.  of  lat.,  290 1.462398 


12.462398 
2.477121 


To  co-sine  of  course  14°  50'. .     9.985277 


TO  FIND  DIFFERENCE  OF  LONGITUDE. 
As  co-sine  of  course,  14°  50' .     9.985280 
Is  to  mer.  dif.  of  lat.,  434.  ..     2.637490 
So  is  sine  course,  14°  50' 9.408254 

12.045744 
9.985280 


To  dif.  of  long.,  114.9 2.060464 


Ex.  2.  A  ship  from  latitude  36°  20'  N.,  and  longitude  22°  30'  W.,  sails  S.  by 
W.  960  miles  and  finds  her  latitude  is  10°  40'  S.  Required  the  course  and  longi- 
tude in. 

Ans.  4S.  28°  57'  W.,  and  longitude  in,  30°  17'  W. 

Ex.  3.  A  ship  from  latitude  56°  30'  N.  has  sailed  south-easterly  257  miles, 
when  she  arrives  at  latitude  54°  47'  N.  Required  the  course  steered,  and  differ- 
ence of  longitude. 

Ans.  Course,  S.  66°  22'  E.;  difference  of  longitude,  418.2. 


MEECATOR  8   SAILING.  35 

r 

CASE  VI. 

One  Latitude,  Course,  and  Departure  given,  to  find   the  Distance, 
Difference  of  Latitude  and  Difference  of  Longitude. 

Ex.  1.  A  ship  from  latitude  50°  10'  S.,  and  longitude  30°  00'  E.,  sails  E.  S.  E., 
until  her  departure  is  957  miles.  Required  the  distance  sailed  and  her  present 
latitude  and  longitude. 

NOTE. — First  find  the  difference  of  latitude,  latitude  in,  and  meridional  difference  of  latitude, 
the  distance  and  difference  of  longitude. 


TO  FIND  DIFFERENCE  OF  LATITUDE. 
As  sine  of  course  67°  30' ....     9.9(55615 

Is  to  departure  957' 2.980912 

So  is  co-sine  of  course  67°  30'    9.582840 


12.563752 
9.965615 


To  dif.  of  lat. 


60)396.4 
63  36'  S. 

Lat.  left.. 
Dif.  of  lat. 

Lat.  in.  . 


2.598137 


50°  10'  S. 
6  36  S. 


56°  46'  S. 


TO  FIND  THE  DISTANCE. 

As  sine  of  course  67°  30' 9.965615 

Is  to  departure  957' 2.980912 

So  is  radius 10.000000 

12.980912 
9.965615 

To  the  distance  1036 3.015297 


Mer.  dif.  of  lat..  3490 
Mer.  dif.  of  lat..  4157 


Mer.  dif.  of  lat..     667 


TO  FIND  DIFFERENCE  OF  LONGITUDE. 


Longitude  left: 30°  00' E. 

Difference  of  longitude 26  50  E. 

Longitude  in 56°  50'  E. 


As  co-sine  of  course  67°  30'. .     9.582840 

Is  to  mer.  dif.  of  lat.  667 2.824126 

So  is  sine  of  course  67°  30'. . .     9.965615 


12.789741 
9.582840 

To  dif.  of  long.        60)1610        3.206901 
26°  50' 


Ex.  2.  A  ship  from  latitude  51°  15'  N.,  and  longitude  9°  50'  W.,  sails  S.  S.  W. 
until  her  departure  is  250  miles.  Required  the  distance  sailed,  and  latitude  and 
longitude  in. 

Ans.  Latitude  in,  41°  11'  N.;  longitude  in,  15°  53'  W.,  and  distance  653.3 
miles. 

Ex.  3.  A  ship  from  latitude  40°  20'  S.,  and  longitude  20°  40'  E.,  sails  N.  N.  E. 
until  her  departure  is  500  miles.  Required  the  distance  sailed,  and  latitude  and 
longitude  in. 

Ans.  Latitude  in,  28°  13'  S.;  distance,  1307  miles;  longitude  in,  30°  24'  E. 


36 


PRACTICAL  NAVIGATION. 


CASE  VII. 

On  Latitude,  Distance,  and  Departure  given,  to  find  the  course,  Differ- 
ence of  Latitude,  and  Difference  of  Longitude. 

Ex.  1.  A  ship  from  latitude  54°  N.  and  longitude  33°  20'  W.,  sails  350  miles 
"between  north  and  east,  until  she  has  made  220  miles  of  departure.  Required 
the  course  steered,  and  her  present  latitude  and  longitude. 

NOTE. — First  find  the  course,  difference  of  latitude,  latitude  in  and  meridional  difference  of 
latitude,  difference  of  longitude  and  longitude  in. 


TO  FIND  THE  COURSE. 

As  the  distance  350 2.544068 

Is  to  radius 10.000000 

So  is  departure  220. 2.342423 


12.342423 
2.544068 


To  sine  course  38°  57' 9.798355 


TO  FIND  DIFFERENCE  OF  LATITUDE. 

As  radius 10.000000 

Is  to  distance  350 2. 544088 

So  is  co-sine  course  38°  57'. .     9.890809 


12.434877 
10.000000 


To  difference  latitude  272. 2 .     2. 434877 


Lat.  left  54°  00'  N.     Mer.  parts. .  3865 
Dif,  lat.     4  32  N. 

Lat.  in    58°  32' N.     Mer.  parts..  4355 

Mer.  dif.  lat.     490 
Long,  left  38°  20'  W. 
Dif.  long.     6  36    E. 


Long,  in    26°  44'  W. 


TO  FIND  DIFFERENCE  OF  LONGITUDE. 

As  co-sine  course  38°  57 9. 890809 

Is  to  mer.  dif.  lat.  490 2.690196 

So  is  sine  course  38°  57' .....     9. 798403 


12.488597 
9.890809 


To  dif.  long.  396. 1 2. 597790 


Ex.  2.  A  ship  in  latitude  49°  30'  N.  and  longitude  25°  W.,  sails  south-easterly 
215  miles,  making  167  miles  departure.  Required  the  course  steered,  and  lati- 
tude and  longitude  in. 

Ans.     Course,  50°  58';  latitude  in  47°  15'  N. ;  longitude  in  20°  50'  W. 


Ex.  3.  A  ship  in  latitude  49°  30'  N.  and  longitude  25"  00'  W.,  sails  south-east- 
erly 645  miles,  making  500  miles  departure.  Required  the  course  steered,  and 
latitude  and  longitude  in. 

Ans.     Course,  S.  50°  49'  E.;  latitude  in.  42°  42'  N.;  longitude  in,  12°  57'  W. 


MERCATOR'S  SAILING. 


37 


CASE  VIII. 

One  Latitude,  Course  and  Difference  of  Longitude  given,  to  find  the 
Distance  and  Difference  of  Latitude. 

NOTE.— This  case  cannot  be  solved  by  middle  latitude  sailing. 

Ex.  1.  A  ship  from  latitude  34°  29'  N.,  sails  S.  41°  W.,  until  the  difference  of 
longitude  is  680  miles.     Required  latitude  in  and  distance  sailed. 

NOTE.- First  find  meridional  difference  of  latitude,  then  latitude  in,  and  difference  of  lati- 
tude in  miles,  then  the  distance. 


TO  FIND  MEE.  DIF.  OF  LATITUDE. 

As  radius 10.000000 

Is  to  dif .  long.  680 2.832509 

So  is  co-tang,  course  41° 10.060837 


12.893346 
10.000000 


To  mer.  dif.  lat.  782.3 2.893346 


Lat.  left  34°  29'  N.       Mer.  parts    2207 
Mer.  dif.  lat  782 

Lat.  in..  23  06  N.      Mer.   parts    1425 

Dif.  lat.  11   23 
60 

In  miles    683 


TO  FIND  THE  DISTANCE. 

As  co-sine  course  41° 9.877780 

Is  to  dif.  lat.  683 2.834421 

So  is  radius..                                        .  10.000000 


12.834421 

9.877780 


To  the  distance  905'..  .    2.956641 


Ex.  2.  A  ship  from  latitude  50°  40'  S.,  sails  N.  50°  00'  E.,  until  her  difference 
of  longitude  is  550  miles.  Required  the  latitude  in  and  distance  sailed. 

Ans.  Latitude  in,  45°  32'  S. ;  difference  of  latitude  in  miles  308;  distance 
479. 2  miles. 


38  PBACTICAL  NAVIGATION. 

MERCATOR'S  SAILING. 

Solutions  of  the  Cases  by  Inspection. 

CASE  I.  Find  the  course  from  the  tables  by  using  the  meridional 
difference  of  latitude,  and  difference  of  longitude,  as  difference  of 
latitude  and  departure.  Thus,  with  23.8  in  the  latitude  column, 
and  12.23  in  the  departure,  27°  as  a  course  will  be  found  at  the  top 
of  the  page.  With  27°  as  a  course  and  the  proper  difference  of  lat- 
itude 23.31  (one  hundredth)  gives  in  the  distance  column  26,  which 
multiplied  by  100,  gives  2600  as  distance. 

CASE  II.  With  the  course  three  points  at  the  top  of  the  page  and 
opposite  the  distance  59.1  (one-tenth)  will  be  found  the  difference  of 
latitude  49.1,  which  multiplied  by  10,  gives  491.  Then  with  the 
same  course  and  the  meridional  difference  of  latitude  628  in  the  lat- 
itude column,  will  be  found  the  corresponding  difference  of  longi- 
tude 42.0,  which  multiplied  by  10,  gives  as  difference  of  longitude 
420. 

CASE  III.  With  the  proper  difference  of  latitude  68.9  (one-tenth) 
and  departure  41.5  (one-tenth)  in  their  proper  columns,  find  the 
course  31°  at  the  top  of  the  page,  and  the  distance  800  in  the  dis- 
tance column.  Then,  with  this  course  31°,  and  the  meridional  dif- 
ference of  latitude  in  the  latitude  column,  the  difference  of  long- 
itude will  be  found  in  the  departure  column  41.4,  multiplied  by  10, 
gives  414. 

CASE  IV.  Find  the  course  S.  W.  J  S.  among  the  points  or  de- 
grees, and  the  proper  difference  of  latitude  26.6,  adjoining  to  which 
will  be  the  distance  340  and  departure  21.4  in  their  respective  col- 
umns. Then,  in  the  same  table,  find  the  meridional  difference  of 
latitude  396  in  the  latitude  column,  stands  321,  in  the  departure  col- 
umn, which  is  the  difference  of  longitude. 

CASE.  V.  Look  in  table  IV  until  30.0,  one-tenth  the  distance,  is 
found  opposite  29.0,  one-tenth  the  difference  of  latitude,  in  their 
columns.  The  course  15°  is  found  at  the  top  of  the  page,  and  the 
departure  78  (78x10)  in  the  departure  column.  WTith  43.4,  one- 
tenth  the  meridional  difference  of  latitude  in  the  latitude  column, 
and  the  course  15°,  the  difference  of  longitude  116  (11.6x10)  will 
be  found  in  the  departure  column. 

CASE  VI.  Find  the  course  6  points  at  the  bottom  of  the  page, 
and  the  departure  96.7  (one-tenth)  in  its  column,  corresponding  in 
their  columns  will  be  found  the  distance  1040  (104.0x10),  and  the 
difference  of  latitude  398  (39.8x10.)  With  the  same  course  and 
the  meridional  difference  of  latitude  66.7  (one-tenth)  in  the  latitude 
column,  opposite  in  the  departure  column  will  be  found  the  differ- 
ence of  longitude  1608  (160.8x10). 


DEVIATION   OF  THE   COMPASS.  39 

CASE  VII.  Look  in  the  tables  until  the  distance  35.0  (one-tenth) 
and  the  departure  22.0  (one-tenth)  are  found  in  their  columns  to 
nearly  agree  (if  not  to  agree),  opposite  to  them  in  the  latitude  col- 
umn \vill  be  found  the  difference  of  latitude  2720  (27. 20x10)  and 
the  course  39°  at  the  top  of  the  page.  With  this  course  and  one- 
tenth  the  meridional  difference  of  latitude  49.0  in  the  latitude  column, 
39. G  will  be  found  adjoining  in  the  departure  column,  this  multi- 
plied by  10,  will  give  396,  the  difference  of  longitude. 

CASE  VIII.  With  the  course  41°  at  the  top  of  the  page,  and  the 
difference  of  longitude  68.0  (one-tenth)  in  the  departure  column,  the 
meridional  difference  of  latitude  785  will  be  found  in  the  latitude 
column.  Then  with  the  difference  of  latitude  683  in  its  column,  the 
distance  910  will  be  found  in  the  distance  column. 


DEVIATION  OF  THE  COMPASS. 

Deviation  of  the  compass  is  caused  by  the  attraction  of  the  iron 
in  and  on  board  the  ship,  such  as  her  equipment,  or  cargo,  etc.  It 
depends,  both  for  its  amount  and  direction,  on  the  position  of  the 
ship's  head;  it  is  named  easterly  when  the  north  end  of  the  needle 
is  drawn,  by  the  attraction  of  the  ship's  iron,  to  the  right  of  the  cor- 
rect magnetic  north,  westerly  when  the  north  end  of  the  needle  is 
drawn  to  the  left  of  the  correct  magnetic  north. 

Method  for  finding  the  Deviation. 

Every  ship  ought  to  be  provided  with  a  good  Azimuth  Compass, 
which  should  be  placed  on  the  mid-ship  line  of  the  poop,  or  quarter 
deck,  and  as  far  as  possible  from  all  iron,  and  in  such  a  position  as 
to  allow  the  bearings  to  be  clearly  observed.  This  is  called  the 
Standard  Compass,  and  by  it  all  bearings  should  be  taken,  and  the 
Binnacle  Compass  frequently  compared  with  it.  When  the  ship  is 
ready  to  proceed  on  a  voyage,  the  deviation  of  the  Standard  Com- 
pass is  to  be  ascertained  by  one  of  the  following  methods: 

First  method.  By  the  known  correct  magnetic  bearing  of  a  dis- 
tant object.  Select  an  object,  the  correct  magnetic  bearing  of  which 
is  known,  and  at  not  less  than  six  or  seven  miles  distant,  if  the  ship 
be  lying  in  a  roadstead;  but  if  in  a  dock  a  less  distance  will  suffice, 
and  swinging  the  ship's  head  very  evenly,  take  the  bearing  of  the 
object  by  the  Standard  Compass  as  the  ship's  head  comes  up  to 
each  point  in  succession,  and  the  difference  between  the  known  and 
observed  bearing  will  be  the  amount  of  deviation  on  each  point  of 
compass.  (See  table  1  for  finding  the  deviation.) 


40  PRACTICAL  NAVIGATION. 

The  second  method  is  fully  explained  in  Table  I  (deviation  card) 
with  this  difference  only,  that  the  correct  magnetic  bearing  not  hav- 
ing been  given,  it  has  to  be  found  by  taking  the  mean  of  the  bear- 
ings of  the  distant  object;  this  method  of  determining  the  devia- 
tion is  sufficiently  correct  for  practical  purposes,  but  bear  in  mind 
that  there  is  no  such  thing  as  an  accurate  "flying"  bearing,  and 
therefore  it  is  preferable  to  swing  the  ship  for  adjustment  while  in  a 
dock,  or  at  anchor  in  a  tide-way;  and  now  to  determine  when  the 
deviation  is  easterly  or  westerly.  Kule :  when  the  correct  magnetic 
bearing  of  the  distant  object  is  to  the  right  of  the  reading  by  com- 
pass on  board,  the  deviation  is  east,  and  when  to  the  left  the  devia- 
tion is  west. 

Thus,  the  rule  is  precisely  the  same  as  that  for  finding  the  varia- 
tion of  the  compass  from  an  Azimuth,  or  Amplitude,  substituting 
correct  magnetic  for  true  bearing.  The  rule  for  applying  the  devi- 
ation is  the  same  as  that  for  applying  the  variation, ^that  is,  easterly 
to  the  right-hand  and  westerly  to  the  left-hand. 

"When  the  deviation  is  to  be  added  to  the  compass  course  to  find 
the  correct  magnetic  course  made  good,  if  the  sum  exceeds  90  de- 
grees take  it  from  180  degrees,  and  the  remainder  will  be  named  N. 
if  previously  S.,  but  S.  if  previously  N. ;  see  example  worked  out- 

Course  by  Standard  Compass  N.  N.  E.  or  N 22°  30'  E. 

Deviation  by  Standard  Compass 20  20  E. 

Correct  magnetic  course  made  good  N 42°  50'  E.  or  N.  E.  J  N. 

Course  by  Standard  Compass  E.  by  N.  or  N.  78°  45'  E. 
Deviation  by  Standard  Compass 13  50  E. 

N.  92  35  E. 
180  00 

Correct  magnetic  course  made  good  S 87°  25'  E.  or  E.  J  S. 

When  the  deviation  is  subtractive,  and  it  exceeds  the  course,  sub- 
tract the  course  from  the  deviation,  and  name  the  remainder  East 
if  the  course  is  West;  but  West  when  the  course  is  East. 

Course  by  Standard  Compass  S.  W.  by  S.  or  S . .  33°  45'  W. 
Deviation  of  Standard  Compass 14  00  W. 

Correct  magnetic  course  made  good 19°  45'  W.  or  S.  by  W.  f  W. 

Course  by  Standard  Compass  N.  by  W.  or  N.   11°  15'  W. 
Deviation  by  Standard  Compass 14    00    E. 

N.  IFIF  E.  or  N.  J  E. 


VARIATION.  41 

VARIATION. 

Next  in  order  comes  variation.  "We  will  say  but  little  on  the  sub- 
ject, as  it  is  well  understood  by  most  seamen.  Variation  is  the  angle 
which  the  direction  of  the  horizontal  magnetic  needle,  when  un- 
affected by  deviaton,  makes  with  the  geographical  meridian,  and  is 
named  easterly  when  the  magnetic  north  is  to  the  right  of  the  true 
north,  and  westerly  when  the  magnetic  north  is  to  the  left  of  the 
true  north;  and  to  know  how  to  apply  it,  suppose  yourself  placed 
at  the  centre  of  the  compass  and  looking  directly  forward  to  the 
point  you  are  to  allow  the  variation  from,  then,  if  the  variation,  is 
easterly,  allow  it  to  the  right-hand  of  the  course  steered;  but,  if 
westerly,  to  the  left-hand.  Precisely  the  same  as  deviation. 

To  fmd  the  True  Course  made  good,  with  the  Deviation  on  the  Course 

steered,  and  the  Variation  proper  to  the  locality. 
If  the  deviation  and  variation  are  of  the  same  name,  take  their 
sum;  but,  if  one  is  east  and  the  other  west,  take  their  difference  and 
give  the  remainder  the  name  of  the  greater  quantity.  Apply  this 
sum  or  difference  to  the  course  steered,  easterly  to  the  right-hand, 
westerly  to  the  left.  (See  example.) 

Ex.1.  Course  steered  W.  S.  W.  or  S.  67°  30' W.        Deviation 15°  (X,  W. 

Correction 31   30  W.         Var.  per  chart. .   16  30  W. 

True  course S.  36°  00'  W.         Correction  (sum)  31 J  30'  W. 

Ex.  2.  Course  steered  N.  E.  or  N 45°  00'  E.        Deviation 22°  00'  E. 

Correction 2  40  E.         Var.  per  chart. .   18  00  W. 

True  course N.  47°  40'  E.         Correction  (dif. ) .  4°  00  E. 

The  True  Course  given  to  find  the  Compass  Course  to  steer,  knowing 
the  Variation  and  Deviation. 

The  variation  and  deviation  must  be  used  separately;  first,  apply 
the  variation  to  the  true  course  to  ascertain  the  correct  magnetic 
course,  and  then  find  (from  the  deviation  table)  what  compass  course 
will  make  that  correct  magnetic. 

The  only  exception  to  this  method  is  when  the  variation  and  de- 
viation are  numerically  the  same,  but  have  different  names,  in  which 
case  the  one  cancels  the  other,  and  the  compass  .course  is  the  true 
course.  In  shaping  the  course  to  steer,  having  given  the  true 
course,  deviation  and  variation,  apply  them  in  the  opposite  way  to 
which  they  were  applied  in  finding  the  true  course  from  the  com- 
pass, that  is  easterly  to  the  left,  and  westerly  to  the  right. 

Suppose  the  true  course  to  be  S.  40'  W.,  with  a  correction  of  de- 
viation 5°  00'  E.  and  the  variation  20°  00'  W.  Subtract  the  east- 


42  PRACTICAL   NAVIGATION. 

erly  deviation  from  westerly  variation  and  the  net  result  will  be 
15°  00'  W.  to  apply  to  tlie  right  hand,  that  will  give  the  magnetic 
course  to  steer  S.  55°  00'  W.  or  S.  "VV.  by  W. 

First.  A  true  course  is  the  angle  between  the  geographical  mer- 
idian and  the  ship's  real  track  on  the  surface  of  the  sphere.  Know- 
ing the  true  course,  it  may  be  converted  into  a  magnetic  course  by 
the  application  of  the  variation,  viz:  easterly  variation  to  the  left, 
westerly  variation  to  right  of  the  true  course. 

Second.  A  true  bearing  is  the  angle  which  the  direction  of  an  ob- 
ject makes  with  the  geographical  meridian.  Knowing  the  true  bear- 
ing, it  may  be  converted  into  a  magnetic  bearing  by  the  application 
of  the  variation,  viz:  easterly  variation  to  the  left,  westerly  variation 
to  the  right  of  the  true  bearing. 

Third.  A  magnetic  course  is  the  angle  which  a  ship's  track  makes 
with  the  magnetic  meridian,  as  a  magnetic  bearing  is  the  angle  be- 
tween the  magnetic  meridian  and  the  direction  of  an  object;  such 
an  angle  can  only  be  shown  by  a  compass  unaffected  with  deviation; 
but  as  the  compasses  of  all  iron  ships  have  more  or  less  deviation,  and 
as  any  course  steered,  or  bearing  taken  by  any  such  compass  is  in  a 
certain  sense  magnetic,  it  has  been  found  necessary  to  distinguish 
these  when  corrected  for  deviation,  as  coriect  magnetic  course  or 
bearings. 

Fourth.  A  compass  course  is  the  angle  which  the  ship's  track 
makes  with  the  direction  of  the  magnetic  needle  of  the  compass; 
such  a  course  is  affected  with  deviation  and  variation;  applying  the 
former,  it  becomes  the  correct  magnetic  course;  applying  both,  it  be- 
comes the  true  course. 

Fifth.  A  compass  bearing  is  similarly  the  angle  contained  between 
the  direction  of  the  object  and  the  direction  of  the  magnetic  needle 
of  the  compass;  like  the  compass  course,  it  is  affected  with  devia- 
tion and  variation;  but  the  deviation  to  be  applied  in  this  case,  is 
that  clue  to  the  Azimuth  of  the  ship's  head,  not  that  on  the  point  of 
bearing;  when  this  correction  is  made  it  becomes  the  correct  mag- 
netic, and  the  further  application  of  the  variation  turns  it  into  a 
true  bearing;  easterly  deviation  and  variation  to  the  right,  westerly 
deviation  and  variation  to  the  left. 

Sixth.  In  "  cross- bearings,"  both  bearing's  must  be  corrected  for 
the  deviation  dug  to  the  direction  of  the  ship's  head  at  the  instant 
of  making  the  observation.  The  correction  or  error  of  the  compass 
obtained  by  means  of  an  Amplitude  or  Azimuth  of  the  Sun,  or  any 
celestial  object,  is  the  variation  and  deviation  combined  on  the 
course  or  direction  of  the  ship's  head  at.  the  moment  of  making  the 
observation;  therefore,  knowing  the  variation  of  the  compass  at  any 
place,  the  deviation  can  readily  be  eliminated  by  one  of  the  follow- 
ing rules: 


LEEWAY.  43 

First.  If  the  correction  is  greater  than  the  variation,  subtract  the 
variation  from  the  correction,  and  the  remainder,  which  is  the  devia- 
tion, will  be  the  same  name  as  the  correction.  Correction  and  varia- 
tion of  the  same  names  both  east  or  both  west: 

Ex.2.  Correction..  .  30°  00' E. 


Ex.  1.  Correction 39°  00'  W. 

Variation..  .   28  00  W. 


Deviation 11°  00'  W. 


Variation 22  00  E. 


Deviation 8°  00'  E. 


Second.  If  the  correction  is  less  than  variation,  subtract  the  cor- 
rection from  the  variation,  and  the  remainder,  which  is  the  deviation, 
will  be  east  when  the  correction  is  west,  but  west  when  the  correction 
is  east. 


Ex.  1.  Correction 17°  00'  W. 

Variation..  .  30  00  W. 


Deviation..  .   13°  00'   E. 


Ex.2.   Correction 10°  00'  E. 

Variation 25°  00'  E. 

Deviation..  .   15°  00' W. 


Correction  and  variation  of  different  names,  one  east  and  the  other 
west.  Add  together  the  correction  and  variation,  their  sum,  which 
is  the  deviation,  will  be  the  same  now  as  the  correction. 


Ex.3.  Correction 10°  00' W. 

Variation..  5   00    E. 


Deviation..  .   15°  00' W. 


Ex.4.  Correction 16°  00'  E. 

Variation 13  00  W. 


Deviation 29°  00'  E. 


Third.  If  the  variation  is  00°  00'  the  correction  is  the  deviation. 

Fourth.  If  the  correction  is  00°  00'  the  deviation  is  of  the  same 
amount  as  the  variation,  but  of  an  opposite  name;  that  is,  east  when 
the  deviation  is  west,  but  west  when  the  variation  is  east. 

NOTE. — For  correcting  courses  for  deviation,  see  table  3,  for  deviation  of  Standard  Compass, 
N.  III. 


LEEWAY. 

When  a  ship  is  close-hauled  and  the  wind  blowing  fresh,  that  part 
of  the  wind  which  acts  upon  the  hull  and  rigging  together  with  a 
considerable  part  of  the  force  exerted  on  the  sails,  tend  to  drive  her 
immediately  from  the  direction  of  the  wind,  or  as  it  is  called  to  lee- 
ward; but  as  the  bow  of  a  ship  exposes  less  surface  to  the  water 
than  the  side,  the  resistance  will  be  less  in  the  first  case  than  in  the 
second;  the  velocity,  therefore,  in  the  direction  of  the  head,  will  in 
most  cases,  be  greater  than  the  velocity  in  the  direction  of  her  side, 
and  the  ship's  real  course  will  be  between  the  two  directions.  Now 
the  angle  contained  between  the  line  of  the  ship's  apparent  course, 
and  the  line  she  really  describes  through  the  water  is  termed  the 
leeway. 

The  quantity  of  leeway  to  be  allowed  will  depend  upon  a  variety 
of  circumstances,  such  as  the  mould  or  build  of  a  ship,  the  draught 
or  the  trim  of  the  ship,  the  quantity  of  sail  she  may  be  under,  her 


PKACTICAL  NAVIGATION. 


speed  through  the  water,  and  the  sails  being1  properly  set  and  trimmed 
to  the  wind,  etc.  No  general  rule  can,  be  laid  down  that  will  deter- 
mine the  quantity  of  leeway  at  all  times.  The  most  accurate  method 
is  to  draw  a  semicircle  on  the  taffrail  with  its  diameter  at  right  angles 
with  the  ship's  keel,  and  apply  as  directed  by  the  following  plate: 


The  semicircle  A.  consists  of  a  small  piece  of  polished  brass  upon  which  the  points  of  the 
compass  are  correctly  laid  off;  this  semicircle  is  attached  to  the  taffrail  of  the  sliip.  On  the 
face  of  this  semicircle  or  dial  plate,  we  have  a  suitable  pointer  C.,  one  end  of  which  turns  on 
the  pin  B.,  and  to  the  other  end  we  attach  the  line  running  to  the  log.  It  wil  be  seen  by  the 
above  sketch,  the  manner  in  which  the  log  line  is  fastened  to  the  pointer,  \\hen  the  1  'g  is  to 
be  drawn  in,  the  line  is  slipped  into  the  crutch  and  is  held  tight  against  the  knot,  as  in  sketch 
D.,  and  the  quantity  of  leeway  is  equivalent  to  the  number  of  points  indicated  from  the  center 
line  of  the  dial  plate,  which  is  to  be  applied  to  the  ship's  course  as  per  rule.  The  leeway  being 
determined  it  is  to  be  allowed  from  the  wind;  that  is,  to  the  right  of  the  course  steered,  when 
the  wind  is  on  the  port  side,  and  to  the  left  when  the  wind  is  on  the  starboard  side. 

How  to  apply  the  Variation,  Deviation  and  Leeway. 

First.  The  calculator  should  suppose  himself  to  be  placed  at  the 
centre  of  the  compass  card,  and  looking  outward  in  the  direction 
of  the  ship's  head;  for  example,  suppose  a  ship  is  on  the  starboard 
tack  with  her  head  at  north  by  compass,  and  the  variation  to  be 
2  points  easterly,  the  deviation  2  points  westerly  and  1  point  leeway; 
now  2  points  east  of  north  will  give  the  course  N.N.E.,  because 
easterly  variation  is  always  applied  to  the  right  hand;  2  points  west- 
erly deviation  gives  the  course  north  again,  because  westerly  devia- 
tion is  always  applied  to  the  left  hand,  and  1  point  leeway  with  the 
wind  on  the  starboard  side  will  give  the  corrected  course  N.  by  "W. , 
because  the  wind  throws  the  ship  to  the  left  hand,  (1  point). 

Second.  Suppose  a  ship's  head  S.E.  by  compass  variation  1^ 
points  east,  deviation  1^  points  east  and  2  points  leeway,  the  wind 
being  from  the  N.E.  Now  1J  points  easterly  variation  gives  S.S. 
E.-rrE.;  1J  points  easterly  deviation  gives  S.  by  E.^E.,  and  2  points 
leeway  with  the  wind  from  the  eastward  gives  the  course  S.f-W. 

Third.  Suppose  a  ship's  head  by  compass  to  be  N.N.W.,  the  va- 
riation to  be  2  points  west,  the  deviation  1^  points  east,  and  leeway 
f  point,  the  wind  being  from  the  S.W.,  2  points  westerly  variation 
gives  N.W. ;  1J  points  easterly  deviation  gives  N.N.W.^W.,  and  f 
point  leeway,  wind  from  S.W.  gives  the  course  N.  by  W.^W. 

Easterly  variation  and  easterly  deviation  go  together;  that  is,  to  the 
right-hand;  westerly  variation  and  westerly  deviation  go  together;  that 
is,  to  the  left-hand,  and  leeway  from  the  wind. 


VAKIATION,    DEVIATION  AND  LEEWAY. 


The  following  examples,  where  the  courses  steered,  and  the  vari- 
ation, deviation  and  leeway  to  be  allowed  on  each,  are  given,  from 
thence  to  find  the  true  courses,  will  serve  to  exercise  the  learner  in 
the  foregoing  rules. 

If  any  corrected  course  exceed  8  points  or  90°,  it  must  be  sub- 
tracted from  16  points  or  180°,  and  the  name  changed  from  north  to 
south,  or  vice  versa. 


Ex.  1.  Ship'  head  N. ;  variation,  2  points  E. ;  deviation,  2  points  W. ;  leeway 
1  point  starboard  tack. 

Ex.  2.  Ship's  head  S.E.;  variation,  1^  point  E.;  deviation,  1J  point  E.  and  2 
points  leeway;  wind  from  N.E. 

Ex.  3.  Ship's  head  N.N.W.;  variation,  2  points  \V. ;  deviation,  1£  point  E.; 
leeway,  f  point;  wind  from  S.W. 

These  examples  are  marked  out  in  degrees,  instead  of  points,  as 
it  is  more  correct,  so  when  points  are  given  turn  them  into  degrees 
and  then  apply  deviation,  variation  and  leeway,  as  per  rules. 


Ex  1.  Given  a  ship's  head,  N.  85°  15' 
W. ;  variation,  16°  W. ;  deviation,  19° 
41'  E. ;  leeway,  22°  30';  wind  being  from 
S.  S.  W. 

Ship's  head N.  85°  15'  W. 

Variation . .  . .-.-  . .       15         W. 


101°  15' 
180 


Deviation. 


S.  78°  45'  W. 
19  41    E. 


98°  26' 
80 


N.  81°  34'  W. 
Leeway 22  30 


True  course N.  59°  04'  W. 


.  Ex.  2. 
Ship's  head S.  78°  45'  E. 


Variation 17 


K. 


S.  Gl°  45'  E. 
Deviation..  22  30  W. 


S.  84°  15    E. 
W'dW.S.W.  1'w'y.        5  45 

True  course . .       . .  S.  90°  00'  E.  =  East. 


PKACTICAL   NAVIGATION. 


COURSES  STEEBED  AND  CORRECTIONS  GIVEN. 

To  FIND 
CORRECTED 
COURSE. 

Courses  steered. 

Wind. 

Variation. 

Deviation. 

Leeway. 

Corrected  course. 

N.  30°  45'  E. 
N.  45°  W. 
N.  45°  E. 
S.   22°30'W. 
South. 
N.  11°30'W. 

N.  W. 
N.  E. 
S.   E. 
West. 
E.  by  N. 
W.  N.  W. 

11°  15'  W. 
22°  30'  W. 
19°41'W. 
16°  W. 
22°  30'  W. 
16°  45'  E. 

20°  30'  W. 
18°  E. 
11°  15'  W. 
22°  30'  W. 
11°  15'  W. 
22°  30'  E. 

11°  15' 
22°30' 
33°  45' 
33°  45' 
22°  30' 
33°  45' 

N.  13°  15'  E. 
N.  72°  90'  W. 
N.  19°  41'  W. 
S.  49°45'E. 
S.  11°15'E. 
N.  61°  30'  E. 

NO.    1. TABLE  FOB  FINDING  DEVIATION. 

Form  of  registering  the  observations  for  determining  the  deviation  of  the 
Standard  Compass  by  means  of  a  known  Correct  Magnetic  Bearing  of  a  distant 
object.  Read  the  rules  on  deviation  carefully. 


Ship's  Head  by 
1  Standard  Compass. 

Bearing  of  Distant 
Object  from  Standard 
Compass  on  Board. 

Correct  Magnetic 
Bearing  of  the  Distant 
Object. 

Deviation  of  Standard 
Compass. 

North. 

N.  76°  00'  W. 

N.  60°  30'  W. 

15°  30'  E. 

N.  by  E. 

N.  78  25  W. 

«           « 

17  55  E. 

N.  N.  E. 

N.  80  50  W. 

"           " 

20  20  E. 

N.  E.  by  N. 

N.  81    10  W. 

it              a 

20  40  E. 

N.  E.    ' 

N.  81   30  W. 

<              it 

21   00  E. 

N.  E.  by  E. 

N.  79  37  W. 

i             ti 

19  07  E.     . 

E.  N.  E. 

N.  77  45  W. 

(             it 

17   15  E. 

E.  by  N. 

N.  74  02  W. 

i              ii 

13  32  E. 

East. 

N.  70  20  W. 

t              ti 

9  50  E. 

E.  by  S. 

N.  66  00  W. 

<              <( 

5  30  E. 

E.  S.  E. 

N.  61   40  W. 

'              " 

1    10  E. 

S.  E.  by  E. 

N.  57  35  W. 

tt             « 

2  25  W. 

S.  E.     ' 

N.  53  36  W. 

a              it 

7  00  W. 

S.  E.  by  S. 

N.  50  37  W. 

«              « 

9  52  W. 

S.  S.  E. 

N.  47  45  W. 

«              « 

12  45  W. 

S.  by  E. 

N.  46   22  W. 

«              o 

14  07  W. 

South. 

N.  45  00  W. 

<                 < 

15   30  W. 

S.  by  W. 

N.  44  40  W. 

t                 < 

15   50  W. 

S.  S.  W. 

N.  44  20  W. 

i                  < 

16   10  W. 

S.  W.  by  S. 

N.  44  53  W. 

'                  ' 

15   35  W. 

S.  W.    ' 

N.  45  30  W. 

1 

15  00  W. 

S.  W.  by  W. 

N.  46  30  W. 

<                < 

14  00  W. 

W.  S.  W. 

N.  47   30  W. 

'                ' 

13  00  W. 

W.  by  S. 

N.  49  00  W. 

'                ' 

11   30  W. 

West. 

N.  50  30  W. 

(                « 

10  00  W. 

W.  by  N. 

N.  52  50  W. 

<                ( 

7  40  W. 

W.  N.  W. 

N.  55   10  W. 

<                < 

5  20  W. 

N.  W.  by  W. 

N.  58   20  W. 

«                < 

2    10  W. 

N.  W.    ' 

N.  61   31  W. 

«                ( 

1   00  W. 

N.  W.  by  N. 

N.  65   15  W. 

it               t 

4  45  W. 

N.  N.  W. 

N.  69  00  W. 

it               f 

8  30  W. 

N.  by  W. 

N.  70  30  W. 

"               ' 

12   00  W. 

Name  the  deviation  east,  when 
the  correct  magnetic  bearing  stands 
to  right  of  that  taken  on  board,  and 
west  when  to  the  left.  Look  at 
compass  in  this  table. 


DEVIATION   OF  THE   COMPASS. 


47 


NO.   2. TABLE  FOR  FINDING  DEVIATION. 

To  determine  the  deviation  at  sea  by  the  bearing  of  a  distant  object,  its  cor- 
rect magnetic  bearing  being  unknown,  take  the  bearing  of  a  distant  object  by 
compass,  on  32  points,  and  divide  the  sum  of  the  bearings  by  32,  the  result  will 
be  the  correct  magnetic  bearing,  approximately.  Then  the  difference  between 
the  correct  magnetic  and  compass  bearing  on  each  point,  will  be  the  deviation. 
Name  the  deviation  East,  when  the  correct  magnetic  is  greater  than  bearing 
from  ship.  Name  the  deviation  West,  when  correct  magnetic  is  less  than  bear- 
ing from  ship.  Remember  that  easterly  deviation  goes  to  the  right  hand  and 
westerly  to  the  left  hand.  Look  at  compass  in  this  table. 


Ship's.Head  by 
Standard  Compass. 

Bearing  of  Distant 
Object  by  Standard 
Compass. 

Correct  Magnetic 
Bearing. 

Deviation  of 
Standard  Compass. 

North. 

N.  59°  50'  W. 

N.  63°  00 

W. 

3°  10'  W. 

N.  by  E. 

N.  65  35  W. 

2  35  E. 

N.  N.  E. 

N.  71    10  W. 

8   10  E. 

N.  E.  by  N. 

N.  76   10  W. 

13   10  E. 

N.  E.    ' 

N.  79  50  W. 

16  50  E. 

N.  E.  by  E. 

N.  82  30  W. 

19  30  E. 

E.  N.  E. 

N.  83  30  W. 

20  30  E. 

E.  by  N. 

N.  84  05  W. 

21   05  E. 

East. 

N.  83  20  W. 

20  20  E. 

E.  by  S. 

N.  82   15  W. 

19   15  E. 

E.  S.  E. 

N.  81   05  W. 

18  05  E. 

S.  E.  by  E. 

N.  79  30  W. 

16  30  E. 

S.  E.     ' 

N.  77  40  W. 

14  40  E. 

S.  E.  by  S. 

N.  75  05  W. 

12  05  E. 

S.  S.  E. 

N.  72  40  W. 

9  40  E. 

S.  by  E. 

N.  69  00  W. 

6  00  E. 

South. 

N.  66   10  W. 

3   10  E. 

S.  by  W. 

N.  63  05  W. 

00  05  E. 

S.  S.  W. 

N.  60  00  W. 

3  00  W. 

S.  W.  by  S. 

N.  56  30  W. 

6  30  W.    ' 

S.  W.    ' 

N.  53  20  W. 

9  40  W. 

S.  W.  by  W. 

N.  50  00  W. 

13  00  W. 

W.  S.  W. 

N.  46  50  W. 

16   10  W. 

W.  by  S. 

N.  43  45  W. 

19   15  W. 

West. 

N.  41   50  W. 

21    10  W. 

W.  by  N. 

N.  39  40  W. 

23  20  W. 

W.  N.  W. 

N.  39  00  W. 

24  00  W. 

N.  W.  by  W. 

N.  39  25  W. 

23   35  W. 

N.  W. 

N.  41   00  W. 

22  00  W. 

N.  W.  by  N. 

N.  44  00  W. 

19  00  W. 

N.  N.  W. 

N.  48   10  W. 

14  50  W. 

N.  by  W. 

N.  53  45  W. 

9   15  W. 

32)2009°  45'(62°  48' 

Call  the  magnetic  bearing  63° 
as  there  is  48'  over. 


48  PEACTICAL  NAVIGATION. 

NO.    3. DEVIATION   TABLE    FOB    STANDARD    COMPASS. 


Ship's  Head  (or  Course) 
by  Standard  Compass. 

Deviation  of  the 
Standard  Compass 

Correct  Magnetic  Course  made  good  by 
Steering  as  in  the  First  Column. 

North. 

15°  30'  E. 

N.  15°  30'  E.      or    N.  by  E.  |  E.       nearly. 

N.  by.  E. 

18  20  E. 

N.  29  35  E. 

N.  N.  E.  |  E. 

N.  N.  E. 

20  20  E. 

N.  42  50  E. 

X.  E.  i  N. 

N.  E.  by  N. 

21    15  E. 

N.  55  00  E. 

N.  E.  $  E. 

N.  E.    ' 

21  00  E. 

N.  66  00  E. 

N.  E.  by  E.  5  E. 

N.  E.  by  E. 

19  45  E. 

N.  76  00  E. 

E.  by  N.  i  N. 

E.  N.  E. 

17   15  E. 

N.  84  45  E. 

E.  \.  N. 

E.  by  N. 

13  50  E. 

S.  87  25  E. 

E.  iS. 

East. 

9  50  E. 

S.  80  10  E. 

E.  JS. 

E.  by  S. 

5  30  E. 

S.  73   15  E. 

E.  by  S.  4  S. 

E.  S.  E. 

1   10  E. 

S.   66  20  E. 

S.  E.  by  E.  1  E. 

S.  E.  by  E. 

3   10  W. 

S.  59  25  E. 

S.  E.  by  E.  4  E, 

S.  E.    ' 

7  00  W. 

S.   52  00  E. 

S.  E.  |  E. 

S.  E.  by  S. 

10  15  W. 

S.   44  00  E. 

S.  E.  1  S. 

S.  S.  E. 

12  45  VV. 

S.   35   15  E. 

S.  E.  1  S. 

S.  by  E. 

14  30  W. 

S.   25  45  E. 

S.  S.  E.  i  E. 

South. 

15  30  W. 

S.    15  30  E. 

S.  bvE.f  E. 

S.  by  W. 

16   15  W. 

S.     5  00  E. 

S.  ^E. 

S.  S.  W. 

16   10  W. 

S.     6  20  W. 

S.  g  W. 

S.  W.  by  S. 

15  40  W. 

S.   18  05  W. 

S.  by  W.  §  W. 

S.  W. 

15  00  W. 

S.  30  00  W. 

S.  S.  W.  §  W. 

S.  W.  by  W. 

14  20  W. 

S.  41  55  W. 

S.  W.  i  S. 

W.  S.  W. 

13  00  W. 

S.   54  30  W. 

S.  W.  |  W. 

W.  by  S. 

11   30  W. 

S.  67   15  W. 

W.  S.  W. 

West. 

10  00  W. 

S.  80  00  W. 

W.  I  S. 

W.  by  N. 

7  50  W. 

N.  86  35  W. 

W.  £  N. 

W.  N.  W. 

5  20  W. 

N.  72  50  W. 

W.  by  N.  4  N. 

N.  W.  by  W. 

2  20  W. 

N.  58  35  W. 

N.  W.  by  W.  1  W. 

N.  W.    ' 

1  00  E. 

N.  44  00  W. 

N.  W.  £  N. 

N.  W.  by  N. 

4  40  E. 

N.  29  05  W. 

N.  N.  W.  §  W. 

N.  N.  W. 

8  30  E. 

N.  14  00  W. 

N.  by  W.  i  W. 

N.  by  W. 

12  15  E. 

N.    1  00  E. 

N.JrE. 

METHOD   OF  WORKING  DEAD  RECKONING.  49 


METHOD  OF  WOBKING  DEAD  BECKONING,  OK  WHAT  IS 
COMMONLY  CALLED  DAY'S  WOKK. 

To  Correct  the  Courses  for  Variation,  Deviation  and  Leeway. 

"When  the  variation  is  westerly  allow  it  to  the  left  hand  of  the 
course  steered.  When  variation  is  easterly  allow  it  to  the  right 
hand  of  the  course  steered. 

When  the  deviation  is  westerly  allow  it  to  the  left  hand  of  the 
course  steered.  When  deviation  is  easterly  allow  it  to  the  right 
hand  of  the  course  steered. 

If  an  azimuth  be  observed,  the  correction  will  be  the  variation  and 
deviation  combined  on  the  azimuth  due  the  ship's  head  on  that  course. 

To  Correct  the  Course  for  Leeway. 

When  on  the  starboard  tack  allow  the  leeway  to  the  left  hand  of 
the  compass  course.  When  on  the  port  tack  allow  it  to  the  right 
hand  of  the  compass  course. 

First  Course  on  Leaving  the  Land. 

Take  the  bearing  of  an  object,  whose  position,  or  latitude  and 
longitude  are  known,  and  estimate  its  distance  off  shore  as  a  dis- 
tance, the  opposite  point  to  which  is  taken  as  a  course,  and  being  cor- 
rected for  variation  and  deviation  due  the  ship's  head  on  that  course. 

This  is  entered  in  the  traverse  table  along  with  the  other  courses. 

If  there  is  a  current,  the  set  and  drift  of  which  is  known,  allow 
the  variation  only  on  its  set,  and  enter  it  in.  the  traverse  table  as  a 
course  and  distance. 

Each  course  is  to  be  corrected  for  variation,  deviation  and  leeway, 
and  entered  in  the  traverse  table,  and  set  against  each  the  distance 
run  on  that  course. 

Traverse  Table. 

Make  a  table  which  divide  into  six  columns,  in  the  first  of  these 
set  down  the  several  courses,  and  opposite  to  them  in  the  second 
column  enter  the  distance  run  on  each  course. 

The  third  and  fourth  columns  are  to  be  marked  north  and  south, 
and  are  to  contain  the  difference  of  latitude. 

The  fifth  and  sixth  are  to  be  marked  east  and  west,  and  to  con- 
tain the  departures. 

Find  the  difference  of  latitude  and  departure  corresponding  to 
each  course  and  distance  in  Table  III;  set  these  down  in  their  proper 
columns;  if  the  difference  of  latitude  is  north,  it  must  be  placed  in 
the  north  column;  and  if  south  in  the  south  column;  if  the  depart- 
ure is  easterly  place  it  in  the  east  column,  and  if  westerly  place  it  in 
the  west  column. 
4 


50  PRACTICAL   NAVIGATION. 

"When  the  course  is  due  north,  south,  east  or  west,  set  down  the 
distance  in  its  respective  column. 

Sum  up  the  columns  of  northing,  southing,  easting  and  westing, 
of  each  column  separately,  then  if  the  northing  be  less  than  the 
southing,  subtract  it  from  the  southing,  and  the  remainder  will  be 
the  whole  difference  of  latitude  made  good,  and  of  the  same  name 
as  the  greater;  in  the  same  manner  the  difference  between  the  sums 
of  the  east  and  west  column  is  the  whole  departure  made,  and  of 
the  same  name  as  the  greater. 

Then  the  whole  difference  of  latitude  and  departure  will  give  the 
direct  course  and  distance  in  Table  IV. 

To  find  the  course  and  distance,  with  the  difference  of  latitude  and 
departure  made  good,  enter  Table  IV;  seek  in  the  columns  until  they 
are  found  to  agree;  opposite  to  which  will  be  found  the  distance  in 
its  column. 

If  the  departure  be  greater  than  the  difference  of  latitude,  the 
course  will  be  found  at  the  bottom  of  the  table,  but  if  the  depart- 
ure be  less  than  the  difference  of  latitude,  the  course  will  be  found 
at  the  top  of  the  table. 

To  find  Latitude  in. 

If  the  latitude  of  the  place  from  which  the  departure  has  been 
taken  and  the  difference  of  latitude  made  be  both  north  or  both 
south,  their  sum  will  be  the  latitude  of  the  same  name;  but  if  the 
difference  of  latitude  is  of  a  contrary  name  to  the  latitude  left,  their 
difference  will  be  the  latitude  in,  and  of  the  same  name  as  the  greater. 

To  find  the  Difference  of  Longitude. 

Add  together  the  latitude  left  and  latitude  in,  and  take  half  their 
sum  for  the  middle  latitude;  then,  with  the  middle  latitude  as  a 
course,  enter  Table  IV  and  seek  for  the  departure  made  good  in  the 
latitude  column,  and  in  the  distance  column  opposite,  will  be  found 
the  difference  of  longitude  made,  which  divided  by  60;  if  over  60, 
will  give  the  degrees  and  minutes  to  be  named  east  or  west,  accord- 
ing to  the  departure. 

To  find  the  Longitude  in. 

If  the  longitude  left  and  difference  of  longitude  made  be  both 
east  or  west,  their  sum  will  be  the  longitude  in  and  of  the  same 
name;  but  if  the  difference  of  longitude  be  of  contrary  name  to  the 
longitude  left,  their  difference  will  be  the  longitude  in  and  of  the 
same  name  as  the  greater;  but  when  their  sum  exceeds  180°  degrees 
the  ship  has  crossed  the  opposite  meridian  to  that  of  Greenwich,  in  that 
case  subtract  it  from  360°  degrees,  and  the  remainder  will  be  the 
longitude  in  of  a  different  name.  In  example  No.  1,  the  courses  are 


METHOD   OF  WORKING  DEAD   RECKOXIXG. 


51 


given  in  points,  the  learner  however,  will  derive  greater  advantage 
by  turning  the  points  into  degrees,  and  practicing  that  system  only, 
as  it  will  facilitate  the  application  of  the  variation  and  deviation 
•which  is  generally  given  in  degrees. 

Ex.  1.  A  ship  from  a  port  in  latitude  38°  42'  N.,  and  longitude  51°  32' W., 
bound  to  another  port  in  latitude  43D  27'  N.  and  longitude  65°  19'  W. ,  sails  the 
following  courses:  S.W.  f  W.  54  miles,  S.W.  by  S.  38  miles,  S.  by  E.  A  E.  37 
miles,  S.E.  by  E.^E.  40  miles,  N.  by  E.£  E.  50  miles,  S.  by  E.J  E.  31  miles.  He- 
quired  the  course,  the  distance  and  latitude  and  longitude  in,  also  the  course 
and  distance  to  the  port  bound  to  by  Mercator  sailing. 


Course. 

Distance. 

Diff.  of  Lat. 

Departure. 

N.W.f  W. 

S.W.  by  S. 
S.  byE.JE. 
S.E.  bvE.iE. 
N.  by'E.m 
S.  byE.^E. 

54 
38 
37 
40 
50 
31 

N. 
47.8 

S. 
32.2 
31.6 
35.4 
18.9 

30.1 

E. 

10.7 
35.3 
14.5 
07.5 

W. 

43.4 
21.1 

'148.2 

47.8 

C8.0 
64.5 

64.5 

Course  S.  2°  00'  E.  =  100 . 4          3.5 

Distance  101  miles. 

The  difference  of  latitude  100.4  miles  and  the  departure  3.5,  being  looked  for 
till  they  are  found  opposite  each  other  in  their  respective  columns  in  Table  IV, 
gives  the  course  S.  2°  00'  E.,  and  the  distance  101  miles. 

To  Find  the  Latitude  and  Longitude. 


Latitude  left 38°  42'  N. 

Difference  of  latitude . .  1    40  S. 


Latitude  in 37°  02'  N. 

Sum 2)75    44 


Middle  latitude . .  .37°  52' 


Longitude  left 51°  32'  W. 

Difference  of  longitude 05  E. 


Longitude  in . .  ...  51°  27' W. 


The  middle  latitude  as  a  course,  and  the  de- 
parture in  a  latitude  column,  will  give  the 
difference  of  longitude  in  a  distance  column, 
5  miles. 

The  course  to  the  port  bound  to,  will  be  found  to  be  N.  58°  09'  W.,  and  the 
distance  729.6.     Work  it  out  as  per  rule  in  case  I,  example  1,  page  30. 

CORRECT  THE  FOLLOWING  COURSES  FOR  LEEWA Y  AND  VARIATION. 


GIVEN. 


Courses  steered. 

Winds. 

Leeway. 

Variation. 

Courses  correct'd 

E.N.E. 

N.W. 

N.E.iE. 

W.  by  S. 
N.W'.  bvN. 
South. 
N.W. 

s.s.w. 

K.  by  N. 
West. 

N.W.  by  N. 
N.E.  byN. 
E.S.E. 
W.S.W. 
SE. 
N.  by  E. 

N.N'.W. 

1 

14 
i 

2 

H 

*j 

1 

H  W. 
2"  W. 
li  E. 
1     \V. 
li  W. 

<>,'  E. 
1    E. 

W.S.W. 

W.  bvN.AN. 
S.  bv'w.  v\V. 
N.W,  byN. 
S.S.W. 
S.  F,  b\-  K.JE. 
W.  i  N. 

TO  FIND  ANSWER 


52 


PKACTICAL   NAVIGATION. 


Ex.  2.  April  11,  1876,  Steamship  "City  of  Panama,"  W.  B.  Seabury,  Com- 
mander, from  San  Francisco,  toward  Victoria,  at  noon  took  our  departure  from 
Point  Bonita  in  latitude  37°  49'  N.,  and  longitude  122°  31  W.;  bearing  by  com- 
pass E.  £S. ,  distant  3  miles. 


HOURS. 

KNOTS. 

10THS. 

COURSES. 

WINDS. 

LEEWAY. 

DEVIATION. 

1 

8 

5 

W. 

*N. 

N 

.  W. 

2 

8 

5 

" 

3 

G 

5 

" 

4 

6 

5 

" 

5 

G 

5 

" 

G 

6 

5 

(i 

7 

6 

5 

N.  W.  byN.  4N. 

" 

8 

6 

0 

" 

9 

6 

5 

" 

10 

6 

5 

" 

11 

6 

5 

it 

12 

6 

5 

N.W. 

byN. 

K 

1 

7 

5 

" 

2 

7 

5 

" 

3 

7 

5 

" 

4 

6 

5 

N.  by  W.  4  W. 

" 

5 

6 

5 

" 

6 

6 

5 

" 

7 

6 

5 

< 

8 

7 

5 

N.  by  W.  |  W. 

1 

9 

7 

5 

1 

10 

8 

5 

< 

11 

8 

5 

< 

12 

9 

5 

' 

COURSES.            DISTANCE. 

N. 

s. 

E. 

W. 

N.  74  W.              43 

04.2 

• 

42.8 

N.  2|  W.              33 

29.1 

' 

15.6 

N.  3    W.              28 

23.3 

' 

15.6 

N.  14  W.              26 

24.9 

< 

07.5 

N.  If  W.              41 

38.6 

' 

13.8 

Dif.  of  lat....  60)120.1 

2l  00'  N. 

Latitude  left 39°  49'  N. 

Difference  of  latitude 2  00  N. 


Departure. 


95.3 


Longitude  left 122°  31'  W. 

Difference  of  longitude ...       2  03  W. 

Longitude  in : 124°  34'  W. 


Latitude  in 39°  49'  N. 

Sum 2)77  38 

Middle  latitude 38°  49 

True  course,  N.  38°  00'  W. ;  distance,  153  miles. 

The  middle  latitude  38°  49'  (call  it  39°  00'  as  you  have  49'  over)  as  a  course  in 
Table  IV,  and  the  departure  95'  in  a  latitude  column,  gives  the  difference  of 
longitude  123  miles  in  a  distance  column,  which  divide  by  60  gives  2°  03'  W., 
to  be  added  to  the  longitude  because  the  ship  has  been  going  to  the  westward. 


METHOD   OF  WORKING   DEAD   BECKONING. 


53 


Ex.3. 


o 

COURSES. 

x 

8 

s 

WINDS. 

I 

VIAT'N. 

REMARKS,  ETC. 

W 

8 

* 

H 
fl 

1 

N.  W.  |  N. 

3 

5 

S.  W.  i  S. 

| 

25°  W. 

A  Point  of  Land. 

2 

" 

3 

5 

II 

In  Latitude          .  .   55°  57'  N 

3 

ii 

3 

5 

« 

In  Longitude  16°  04'  W. 

4 

" 

3 

5 

« 

Bearing  by  Compass  S.  J  W. 

5 

W.  S.  W. 

5 

5 

N.  W.  by  N. 

1 

11°W. 

Head  South.    Deviat'n  14°  W. 

6 

" 

5 

5 

M 

7 

II 

4 

5 

ii 

Distance  22  miles. 

8 

" 

4 

5 

" 

9 

W.byN.^N. 

5 

5 

S.  W.  4  W. 

lj 

28°  W. 

10 

" 

6 

5 

" 

Variation  25°  E. 

11 

" 

6 

5 

" 

12 

" 

7 

5 

II 

1 

N.  E.  |  E. 

7 

5 

N.  W.  by  N. 

| 

20°  E. 

2 

" 

7 

5 

M 

3 

•' 

7 

" 

4 

•• 

7 

" 

5 

N.  N.  E. 

7 

5 

N.  W.  by  W. 

1 

11°  E. 

6 

" 

6 

5 

" 

7 

" 

6 

5 

" 

8 

" 

6 

6 

'« 

9 

N.  E.  4  E. 

6 

5 

S.  E.  by  E. 

1 

20°  E. 

A  Current  set  Correct  Mag- 

10 

" 

6 

7 

11 

netic  S.  22°  E.  26  miles  from 

11 

•• 

6 

9 

" 

the  time  the  departure  was 

12 

5 

9 

taken  to  the  end  of  the  day. 

BEARING  OF  LAND. 

FIBST   COUBSE. 

THIRD  COURSE. 

FIFTH  COUBSE. 

S.  i  W.  =  S.  3°  W. 

N.  W.  f  N.  Leeway 

W.    by  N.    4  N. 

N.  N.  E.  Leeway  1 

OPI 

|  point  to  the  right 
hand  makes  it  into 

Leeway    1|   point 
to  the  right  hand 

point  to  the  right 
hand  makes  it  into 

>osite  =  N.  3°  E. 

Dev.  14°  W.  )    ,    ,  i  o  p 

N.N.W.  4\V. 

makes  it  into  N. 

N.  E.  by  N. 

Var.  25°  E.)  "•"   Li    •Cj' 

=  N.  28°  W. 

W.  by  W.  i  W. 

=  N.  34°  E. 

Cor.  b'r'g,  N.  14°  E. 

Dev.  25°  W.  )       f.o 
Var.  25°  E.  J  ~ 

—  N.  59°  VV. 

Kr-ffi^v+a-w. 

Dev.  11°  E)     ,    nf>vn< 
Var.  25°  EJ  +  -^    -c" 

Cor'd  1st.)  -vr  90°  TV 
Course.  )  -^' 

V  «I  .    —'-> 

Cor'd  3rd  ; 
Course.  ; 

Cor'd  5th  1  -M-    i-^o  -p 
Course.  J         ' 

N.  62°  W. 

CUEBENT. 

SECOND  COUESE. 

FOUBTH  COURSE. 

SIXTH  COUESE. 

S.  S.  E.  =  S.  22°  E. 

W.  S.  W.  Leeway 

N.  E.  f  E.  Leeway 

N.  E.  i  E.  Leewav 

Variation    25°  E. 

1  point  to  the  left 

Vi*niirl  mnlrpQ  it  intr* 

f  point  to  the  right 
hand  makes  it  into 

J  point  to  the  left 
hand  makes  it  into 

Cor.  Cur.,  S.  3°  W. 

11(1111  L    llltlK(    >  lltJ.lJ.vU 

S.  W.  byW. 

N.  E.  byE.  JE. 

N.  E.  i  N. 

=  S.56°W. 

=  N.  62J  E. 

=  N.  42°  E. 

Var.  25°  E)    ,  •,  ,0  v 
Dev.ll°WJ  +i*     L" 

Var.  25°  E)       4,-(,F 
Dev.  20°  E  J  +          •c" 

Dev.  20°  E)    ,   4rop- 
Var.  25°  E/  +  4o   •L- 

Cor'd  )  -KT    107o  -p 
Course.}  IN>  1U/     *•• 

exceeds  90° 

Subtract  )         i  QAO 
from      J         18U 

Cor'd  2nd)  Q   7n°  \V 
Course.  }  °-  'u 

Cor'd  4th)  Q    700  17 
Course,    f  »•  's    J^- 

Cor'd  6th)  -vr    070  77 
Course,  f  JN-  87   *•• 

Ans.  True  course,  N.  66Q  E. ;  distance,  38  miles;  difference  of  latitude,  15.2 
departure,  34.6;  latitude  in,  56°  12'  N.;  longitude  in,  15°  02'  W. 


PRACTICAL  NAVIGATION. 


Ex.  4. 


i 

COURSES. 

i 

B 

"\VlXD. 

1 

ri 

i 

KEMABKS. 

0 

f, 

o 

w 

E 

W 

M 

H 

H 

Hi 

n 

1 

S.E.iS. 

4 

5 

NE  by  EiE 

8° 

14°  W. 

Noon.     A  Point  of  Land. 

2 

i  ( 

4 

5 

1  1 

mlatifmlp  °0J  0°'  S 

3 

<( 

4 

5 

<( 

JilLlt  IHIU    £t<3      \J  —      O. 

in  longitude  138°0°'E 

4 

« 

5 

5 

« 

Bear'gbyCoiup  —  NAY.  byAV. 

5 

S.E.  byS. 

7 

5 

S.  W. 

10° 

18°  W. 

Ship's  he'd  at  1st  c'rse,  per  log. 

6 

«  " 

6 

5 

" 

Distance  22  miles. 

7 

" 

6 

5 

" 

8 

" 

6 

5 

" 

9 

N.W.JN. 

5 

5 

SWbyWiW 

8° 

3°E. 

10 

" 

5 

5 

'" 

Var.  1  1°  E.  (to  the  right  hand) 

11 

" 

4 

5 

" 

12 

« 

4 

5 

" 

1 

W.  by  S. 

5 

5 

South. 

11° 

14°  E. 

2 

" 

4 

5 

" 

3 

« 

5 

5 

" 

4 

" 

4 

5 

a 

5 

W.byN.£N. 

3 

5 

N.iE. 

13° 

13°  E. 

6 

" 

3 

5 

" 

A  Curr'nt  set  |  N.  by  W.  1  W. 

7 
8 

ii 

2 

2 

5 

5 

M 

by  Comp'ss  \  (corr't  magn'c) 
20  miles  from  the  time  the  de- 

9 

S.fE. 

4 

5 

E4S. 

12° 

3°  W. 

parture  was  taken  to  the  end 

10 

" 

G 

5 

" 

of  the  day. 

11 

" 

7 

5 

t< 

12 

7 

5 

THCE  COUBSES. 

DlST. 

DIF.  LATITUDE. 

DEPAETUHE. 

Latitude  left  29°  02'  S. 

Dif.  of  Latitude...    +    16  S. 

N.            S. 

E. 

W. 

Lat.  in  at  Noon.  .  .  29°  18'  S. 

Sr;O°    Tf 

99 

-•             1  1  -Q 

1  Q-O 

„ 

OU      Hi. 

N.    9  W. 

2C2Q 

20 

11  tj 

19-8 

lo  U 

.< 

31 

Sum  of  Latitude...  58°  20' 

S.  37     E. 

19 

15-2 

11-4 

«• 

S.   51     E. 

27 

17-0 

21-0 

" 

Middle  Latitude.  .  .  29°  10' 

N.  17  W. 

20 

19-1 

a 

5-8 

X.  Go  W. 

20 

8-5 

" 

18-1 

Longitude  left  168°    2'  E. 

N.  G2  W. 

12 

5-6 

" 

10-6 

*Dif.  of  Longitude   +    10  E. 

S.    12   W. 

26 

25-4 

« 

5-4 

Long,  in  at  Xoon.l68°  12'  E. 

53-0      68-9 

51-3 

43-0 

True  Course. 

Dist. 

53-0 

43-0 

*The  middle  latitude  29°  as  a  course, 
and  the  departure  8'-3  in  a  latitude 

S.  27°  E. 

18' 

D.Lat    15-9 

8-3 

Dep. 

column,  give  the  difference  of  longi- 
tude 10'  (nearly)  in  a  dist'ce  col  'inn. 

TIME.  55 


TIME. 

Time  is  measured  by  the  motions  of  the  heavenly  bodies.  Its 
divisions  are  years,  mouths,  days,  hours,  minutes  and  seconds.  The 
day  is  the  interval  between  two  successive  transits  of  the  sun,  moon, 
or  a  star  over  the  same  meridian. 

The  solar,  or  apparent  day,  is  the  interval  between  the  sun's  de- 
parture from,  and  its  return  to  the  same  meridian.  This  day  is 
divided  into  24  hours,  each  hour  into  60  minutes,  and  each  minute 
into  60  seconds.  The  length  of  the  day  is  subject  to  continual 
changes,  owing  to  the  obliquity  of  the  plane  of  the  sun's  path  to  the 
equinoctial,  and  to  the  eccentricity  of  the  earth's  orbit.  Astrono- 
mers, so  as  to  have  a  uniform  measure  of  time,  use,  what  is  named, 
a  mean  solar  day,  the  length  of  this  day  is  equal  to  the  average  of 
all  the  apparent  solar  days  in  a  year;  in  other  words,  it  is  the  day 
that  would  be  shown  by  the  stin  if  it  moved  uniformly  in  its  path, 
the  ecliptic. 

As  only  apparent  time  can  be  obtained  from  observations,  a  cor- 
rection must  be  applied  to  this  in  order  to  reduce  it  to  mean  time, 
this  correction  is  called  the  equation  of  time.  When  it  is  required 
to  reduce  apparent  time  to  mean  time,  the  equation  of  time  must  be 
taken  from  the  first  page  of  the  Nautical  Almanac  for  the  given 
month  and  opposite  the  given  day. 

This  equation  must  be  applied  as  directed  at  the  head  of  its  col- 
umn. To  find  the  corrected  equation  of  time  take  it  out  of  its  col- 
umn opposite  the  required  day,  also  take  out  the  hourly  difference 
for  the  same  day,  and  multiply  it  by  the  number  of  hours  and  dec- 
imals of  an  hour  that  are  given  as  a  part  of  that  day,  add  this  cor- 
rection for  hourly  difference  if  the  equation  of  time  is  increasing,  or 
subtract  if  decreasing. 

Suppose  the  apparent  time  is  three  hours  P.M.,  March  5,  1878,  at 
the  meridian  of  Greenwich,  that  is,  the  sun  has  passed  this  meridian 
three  hours,  it  is  required  to  find  the  corresponding  mean  time. 

March  5, 1878,  equation  of  time,  N.  Aim.          llm:  40.95s.       Hourly,  dif.     0.573 
Correction  for  3  nours,  decreasing  (sub. )  1.71  3 

To  be  added  to  app.  time  +   llm:  39.24s.  1.719 

Apparent  time 3h:  00m:  OO.OOs. 

Mean  time 3h:  llm:  39.24s. 

When  it  is  required  to  change  mean  into  apparent  time  find  the 
equation  of  time  from  the  second  page  of  the  almanac  for  that 
month.  Find  the  correction  the  same  way  as  above,  and  apply  the 
equation  of  time  as  directed  at  the  head  of  the  column. 


56  PEACTICAL  NAVIGATION. 

March  5,  1878,  mean  time  at  the  meridian  of  Greenwich  3hr.  P.M. 
Required  the  apparent  time. 

March  5, 1878,  equation  of  time,  N.  Aim.         llm:  41.06s.         Hourly  dif.     0.573 
Correction  for  3  hours  decreasing  (sub. )  -       1.71s.  3 

To  be  subtracted  from  mean  time         llm:  39.35s.  1.719 

Mean  time..  ..  3h:  00m:  OO.OOs. 


Apparent  time 2h:  48m:  20.25s. 

There  are  three  ways  of  reckoning  time,  called  civil,  astronomical 
and  nautical,  the  last  is  now  obsolete. 

The  civil  day  begins  at  midnight  and  ends  the  following  midnight; 
it  is  divided  into  two  parts,  each  of  twelve  hours;  the  first  part  is 
called  A.M.,  meaning  ante-meridian  or  before  noon;  the  latter  part 
is  called  P.M.,  meaning  post-meridian  or  afternoon. 

The  astronomical  day  begins  at  noon  and  ends  the  following  noon; 
that  is,  it  begins  12  hours  alter  the  civil  day,  it  is  reckoned  through 
the  whole  24  hours  from  noon  to  noon.  Thus  from  noon  to  mid**' 
night  the  day  of  the  month  and  the  hours  of  the  day  are  the  same 
for  both  methods,  but  from  midnight  to  noon  the  civil  day  is  12 
hours  ahead  of  the  astronomical  day.  So  to  turn  A.M.  civil  time 
into  astronomical  time  add  12  hours  to  it,  and  call  it  the  day  be- 
fore, civil  date,  for  example: 

10  o'clock  A.M.,  June  5,  civil  time,  is  June  4,  22,  astronomical 
time,  and  23  hours  June  4,  astronomical  day,  is  12  o'clock  A.M.  June 
5,  civil  time. 

All  the  computations  of  the  Nautical  Almanac  are  made  for  as- 
tronomical time  at  the  meridian  of  Greenwich,  it  is  therefore  neces- 
sary,, in  taking  quantities  out  of  the  almanac  to  reduce  the  ship's 
time  to  Greenwich  time.  One  complete  revolution  of  a  heavenly 
body,  over  three  hundred  and  sixty  degrees  of  longitude  takes  place 
in  24  hours.  This  is  at  the  rate  of  15°  in  one  hour  of  time,  there- 
fore at  any  place  situated  eastward  of  the  meridian  of  Greenwich  it  . 
will  be  noon  before  it  is  noon  at  the  meridian  of  Greenwich,  and  at 
any  place  situated  to  the  westward  of  Greenwich  it  will  be  noon 
after  it  is  noon  at  the  meridian  of  Greenwich.  All  the  reduction  of 
time  must  be  made  at  the  rate  of  15°  to  an  hour.  The  rule  for  ap- 
plying longitude  in  time  is  this:  Reduce  the  given  longitude  by 
multiplying  by  4  and  dividing  by  6,  Table  XI,  into  time,  and  add  it 
to  the  astTonomical  time  of  the  given  place,  if  the  longitude  iu  is 
west,  and  subtract  it  from  the  astronomical  time  if  the  longitude  in 
is  east,  the  sum  or  the  remainder  is  the  corresponding  Greenwich 
time.  If  the  longitude  in  is  west,  and  the  sum  of  the  longitude  in 
time,  and  the  time  at  the  given  meridian  is  more  than  24  hours,  sub- 
tract 24  hours  from  it  and  call  the  remainder  the  time  past  noon  of 


TIME.  57 

the  day  that  follows.  If  the  longitude  in  is  east  aud  the  longitude 
in  time  is  more  than  time  at  the  given  meridian,  add  24  hours  to  the 
latter,  and  subtract  the  longitude  in  time,  the  remainder  must  be 
called  the  time  past  noon  of  the  day  before. 

"What  will  be  the  Greenwich  time  when  it  is  5  hours  P.M.  in  longi- 
tude 50°  W. 

Time  at  the  given  meridian 5h:  00m:  P.M. 

Longitude  in  time. .  . .    +3h:  20m:  w. 


Corresponding  time  at  meridian  Green ..       8h:  20m. 

Required  the  time  at  Greenwich   when   it   is   7h:30m:l5s:  P.M., 
in  longitude  100°  30' 

Time  at  the  given  meridian 7h:  30m:  los:  P.M. 

Longitude  in  time . .  .    -  6h :  42m :  OOs :  E. 


Corresponding  time  at  mer.  Green...       Oh:  48m:  15s. 

Required  the  astronomical  time  at  Greenwich  corresponding  to 
7h:50m:25s:  A.M.,  civil  time;  145°  16'  "W.  longitude;  May  5. 

May  5.     Time  at  the  given  meridian 7h:  50m:  25s:  civil  time. 

12h: 


May  4 19h:  50m:  25s:  astron.  time. 

Longitude  in  time^^« +9h:  41m:  04s:  W. 

29h:  31m:  29s: 
24h:  00m:  OOs: 

May  5.     Astronomical  time  at  Greenwich.       5h:  31m:  29s: 

February  18;  longitude  116°  37'  E.;  time  at  ship,  llh:37m:14s: 
M.  civil  time;  required  the  astronomical  time.  , 

Feb.  18.     Time  at  the  given  meridian llh:  37m:  14s:  civil  time. 

12h: 


Feb.  17 23h:  37m:  14s:  astron.  time. 

Longitude  in  time . .  -  7h :  46m :  28s :  E. 


Feb.  17.     Greenwich  astronomical  time..       15h:  50m:  46s: 

May  17;  in  longitude  125°  25'  E.;  astronomical  time  at  ship,  3h: 
10m;  required  the  astronomical  time  at  Greenwich. 

May  17.     Time  at  ship..  3h:  10.00m:  P.M. 

24h: 


May  16 27h:  10m:    • 

Longitude  in  time -  8h:  21m:  40s:  E. 

May  16.     Greenwich  astron.  time..     ISh:  48m:  20s: 


58  PRACTICAL  NAVIGATION. 


AMPLITUDE. 

To  find  the  Correction  and  Deviation  of  the  Compass  by  an  Amplitude. 

(Table  II,  secant  and  sine  for  amplitude.) 

First.  To  the  apparent  astronomical  time  at  ship  apply  the  longi- 
tude in  time;  adding  west,  and  subtracting  east  longitude  for  the 
apparent  astronomical  time  at  Greenwich. 

(NOTE. — Turn  the  degrees  into  time  by  multiplying  the  degrees  by  4,  and 
dividing  by  60.  Or  by  Table  XI. ) 

Ex.     35°    25' 

x       4 

60)141°  40' 


2h:21m:40s: 

Second.  P.M.  time  is  astronomical;  A.M.  is  civil  time,  and  re- 
quires 12  hours  added  to  make  it  astronomical  time  of  the  day  before, 
(therefore  add  12  hours  when  the  time  is  A.M.  and  call  it  a  day  back) 
then  apply  the  longitude;  when  west,  add;  when  east,  subtract. 

Ex.  June  20th,  A.  M.  at  ship  time 9h  :35m : 

12h: 


21h:35m: 

Third.  In  adding  west  longitude  the  time  may  exceed  24  hours, 
when  it  is  so  take  24  hours  from  it,  and  call  the  day  one  more. 

(NOTE. — Read  carefully  the  rules  on  time.) 

Fourth.  In  subtracting  east,  the  longitude  (in  time)  may  exceed 
the  time  at  ship;  then  borrow  24  hours  to  the  time  at  ship,  and  sub- 
tract as  before,  but  call  the  day  one  less,  as  you  have  borrowed  a 
day  by  adding  the  24  hours  to  the  ship's  time.  This  case  only  hap- 
pens when  it  is  P.M.  at  ship.  For  example:  January  20,  6h:40m: 
P.M.,  and  longitude  in  time  10h:40m:  east,  you  require  24h:  to  the 
6h:  making  30h:40m:  and  take  10h:40m:  from  that,  leaves  20h: 
on  January  19.  Again  January  20,  6h:40m:  A.M.,  you  will  always 
add  12h:  to  A.M.,  making  18h:40m:  on  January  19;  the  longitude 
10h:40m:  west  added  on  to  18h:40m:  makes  29h:  and  29m:  then 
take  24h:  from  the  29h:  and  you  have  5h:  and  20m:  on  January  20. 

Fifth.  To  the  apparent  astronomical  time  at  Greenwich,  correct 
the  sun's  declination^  taken  from  first  page  of  the  month  in  -the  Nau- 
tical Almanac,  by  the  hourly  difference  in  adjoining  column;  multi- 
ply the  hourly  difference  by  Greenwich  time,  turning  the  minutes 


AMPLITUDE.  59 

into  tenths  of  an  Lour  by  dividing  them  by  G,  and  if  any  over,  annex 
a  cipher,  and  divide  by  6  again  for  a  second  decimal.  For  example: 
Should  the  time  be  10h:33m:  then  6  into  33=5  times  and  3  over; 
to  the  3  over  annex  a  cipher,  and  you  have  6  into  30,  5  times,  mak- 
ing the  time  to  multiply  the  hourly  difference  by  10h:55m. 

Ex.  Suppose  the  declination  to  be..  22°  58' 57"        Hours  difference ..   P2"  83 

-      2  15         Time..  .   10  55 


Correct  declination 22°  56'  42"  6415 

6415 
12830 

60)1353565 


It  will  be  seen  by  the  above  example  that  there  are  four  decimals, 
viz:  Two  in  the  hourly  difference,  and  two  in  the  longitude  in  time; 
therefore,  cut  off  four  from  the  right  hand  of  the  product,  and  you 
have  left  135',  and  after  dividing  by  60  there  will  be  a  correction  of 
2'  15"  to  apply  to  the  declination,  and  as  the  declination  is  decreas- 
ing subtract  the  correction,  but  if  the  declination  is  increasing  add 
the  correction  and  you  have  the  correct  declination.  This  rule  is  to 
be  observed  in  all  cases  except  in  a  meridian  altitude. 

Sixth.  To  the  secant  (Table  2)  of  the  latitude  add  the  sine  (Table 
2)  of  the  reduced  declination.  Their  sum  less  10  of  the  index  is  the 
log.  sine  (Table  2)  of  the  true  amplitude;  to  be  reckoned  from  the 
west  when  P.M.  at  ship,  and  east  when  A.M.;  toward  the  north  when 
the  decimation  is  north,  or  south  when  the  declination  is  south. 

Seventh.  Under  the  true  amplitude  place  the  sun's  bearing  by 
compass,  and  take  notice  how  you  put  it  down,  because  it  is  given 
in  points,  and  you  must  turn  it  into  degrees,  counting  from  the  east 
or  west,  toward  the  north  or  south.  If  in  the  example  the  bearing 
is  given  TV.  by  S.  that  would  be  1  point  from  west  toward  the  south. 
Turn  1  point  into  degrees  and  it  will  be  "W.  11°  15'  S. ;  or  suppose 
the  bearing  was  given  S.S.E.,  in  this  case  it  would  be  6  points  from 
east,  and  turned  into  degrees  would  be  E.  67°  30'  S.  After  getting 
the  bearing  by  compass  into  proper  form,  proceed  to  find  the  correc- 
tion of  the  compass  in  the  following  manner. 

Eighth.  If  the  true  amplitude  and  sun's  bearing  from  ship  are 
both  north  or  both  south,  subtract  the  less  from  the  greater  for  the 
correction  of  the  compass. 

• 

Ninth.  If  the  true  amplitude  and  sun's  bearing  are  one  north  and 
the  other  south,  add  them  for  the  correction. 


60 


PRACTICAL  NAVIGATION. 


Tenth.  If  the  true  amplitude  is  reckoned  from  the  east,  and  the 
sun's  bearing  by  compass  from  the  west,  or  vice  versa,  add  them 
together  and  take  the  sum  from  180°,  the  remainder  will  be  the 
correction  of  the  compass. 

Eleventh.  Name  this  correction  east,  when  the  sun's  true  amplitude 
is  on  the  right-hand  of  the  sun's  bearing  from  ship,  and  west  when  it 
is  on  the  left-hand. 

Twelfth.  The  correction  of  the  compass  is  deviation  and  variation 
combined. 

Thirteenth.  To  find  the  deviation  underneath  the  correction  of 
the  compass,  place  the  variation  for  that  locality  from  the  chart. 
Then  if  one  is  east  and  the  other  west,  add  them  together,  and  the 
sum  is  the  deviation;  but  if  they  are  of  like  names,  that  is,  both 
east  or  both  west,  subtract  them  for  the  deviation. 

Fourteenth.  To  know  if  the  deviation  is  east  or  west,  draw  the 
compass  and  lay  off  the  variation  to  the  left  of  north  if  westerly, 
but  to  the  right  of  north  if  easterly;  lay  off  the  correction  in  the 
same  manner;  then  if  the  correction  is  on  the  right-hand  of  the 
variation,  the  deviation  is  easterly,  but  if  to  the  left,  it  is  westerly 

deviation. 

\ 

NOTE. — The  deviation  thus  found  must  only  be  applied  to  that  point  of  the  compass  the 
ship's  head  was  at  when  the  observation  was  made.  Observe  carefully  how  the  examples  are 
worked  out,  and  you  will  seldom  make  a  mistake. 


Ex.  1.  1878,  April  28th,  at  6h:56m:  P.M.,  apparent  time  at  ship  in  latitude 
43°  40'  S.,  and  longitude  6°  30'  E.  The  sun's  bearing  setting  was  W.£S. 
Required  the  true  amplitude,  the  correction  and  deviation  of  the  compass. 
Variation  per  chart  22°  W. 


H.  M. 


Apr.  28,  App.  T.  ship  6  56  P.M. 
Longitude  6°  30'  E.  -0  26 

Greene-time,  Apr.  28  6  30 


Sun's  Dec.  Apr.  28,  14°11'56"N.   Hourly  diff.  47"'l 
Cor.  for  6h:  30m:  .+     56         Green'b- time  6  '5 


Sun'sCor.  declinat'n  14°17'02"N. 


Latitude  of  ship  43°40'. .  Sec. .  10  -140640 
Sun'sCor.  Decl.14  17. .Sine.  9'392199 


23555 

282G6 

60)30,6,215 


5-6 


TrueAmpl.W.  19°57'N.Sine  9 '532839 
Sun's  bearingW.  2  49S.  (Setting) 

Cor.  of  Compass  22°46'E. 
Yar.  per  Chart  22  00  W. 

Deviation. . .  44°46'E.  for  the  point  of  the  compass  her  head  was  at  when  the 
'  observation  was  made. 


AMPLITUDE.  Gl 

Ex.  2.  1878,  January  1st,  9h:12m:  A.M.,  apparent  time  at  ship  in  latitude 
62°  10' S.,  longitude  138300'W.  The  sun's  bearing  rising  was  S. £W.  Required 
the  true  amplitude,  the  correction  and  deviation  of  the  compass.  Variation  per 
chart  45°  W. 

H.  M. 


Jan.  1,  App.  T.  ship  9  12  A.M. 
A.M.  at  ship. . .  +   12 


Dec.  31,  Ast.  time    21  12 
Longitude  138C00'W.  9  12 

Sum 3024 

Less,  24h 24 


Sun's  Dec.  Jan.  1st,  23°00'02"S.  Hourly  diff.  12"-64 
Cor.  for  6h.  40m...  -     1  21  6  •  4 


Sun's  Cor.  Decl. . .  22°5S'41"S.  5056 

7584 


60)8,0,896 


Gr'h  time.  Jan.  1st,  6  24 

Latitude 62°  10' Secant  10'330775 

Declination...  .22    59 Sine..     9'591580 


Sun's  true  amplitude  E 56°  45'  S'. . .  .Sine. .     9 '922355 

Sun's  bearing  by  Corn.  W.   84    22   S. 

Sum 141°  07' 

From..  ..180    00 


Cor.  of  the  compass 38°  53'  W. 

Variation  per  chart 45    00  W. 

Deviation 6°  07'  E.  for  the  point  her  head  was  at. 

Ex.  3.  1878,  May  31st,  7h:10m:  P.M.,  apparent  time  at  ship,  in  latitude 
40°  26'  N.,  longitude  68°  15' W.,  the  sun's  bearing  setting  was  W.fN.  Re- 
quired the  true  amplitude,  the  correction  and  deviation  of  the  compass.  Varia- 
tion per  chart,  8J  W. 

Ans.  True  amplitude  W .  29°  30'  N. ;  correction,  21°  04'  E. ;  deviation,  29C  04'  E. 

Ex.  4.  1878,  September  5th,  6h:20:  A.M.,  apparent  time  at  ship,  in  latitude 
46°  05' 1ST. ,  longitude  37°45'E.,  the  sun's  bearing  rising  was  E.fS.  Required 
the  correction  and  deviation  of  the  compass.  Variation  per  chart,  4°  W. 

Ans.  14°  24'  West. 

Ex.  5.  1878,  September  23d,  5h:43m:  A.M.,  apparent  time  at  ship,  in  latitude 
53°  57'  N.,  longitude  17°  15'  E.,  the  sun's  bearing  rising  was  E.  Required  the 
correction  and  deviation  of  the  compass.  Variation  per  chart,  11°  W. 

Ans.  11°0'E. 

Ex.  6.  1878,  October  15th,  6h:39m:  P.M.,  apparent  time  at  ship,  in  latitude 
58°04'N.,  longitude  173°  30'  E.,  the  sun's  bearing  setting  was  W.JN.  Re- 
quired the  correction  and  deviation  of  the  compass.  Vai'irtion  per  chart  10°  E. 

Ans.  True  amplitude  W.  16U  14'  S. ;  correction,  19°  03'  W. ;  deviation,  29°  03'  W. 

Ex.  7.  1878,  May  29th,  6h:33m:  A.M.,  apparent  time  at  ship,  in  latitude  0°0', 
longitude  126°  45'  W.,  the  sun's  bearing  rising  E.^S.  Required  the  correction 
and  deviation  of  the  compass.  Variation  of  the  chart,  5°  E. 

Ans.  32°  17'  W. 

Ex.  8.  1878,  June  21st,  9h:40m:  P.M.,  apparent  time  at  ship,  in  latitude  62° 
29'  N.,  longitude  60045'W.,  the  sun's  bearing  setting  was  N.N.E.^E.  Re- 
quired the  correction  and  deviation  of  the  compass.  Variation  per  chart,  53°  W. 

Ans.  5°40'W. 

NOTE. — When  the  latitude  is  0°  0'  0"  the  declination  is  the  sun's  true  amplitude,  reckoned 
from  the  east  when  the  observation  is  made  in  the  morning;  west  if  made  in  the  afternoon; 
north  or  south  according  to  the  declination.  When  the  BUU'B  declination  is  O1 0'  0"  the  nun's 
true  amplitude  is  east  when  the  observation  is  made  in  the  moruiug;  -west  if  made  in  the 
afternoon. 


62  PRACTICAL   NAVIGATION. 


CORRECTION  AND  DEVIATION  OF  THE  COMPASS  BY 
AN  AZIMUTH. 

(Use  Table  II.  for  working  out  Azimuth.) 

First.  To  the  mean  time  at  ship  add  the  longitude  if  west,  and 
subtract  it  if  east,  in  the  same  manner  as  shown  in  working  ampli- 
tude, for  finding  the  mean  time  at  Greenwich;  be  sure  and  always 
date  it. 

Second.  To  the  observed  altitude  apply  the  index  error  first  (if 
any);  next  the  dip  (Table  VII.),  always  to  be  subtracted;  then  the 
refraction  (Table  VI.),  also  subtracted.  Sun's  pai-allax  (Table  VIII.) 
that  add  always.  Sun's  semi-diameter  for  the  day  of  the  month,  from 
the  Nautical  Almanac,  always  to  be  added  to  the  sun's  lower  limb, 
and  subtracted  from  the  upper  limb,  that  will  give  the  sun's  true 
altitude. 

Third.  Take  the  sun's  declination  from  page  2d  of  the  month, 
niid  correct  it  by  the  hourly  difference  as  before  shown  in  amplitude, 
and  find  the  polar  distance  as  follows:  if  the  declination  and  the 
latitude  are  of  the  same  name,  take  the  declination  from  90°;  but  if 
of  contrary  names  add  the  declination  to  90°.  Then  add  together 
the  sun's  true  altitude,  the  latitude  and  the  polar  distance,  divide 
this  sum  by  2  and  call  it  the  half  sum,  then  take  the  difference 
between  the  half  sum  and  the  polar  distance  and  call  it  the  re- 
mainder. 


Fourth.  Now  add  together  the 
Secant  (Table  II.)  of  the  true  altitude. 
Secant  (Table  II.)  of  the  latitude. 
Co-sine  (Table  II.)  of  the  half  sum. 
Co-sine  (Table  II.)  of  the  remainder. 


To  the  nearest  mile  only. 


Fifth.  Half  the  sum  of  these  four  logarithms  will  give  the  sine 
(Table  II.)  of  half  the  true  azimuth,  which  double  and  call  it  north 
in  south  latitude,  and  south  in  north  latitude;  east  when  the  time 
is  A.M.;  west  when  the  time  is  P.M. 

Sixth.  Subtract  the  true  bearing  and  bearing  by  compass  when 
they  have  the  same  name  for  the  correbtion. 

Seventh.  If  one  bearing  is  north  and  the  other  south,  take  the 
true  azimuth  (that  is,  the  true  bearing)  from  180°,  and  change  the 
north  or  south  name  only.  Then  the  difference  is  the  correction; 


AZIMUTH. 


except  one  bearing  is  east  and  the  other  west,  when  the  sum  of  the 
two  bearings  is  the  correction. 

NOTE. — Bo  careful  when  taking  the  true  bearing  from  180°,  you  do  not  change  the  east  or  •west 
i;auie,  only  the  north  and  south. 

Eighth.  The  correction  will  be  easterly  when  the  true  bearing  is 
on  the  right-hand  of  the  bearing  by  compass;  westerly  when  on  the  left. 

Ninth.  If  the  correction  and  variation  are  of  the  same  name,  sub- 
tract them  for  the  deviation.  But  if  they  are  of  different  names, 
add  them  for  the  deviation. 

Tenth.  To  know  if  the  deviation  is  easterly  or  westerly,  draw  the 
compass  and  lay  off  the  variation  to  the  left  of  north  if  westerly, 
but  to  the  right  of  north  if  easterly;  lay  off  the  correction  in  the 
same  manner;  then  if  the  correction  is  on  the  right-hand  of  the 
variation,  the  deviation  is  easterly,  but  if  to  the  left-hand,  it  is 
westerly  deviation. 

NOTE.— Bear  in  mind  that  azimuths  reckon  from  north  and  south  points  of  the  compass,  not 
the  same  as  amplitudes.  When  the  latitude  is  0  in  au  azimuth,  assume  a  name  for  it,  taking 
care  to  use  the  name  when  naming  the  true  azimuth.  Name  the  true  azimuth  opposite  to  the 
name  you  have  assumed,  and  proceed  without  any  latitude. 

Ex.  1.  1878,  June  4th,  61i:  8m:  P.M.,  mean  time  at  ship,  in  latitude  47°  30'  N., 
longitude  16J  00'  W.  The  sun's  bearing  by  compass  was  W.^N.  Altitude  of 
sun's  lower  limb  33°  44'  40".  Index  error  -  2'  20".  Eye  19  feet.  Required  the 
true  azimuth,  correction  and  deviation  of  the  compass.  Variation  per  chart,  4°  W. 


H.  M.  0      ,      ff 

June  4,  M.T.S.  6    8  P.M.  Obs.  alt 33  44  40    Sun's  dec.  .. 

Long'del6=0'  1    4  W.     Index  error..  -     2  20    Correction  .. 


27  33  N.    Hourly  diff. ....  17-37 
2    5  M.T.G..       7-2 


M.T.G.June4  7  12  33  42  20    Sun'sRed.dec.22  29  38 

Dip -     4  11  90  00  00 

33  38  09    Polar  dist.  ..  67  30  22                           60)  12,5,064 
Kef -124  

33  36  45 
Palx 7 

33  36  52 
S.  Semd 15  47 

True  alt 33  52  39      Secant  .  0-080831 

Latitude  ....  47  30  00      Secant  .  0-170317 

Polar  diet.  . .  67  30  22  —^— i_      °-\] 

Sum 1485301  »o'wv- 

Half-sum. ...  74  26  30M  Co-sine.  9'428263 

Kemainder..    656    8M  Co-sine.  9-996812  «*>l 

4W'>  2)19-676223 

2   )  -.-Sine....  9-838111 

Sun's  true  azimuth  S 87  04W.  . 

18000  \  Taking  the  true  azimuth  from  180°,   do  not 

777.7  (  chanye  the  West. 

Sun  s  true  bearing  N 92  56  W.  \ 

Sun's  bearing  by  compass  N 8711W. 

Correction 5  45  W.     being  variation  and  deviation  combined. 

Variation  per  chart 4  00  \V. 

Deviation  of  the  compass 1  45\V.    for  Vie  point  her  head  was  at. 


64  PEACTICAL  NAVIGATION. 

Ex.  2.  1878,  July  2d,  8h:17m:  P.M.,  mean  time  at  ship  in  latitude  61°  KX  N., 
longitude  51°  15'  W.     The  sun's  bearing  by  compass  was  N.JE.     Altitude  of 
the  sun's  lower  limb  5°  35'  15".     Eye  19  feet.     Required  the  true  azimuth,  cor- 
rection and  deviation  of  the  compass.     Variation  per  chart,  56°  W. 
H.  M. 


July  2,  M.T.S.  ..  8  17P.M. 
Longitude "  "  W. 

M. T.G.July  2, 11  42 


5° Si' 5l"  Secant  0- Sun's  dec.  23°  2' 54%.  H.  D.  Il'l9 

"   "   "     Secant  0. -     2  11  11-7 


True  alt. 
Latitude. 
Polar  dist 

Sum 

Half-sum 

Remaind'rO  05  42    Co-sine  9- 66  59  17 


Co-sine  D-- 


23    0  43  N. 
90 


60)10,0,923 

19-912477  

o    ,  2M1" 

64  43.  Sine...  9-95G238 
2 


(  8.  "   "  W. 
Taking  from  180°  do  not  change  1       180 

thewestname 1      

(  N.50  34W.   ) 

Sun's  bearing  by  compass N.   5  37  E.    \  Add-when  one  E.  and,  the  other  W. 

~~^~^~'        ) 

Correction  (being  variation  and  de- 
viation)       56  11W. 

Variation  per  chart 66  OOW. 

Deviation  of  the  compass 0  11  W.  for  the  point  her  head  was  at. 

Ex.  3.  1878,  August  20th,  9h :  40m :  A.  M. ,  mean  time  at  ship  in  latitude  38°  30  S. , 
longitude  95°  15' E.,  the  sun's  bearing  by  compass  was  N.E.  by  E.  Altitude 
sun's  lower  limb  25°  30'  00".  Eye  20  feet.  Required  the  true  azimuth,  correc- 
tion and  deviation  of  the  compass.  Variation  per  chart,  16°  W. 

Ans.  True  azimuth  N.  46°  22'  E. ;  correction,  9°  53'  W. ;  deviation,  6°  07'  E. 
NOTE. — When  the  correction  and  variation  per  chart  are  contrary  names,  add  them  for  the 
deviation. 

Ex.  4.  1878,  November  llth,  4h:52m:  P.M.,  mean  time  at  ship  in  latitude 
32°  30' 45"  N.,  longitude  45°  30'  W.,  the  sun's  bearing  by  compass  was  W.^N. 
Altitude  sun's  lower  limb  15°  55'  30".  Index  error  +  1'  40".  Eye  20  feet.  Re- 
quired the  true  azimuth,  correction  and  deviation  of  the  compass.  Variation 
per  chart,  14°  W. 

Ans.  True  azimuth  S.  56  J  12'  W.;  correction,  39°  26'  W.;  deviation,  25°  26'  W. 

Ex.  5.  1878,  December  15th,  8h:51m:  A.M.,  mean  time  at  ship  in  latitude 
48°  56'  N.,  longitude  59°  17'  30"  W.,  the  sun's  bearing  by  compass  was  S.  Alti- 
tude sun's  lower  limb  12°  16'  30".  Index  error  -  3'  10".  Eye  20  feet.  Required 
the  true  azimuth,  correction  and  deviation  of  the  compass.  Variation  per 
chart,  31°  W. 

Ans.  True  azimuth  S.  29°  52'  E.;  correction  29°  5?  W.;  Deviation,  1°  OS'  E. 

Ex.  6.  1878,  June  17th,  3h:  40m:  P.M.,  meantime  at  ship  in  latitude  29°  30'  N., 
longitude  125°  45' E.,  the  sun's  bearing  by  compass  was  N.  W.^N.  Altitude 
sun's  lower  limb  11°  30'  20".  Index  error  +  1'  29".  Eye  20  feet.  Required  the 
true  azimuth,  correction  and  deviation  of  the  compass.  Variation  per  chart, 
2°  W. 

Ans.  True  azimuth  S.  110°  26' W.;  correction,  30°  12' W.;  deviation,  28°  12' W. 

Ex.7.  1878,  December  10th,  9h:  10m:  A.M.,  mean  time  at  ship  in  latitude 
60°  10'  N.,  longitude  169°  10'  30"  E.,  the  sun's  bearing  by  compass  was  S.E.  by 
S.  Altitude  sun's  lower  limb  4"  20'  30".  Index  error  +  1'  20".  Eye  20  feet. 
Required  the  true  azimuth,  correction  and  deviation  of  the  compass.  Variation 
per  chart,  12°  E. 

Ans.  True  azimuth  S.  23°  26'  E.;  correction,  10°  19'  E.;  deviation,  1°  41'  W. 

NOTE.— The  deviation  found  is  for  that  point  of  the  compass  the  ship's  head  was  at  \vhen  the 
observation  was  made. 


LATITUDE  BY  MERIDIAN  ALTITUDE  OF  SUN.  65 


LATITUDE  BY  THE  MERIDIAN  ALTITUDE  OF  THE  SUN. 

First.  Reduce  the  ship's  longitude  into  time  by  multiplying  the 
degrees  by  4  and  dividing  by  60. 

Second.  In  page  one  of  the  month,  Nautical  Almanac  (in  this  book) 
find  the  sun's  declination  for  that  day,  and  the  hourly  difference 
from  the  column  of  difference  on  the  right;  multiply  this  hourly 
difference  by  the  hours  and  tenths  of  an  hour  of  the  longitude  in 
time;  point  off  from  the  right,  the  number  of  figures  equal  to  the 
number  of  decimals  on  the  hourly  difference  and  longitude  in  time, 
the  remaining  figures  will  be  seconds,  which  divide  by  60  when  it 
exceeds  60,  and  you  have  the  correction,  to  be  added  to  the  declina- 
tion when  the  declination  is  increasing,  but  subtracted  when  de- 
creasing and  in  west  longitude  only.  When  the  longitude  is  east, 
you  must  reverse  the  way  of  applying  the  correction;  that  is,  when 
the  declination  is  increasing  subtract  the  correction,  and  when  de- 
creasing add  the  correction. 

NOTE.— See  Table  XII.  for  reducing  the  sun's  declination  at  any  meridian. 

Third.  To  the  observed  altitude  apply  the  index  error  of  the 
sextant  (if  any)  according  to  the  sign  +  add,  or  -  subtract. 

Fourth.  From  Table  VII.  get  the  dip  for  the  height  of  the  eye, 
which  is  always  subtracted. 

Fifth.  From  Table  XIII.  get  the  correction  for  apparent  altitude, 
this,  also,  always  subtracted,  (this  correction  is  the  refraction  and 
parallax,)  or  take  out  the  refraction  from  Table  VI.  which  subtract, 
and  the  sun's  parallax,  Table  VIII.  which  is  always  to  be  added. 

Sixth.  From  page  two  of  the  month,  Nautical  Almanac  (this  book), 
get  the  sun's  semi-diameter  for  that  day,  and  add  it  to  the  altitude 
of  the  sun's  lower  limb,  but  subtract  it  if  the  upper  limb  is  observed. 
This  is  called  the  true  altitude  of  the  sun's  centre. 

Seventh.  Take  the  true  altitude  from  90°,  which  will  give  the 
sun's  zenith  distance,  and  give  it  the  opposite  name  to  the  bearing 
of  the  sun;  that  is,  if  the  sun  bears  north  the  zenith  distance  will  be 
south,  and  if  south  call  it  north. 

Eighth.  To  find  the  latitude,  add  the  zenith  distance  and  declina- 
tion together  when  they  are  of  the  same  name,  but  if  one  is  north 
and  the  other  south,  subtract  the  less  from  the  greater  and  call  the 
latitude  the  same  name  as  the  greater. 
5 


66 


PRACTICAL  NAVIGATION. 


Ex.  1.  1878,  August  10th,  in  longitude  124°  30'  W.  the  observed  meridian  alti- 
tude of  the  sun's  lower  limb  was  37°  10'  30",  bearing  north,  the  index  error  + 
2'  40".  Height  of  the  eye  20  feet;  required  the  latitude. 


Longitude 


124°  30'  W. 
x        4 


60)498°  00 
Long,  in  time    8h :  18m : 


Sun's  dec.  Aug.  10  15°32'46"N. 
-    6    5 


Cor.  dec 15°26'41"N. 


Hourly  diff.   43". 95 
8.3 


13185 
35160 

60)36,4,785 

6'04"785 

Cor.  6'5"for  8h:  18m: 
To  be  subtracted  because 
Declination  decreasing, 
and  longitude  west. 


Obs.  alt.... 
Index  error. 


37°  10'  30"  N. 
+      2  40 


Cor.  obs.  alt 37    13  10 

Dip  Table  VII -       4  17 

App.  Alt 37  08  53 

Cor.  Table  XIII..  .-19 


True  alt 37  07  44 

Sun's  semid +    15  49 


Sun's  true  alt 37  23  33 

90  00  00 


Zenith  distance 52  36  27  S. 

Sun's  cor.  dec. .  .   15   26  41  N. 


Subtract  when  contrary  name*. 
Latitude  in 37 J  09'  46"  S.     Called  after  the  greater. 


Ex.  2.  1878,  January  14th,  in  longitude  51°  00'  W.  the  observed  meridian  alti- 
tude of  the  sun's  lower  limb  was  78°  14'  10",  bearing  south,  index  error  -  5'  50". 
Eye  18  feet;  required  the  latitude. 

Ans.  Sun's  cor.  dec.  21°  15'  10"  S.;  latitude  9°  35' 34"  S. 

Ex.  3.  1878,  September  23d,  in  longitude  159°  00'  W.  the  observed  meridian 
altitude  of  the  sun's  lower  limb  was  70°  54'  20",  bearing  north,  index  error  -  3' 
45".  Eye  21  feet;  required  the  latitude. 

Ans.  Sun's  cor.  dec.  0°  17'  35"  S.;  latitude  19°  15'  41"  S. 

Ex.  4.  1878,  May  20th,  in  longitude  5°  43'  W.  the  observed  meridian  altitude 
of  the  sun's  upper  limb  was  54°  23'  10",  bearing  south,  index  error  +  2'  10"  Eye 
20  feet;  required  the  latitude. 

Ans.     Sun's  cor.  dec.  20°  01'  00"  N.;  latitude  55°  56'  23"  N. 

Ex.  5.  1878,  January  20th,  in  longitude  5°  20'  W.  the  observed  meridian  alti- 
tude of  the  sun's  lower  limb  was  22°  10'  30",  bearing  south;  index  error  -  3'  10". 
Eye  20  feet;  required  the  latitude. 

Ans.  Sun's  cor.  dec.  20°  04'  59"  S.;  latitude  47°  37'  53"  N. 

Ex.  6.  1878,  March  20th,  in  longitude  139°  20'  W.  the  observed  meridian  alti- 
tude of  the  sun's  upper  limb  was  31°  19'  40",  bearing  south,  index  error  4-  4'  15". 
Eye  20  feet;  required  the  latitude. 

Ans.  Cor.  dec.  0°  3'  38"  N.;  latitude  59°  01'  31"  N. 


LATITUDE  BY  MERIDIAN  ALTITUDE  OF  SUN. 


67 


Ex.  7.  1878,  November  16th,  in  longitude  171°  00'  E.,  the  observed  meridian 
altitude  of  the  sun's  lower  limb  was  71  "'43'  10",  bearing  South,  index  error - 
1  20".  Height  of  the  eye  24  feet;  required  the  latitude. 


Long 171°  00'  E. 

4 


60)684  00 
Long,  in  time  llh:  24m: 


Sun's  dec.  Nov.  16.  18°  47'  29"  S. 
-      7     6 


Cor.  Dec 18°  40'  23"  S. 


Obs.  Altitude. 


71°  43'  10"  S. 
-      1  20 


-      4  4 


71   37  08 
-      0  16 


+    16  13 


Hr.  dif 37".38 

11  .  4 

14952 
3738 

0*700 

37  00 

6.0)42.6.132 

7' 06."  132 
To  be  subtracted   be- 
cause declination  in- 
creasing, and  longi- 
tude Eabt. 


90  00  00 

~7r~"    "  N. 

"     "    "    S. 


Latitude  in 00°  33' 28"  S. 

Ex.  8.  1878,  March  31st,  in  longitude  155°  45'  E.,  the  observed  meridian  alti- 
tude of  the  sun's  lower  limb  was  68°  55'  10",  bearing  south,  index  error -5'  40". 
Eye  19  feet;  required  the  latitude. 

Ans.  Sun's  cor.  dec.,  4°  3'  3"  N. ;  latitude,  25°  02'  01"  N. 

Ex.  9.  1878,  September  23rd,  in  longitude  168°  00'  E.,  the  observed  meridian 
altitude  of  the  sun's  upper  limb  was  56°  12'  20",  bearing  north,  index  error +3' 
38".  Eye  20  feet;  required  the  latitude. 

Ans.  Sun's  cor.  dec.,  0°  3'  40"  N.;  latitude,  34°  01'  12"  S. 

Ex.  10.  1878,  March  20th,  in  longitude  45°  30'  E.,  the  observed  meridian  alti- 
tude of  the  sun's  lower  limb  was  63°  5'  10",  bearing  north,  index  error  -  4'  20". 
Eye  22  feet;  required  the  latitude. 

Ans.  Sun's  cor.  dec.,  0°  8'  30"  S. ;  latitude,  26°  56'  30"  S. 

Ex.  11.  1878,  July  15th,  in  longitude  151°  22' E.,  the  observed  meridian  alti- 
tude of  the  sun's  lower  limb  was  34°  30'  20",  bearing  north,  index  error +4'  30". 
Eye  20  feet;  required  the  latitude. 

Ans.  Sun's  cor.  dec.,  21°  35'  34"  N.;  latitude,  33°  39'  22"  S. 

Ex.  12.  1878.  June  10th,  in  longitude  130°  55'  E.,  the  observed  meridian  alti- 
tude of  the  sun's  upper  limb  was  55°  25'  40",  bearing  north,  index  error -2'  57". 
Eye  20  feet;  required  the  latitude. 

Ans.  Sun's  cor.  dec.,  23°  0'  27"  N.;  latitude,  11°  57'  28"  S. 


G8  PRACTICAL   NAVIGATION. 


TO  FIND  THE  LATITUDE  BY  SEDUCTION  TO  THE 
MERIDIAN. 

NOTE. — Tables  required:  log  rising  Table  XVII;  log  co-sine  Table  II;  log  co-sine  Table  II;  log 
natural  number  Table  I;  log  natural  sine  Table  XIV;  natural  co-sine  Table  XIV. 

First.  Correct  the  watch,  for  what  it  is  slow  or  fast  for  apparent 
time,  and  then  apply  the  ship's  run,  viz:  The  difference  of  longitude 
made  (in  time)  to  the  apparent  time.  If  the  time  thus  made  is  east, 
add,  and  if  west,  subtract;  remember  going  east  your  time  is  behind, 
going  west,  your  time  will  be  too  fast  for  the  place  you  have  got  to.  This 
will  give  the  hour,  angle,  or  time  from  noon.  If  the  observation  was 
made  in  the  afternoon  that  is  P.M. 

Second.  Find  the  apparent  time  at  Greenwich  by  turning  the 
longitude  into  time  by  the  usual  method,  viz:  Multiplying  by  4  and 
dividing  by  6;  if  the  longitude  in  time  is  west,  add  it  to  the  hour 
angle  (or  apparent  time  at  ship);  and  if  east,  subtract  it. 

Third.  If  the  time  is  A.M.  add  12  hours  to  the  time  shown  by 
watch,  and  change  the  date  (as  per  rule)  then  apply  the  rate  of  the 
watch;  if  slow,  add;  if  fast,  subtract;  next  the  ship's  run  if  east, 
add;  if  west,  subtract.  This  will  give  the  apparent  time  at  ship, 
which  is  to  be  subtracted  from  24  hours,  for  the  hour  angle  (or  time 
from  noon.) 

Fourth.  To  the  apparent  time  at  ship  apply  the  longitude  (in 
time),  add  if  west,  subtract  if  east;  should  the  sum  exceed  24  hours 
subtract  24  hours  from  the  sum,  and  the  remainder  will  be  the 
Greenwich  apparent  time  of  the  same  name  as  date  at  ship. 

Fifth.  Correct  the  sun's  declination  for  the  Greenwich  time  (as 
per  rule),  from  page  one  of  the  month,  Nautical  Almanac,  by  the 
hourly  difference. 

Sixth.  Find  the  sun's  true  altitude  by  applying  the  index  error, 
dip.  correction  from  Table  XIII  and  sun's  semi-diameter. 

Seventh.  Add  together  the  log  rising  of  the  hour  angle  (Table 
XVII),  log  co-sine  of  the  latitude,  and  co-sine  of  the  sun's  corrected 
declination  (Table  II).  The  sum  of  these  logs  (less  tens  in  their 
index)  will  be  the  log  of  a  natural  number  (Table  I),  to  be  added  to 
the  natural  sine  of  the  sun's  true  altitude  (Table  XIV),  which  gives 
the  natural  co-sine  (Table  XIV)  of  the  sun's  meridian  zenith  distance, 
of  the  opposite  name  to  the  bearing  of  the  sun. 

Eighth.  The  zenith  distance  and  the  sun's  corrected  declination 
will  give  the  latitude.  If  of  the  same  name  add  them;  if  one  north 
and  the  other  south,  subtract  the  less  from  the  greater,  and  call  the 
latitude  after  the  greater. 


LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 


69 


Ex.  1.  1878,  June  20th,  P.M.  at  ship,  in  latitude  by  account  27°  30'  S.,  longi- 
tude 75°  30'  \V.  The  observed  altitude  of  the  sun's  lower  limb  north  of  the  ob- 
server was  38°  20' 00"'  Eye  16  feet.  Time  by  watch  Oh:29m:01s:  P.M.,  which 
had  been  found  fast  for  apparent  time  at  ship  lm:12s.  The  difference  of  longi- 
tude made  since  to  the  East  was  9  miles;  required  the  latitude  by  the  reduction 
to  the  meridian. 


June  20th..  .. 
Fast  

Dif.  Ion.  9'= 

Hour  angle  .  . 
Long.  75J  30' 

App.  Gr'n'h) 

H.  M.   S. 

0  29  01  P.M. 
—  1  12 

Sun's  dec.  . 
(Jr.  5h:3Um. 

23°  27' 

10"  K. 
6 

Hr.  dif  .  1".13 
5.5 

Obs.  alt.  . 
Dip  

.  38°  20'  00" 
.  —     3  50 

Cor 

0  27  49 
0  36  E. 

Cor.  dec  23°  27' 

75°  30'  W. 
4 

10"  N. 

565 
565 

38   1C   10 
1     5 

Semid  
True  alt.  . 

0  28  25 
5  02  00  W. 

6.215 

38   15  05 
15  46 

60)302  00 

5  30  25 

.  38°30'G1" 

KVi-  no 

Time  from  noon  ..............  28m:  25s: 

Latitude  by  account  ..........  27 

Sum's  corrected  declination...  23 


Log  rising 
30'  S  .....................  Log  cosine 

27   N  ....................  Log  cosine 


2.88519 
9.94793 
9.96256 


Natural  number 625  Log. 

Hun's  true  altitude...  ...38       31        Nat.  sine...  62274 


2.79568 


Meridian  zenith  distance 51 

bun's  declination 23 


01  S.  Nat.  cosine. 

27  N. 


.G2899 


Latitude 27°      34' S. 

Ex.  2.  1878,  October  28th,  A.M.  at  ship,  in  latitude  by  account  25°  40'  N., 
longitude  45°  35'  W.  The  observed  altitude  of  the  sun's  lower  limb  south  of  the 
observer  was  50°  53'  20".  Eye  20  feet.  Time  by  watch  llh:23m:30s:  A.M., 
which  was  slow  to  apparent  time  at  ship  19m:OOs.,  and  the  difference  of  longi- 
tude made  since  to  the  east  was  40  miles;  required  the  latitude  by  the  reduction 
to  the  meridian. 


Oct.  28  

.11  23  30A.M. 

Sun's  dec.  .  . 

13°  10'  44"  8. 

Hr.  dif.50"25 

Obs.  alt.. 

.  50°  53'  20" 

12 

Cor  

2  21 

Ap.  T.  G.    2.8 

Dip  

.  —     4   17 

Oct.  27  

.23  23  30 

Cor.  dec...  . 

13°  13'  05"  S. 

40200 

50  49  03 

Slow 

19  00 

1005  i 

Cor  

—          41 

Oct.  27  

.23  42  30 

60)140.700 

50  48  22 

Semid 

16     9 

Ap.  time  at 

23  45  10  

24  00 

QO 

True  alt.. 

.  51°  04'  31" 

ship  27th    ) 

>    a    o  on  w 

23  4.) 

10 

Hr.  angle.      14  50 

G.  T.  Oct.  27.26  47  30 
24 

App.  Gr'n'h)    „  ._  „„ 
time  Oct.  28 }    2 

Time  from  noon 14m:  50s Log  rising 2.32093 

Latitude  by  arcount 25°      40' N Cosine 9.15488 

Sun's  decliuatioii 13       13  8 Cosine 9.98834 


Natural  number , 

Sun's  true  altitude 61°       5 Nat.  Sine , 


...  l  184  Log. 
..  77806 


2.26415 


Meridian  zenith  distance 38°     45' N.  Nnt.  Cosine  : 77990 

Hun's  declination 13       13   S. 


Latitude 25°     3U' N. 


70  PRACTICAL  NAVIGATION. 

Ex.  3.  1878,  January  1st,  A.M.  at  ship  in  latitude  by  account  6°  0'  N.,  longi- 
tude 87°  45'  west.  The  observed  altitude  of  the  sun's  lower  limb  was  60°  20'  10" 
south  of  the  observer.  Eye  16  feet.  Time  by  watch  llh:38m:20s:  A. M.,  which 
was  slow  for  apparent  time  at  ship  lm:20s;  the  difference  of  longitude  made 
since  to  the  west  was  2  miles;  required  the  latitude  by  reduction  to  the  meridian. 

Ans.  6°3'N. 

Ex.  4.  1878,  March  6th,  P.M.  at  ship  in  latitude  by  account  42°  2'  S.,  longitude 
166°  0'  west.  The  observed  altitude  of  the  sun's  lower  limb  north  of  the  observer 
was  52U  48'  30".  Index  error  + 1 '  20".  Eye  at  20  feet.  Time  by  watch  Oh  :25m : 
30s:  PM.,  which  was  fast  for  apparent  time  at  ship  1m:  40s.  The  difference  of 
longitude  made  since  to  the  east  was  38  miles;  required  the  latitude  by  reduction 
to  the  meridian. 

Ans.  41°  55'  S. 

Ex.  5.  1878,  October  20th,  A.M.  at  ship  in  latitude  by  account  23°  32'  N., 
longitude  135°  50'  east.  The  observed  altitude  of  the  sun's  lower  limb  south  of 
the  observer  was  55°  20'  10".  Index  error  + 1'  10" .  Eye  20  feet.  Time  by  watch 
Oh:20m:OOs:  which  was  fast  48m:OOs:  for  apparent  time  at  ship.  The  difference 
of  longitude  made  since  to  the  west  was  25  miles;  required  the  latitude  by  the 
reduction  to  the  meridian. 

An.  23°  26'  N. 

Ex.  6.  1878,  September  24th,  A.M.  at  ship  in  latitude  by  account  36°  GO'S., 
longitude  159°  30'  east.  The  observed  altitude  of  the  sun's  lower  limb  north  of 
the  observer  was  53°  45'  35".  Eye  at  20  feet.  Time  by  watch  10h:20m:30s: 
A.M.,  which  had  been  found  to  be  slow  lh:20:10s:  of  apparent  time  at  ship. 
The  difference  of  longitude  made  to  the  east  was  25  miles  after  the  error  on  ap- 
parent time  at  ship  was  determined.  Index  error- 1'  20";  required  the  latitude 
by  the  reduction  to  the  meridian. 

Ans.  36°  11'  S. 


LATITUDE  BY  THE  MERIDIAN  ALTITUDE  OF  A  STAR.  71 


TO  FIND  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUDE 

OF  A  STAR. 

First.  Correct  the  observed  altitude  for  index  error  (when  any). 

Second.  Dip  of  the  horizon  (Table  VII). 

Third.  Correction  for  apparent  altitude  (Table  XIII). 

NOTE. — Re  careful  in  taking  out  the  correction  from  this  table  not  to  take  out  the  sun's  correction,  in 
place  of  the  star's  correction. 

Fourth.  Take  the  star's  true  altitude  from  90°  for  the  zenith  dis- 
tance, and  call  it  of  contrary  name  to  the  bearing  of  the  star  when 
observed. 

Fifth.  To  the  zenith  distance  apply  the  star's  declination,  found 
in  the  (Table  of  Fixed  Stars)  pages  (242  to  245)  of  the  American 
Ephemeris  and  Nautical  Almanac  for  1878. 

NOTE. —  The  sign  -f*  (placed  before  the  declination)  stands  for  north  declination.  The  sign  — * 
stands  for  south  declination. 

Sixth.  If  the  declination  and  zenith  distance  are  of  same  name, 
add  them  for  the  latitude;  when  of  contrary  names,  subtract  them, 
and  call  the  latitude  of  the  same  name  as  the  greater. 

Ex.  1.  January  1st,  1878,  the  meridian  altitude  of  the  star,  a  Virginis  (Spica) 
was  31°  27' 40"  bearing  south,  index  error +5' 20".  Eye  at  20  feet.  Required 
the  latitude  in. 

Observed  altitude 31°  27'  40"  S. 

Index  error . .  . . . .    +      5  20 


31    33  00 
Dip.  Table  VII -       4  17 


31  28  43 

Correction  Table  XIII....    -  133 

Star's  true  altitude 31  27  10 

90  00  00 


Zenith  distance 58  32  50  N. 

Star's  declination 10  31  25+S. 


Latitude 48°  01'  25"  N. 

Ex.  2.  January  1st,  1878,  the  meridian  altitude  of  the  star,  a  Aurigoe  (Capella) 
was  87 J  30'  40"  bearing  north.     Eye  20  feet.     Required  the  latitude  in. 
Ans.  Latitude,  43°  18'  38"  N. 


72  PEACTICAL   NAVIGATION. 

N 

Ex.  3.  January  1st,  1878,  the  meridian  altitude  of  the  star,  a  Geminor  (Castor) 
•was  70°  50'  30"  bearing  south,  index  error  -  3'  10"  to  subtract.  Eye  20  feet.  Re- 
quired the  latitude  in. 

Ans.  51°  26'  12"  N. 

Ex.  4.  January  1st,  1878,  the  meridian  altitude  of  the  star,  b  Orionis  (JRigel) 
was  50°  31'  50"  bearing  north,  index  error-f2'  10"  to  add.  Eye  18  feet.  Re- 
quired the  latitude  in. 

Ans.  47°  51'  39"  S. 

Ex.  5.  January  1st,  1878,  the  meridian  altitude  of  the  star,  6  Geminor  (Pollux) 
was  33°  30'  20"  bearing  north.  Eye  18  feet.  Required  the  latitude  in. 

Ans.  28°  16' 01"  S. 

Ex.  6.  January  1st,  1878,  the  meridian  altitude  of  the  star,  a  Argus  (Conopus) 
was  30°  10'  15"  bearing  south,  index  error --3'  15"  to  subtract.  Eye  16  feet. 
Required  the  latitude  in. 

Ans.  7°  20'  42"  N. 

Ex.  7.  January  1st,  1878,  the  meridian  altitude  of  the  star,  a  Aquilae  (Altair) 
was  67°  42'  30"  bearing  south,  index  error  -  3'  40"  to  subtract.  Eye  at  20  feet. 
Reqnired  the  latitude  in. 

Ans.  30°  58'  42"  N. 


LONGITUDE   BY  CHRONOMETER.  73 


TO  FIND  THE  LONGITUDE  BY  CHEONOMETEE. 

Rules  for  finding  the  Accumulated  Rate,  and  whether  the  Chronometer  is  Losing 

or  Gaining,  etc. 

First.  Take  the  given  time  by  the  chronometer,  and  apply  the 
error  giveii  on  the  last  date. 

Second.  If  fast  the  error  is  to  be  subtracted,  if  slow  the  error  is 
to  be  added;  then  you  have  the  chronometer  regulated  up  to  the 
time  the  last  error  was  given. 

Third.  Get  the  difference  between  the  two  errors  and  their  dates; 
when  both  errors  are  slow  or  both  fast,  subtract;  one  slow  and  the 
other  fast  add  them  together,  then  bring  this  difference  into  seconds 
(if  in  minutes  and  seconds)  by  multiplying  by  60,  then  the  difference 
in  seconds  between  the  two  errors  is  to  be  divided  by  the  number  of 
days  between  the  given  errors,  and  to  what  remains  annex  a  cipher, 
and  divide  again  for  the  tenths  or  decimal  part  of  the  daily  rate. 

Fourth.  Next,  the  number  of  days  from  the  date  of  the  last  error 
and  date  of  the  chronometer  is  to  be  multiplied  by  the  daily  rate, 
(taking  in  the  hours  of  the  chronometer  time  as  a  decimal  of  a  day 
by  annexing  a  cipher  to  the  hours,  and  dividing  by  24),  after  cutting 
off  the  decimals,  you  have  the  accumulated  rate  from  the  last  error 
given  to  the  time  shown  by  chronometer,  which  is  to  be  added  to 
the  chronometer  time  when  losing  and  subtracted  when  gaining. 

Fifth.   To  know  when  gaining  or  losing,  use  the  following  rules: 

(  When  the  chronometer  is  slow  at  1st  date,  and  at  2d  date  still  slower. 
LOSING.     <  When  the  chronometer  is  fast  at  1st  date,  and  at  2d  date  not  so  fast. 
(  When  the  chronometer  is  fast  at  1st  date,  and  at  2d  date  is  slow. 

(  When  the  chronometer  is  fast  at  1st  date,  and  at  2d  date  still  faster. 
GAINING,  -j  When  the  chronometer  is  slow  at  1st  date,  and  at  2d  date  not  so  slow. 
(  When  the  chronometer  is  slow  at  1st  date,  and  at  2d  date  is  fast. 

Ex.  1.  Suppose  the  first  date  to  he  July  1st,  and  the  second  date  September 
20th.  Interval  or  elapsed  time  81  days. 

H.  M.  s. 

July  1st,  slow 1  03  20 

Sept.  20th,  slow. .  .  1    5  13.4     Slow  and  more  slow,  losing. 

Difference  lost 1  53.4 

60 


Days  elapsed 81)113. 4(ls.4  daily  rate  losing. 

81 

32.4 
32.4 


74  PKACTICAL  NAVIGATION. 

Ex.  2.  H.  M.  S.  H.  M.  s. 

January  28th 3  27  18        Slow,  January  1st 1  25  55  j 

January  1st,  slow. .   1  25  55        Slow,  January  llth.' 1  25  20  j 

M.  T.  G.,  Jan.  1st.  4  53  13        As  10  days  is  to =35:27.2 

Gain  in  27d:5h -      1  35.2     Days  from  Jan.  1  to  Jan.  28th.  27. 2 

M.  T.  G.,  Jan.  28th  4  51  37.8  70 

245 
70 


1.0)95/2.0 


6.0)9.5.2 


Gain  in  27.2  days 1.35.2 

Ex.  3.  M.  s.     } 

July  1st,  fast 0  10.4  >  *Fast  and  then  slow,  losing. 

Sept.  20th,  slow....   1  43     ) 

Difference  lost. .   .   1  53.4=ls.4  losing  daily. 
*  Fast  and  slow,  the  sum  is  the  difference. 


Ex.  4.  M.  s.      ) 

July  1st,  fast 3  20     >  Fast  and  more  fast,  gaming. 

Sept.  20th,  fast 5  13.4  ) 

Difference  gained.   1  53. 4= Is. 4  gaming  daily 

Ex.  5.  M.  s.      } 

July  1st,  slow 5  13.5  >  Slow  and  less  slow,  gaining. 

Sept.  20th,  slow 3  20     ) 

Difference  gained .   1  53. 4 = 1  s.  4  gaining  daily. 

Ex.  6.  M.  s.     )    ' 

July  1st,  slow 1  43     >  *Slow  and  fast,  gaining. 

Sept.  20th,  fast 0  10.4  ) 

Difference  gained.   1  53. 4=  Is. 4  gaining  daily. 
*  Slow  and  fast,  the  sum  is  the  difference. 


RULES  FOB  FINDING  THE  LONGITUDE.  75 


KULES  FOR  FINDING  THE  LONGITUDE. 

First.  After  finding  the  mean  time  at  Greenwich  take  out  the 
declination  from  page  two  of  the  month.  Nautical  Almanac  (this 
book)  (or  from  the  American  Almanac,  1878)  and  correct  it  by 
the  hourly  difference  found  on  page  one  of  the  month;  multiply 
this  hourly  difference  by  the  mean  time  at  Greenwich,  after  divid- 
ing the  minutes  by  G,  same  as  in  azimuth;  this  will  give  the  cor- 
rection to  be  added  to  the  declination  when  increasing,  and  sub- 
tract when  decreasing.  If  correcting  back  from  the  following  day, 
which  may  be  done  (when  the  hours  of  Greenwich  time  exceed  15); 
then  by  taking  the  mean  time  at  Greenwich  from  24  hours,  you  can 
get  the  next  day's  declination,  and  correct  it  back  for  what  it  wants 
(in  time)  of  being  noon  of  the  next  day,  in  which  case  you  must  sub- 
tract the  correction  when  increasing,  and  add  it  when  decreasing; 
this  method  has  to  be  done  on  account  of  the  difference  for  an  hour 
in  the  Almanac  being  different  in  quantity 

Second.  Take  out  the  equation  of  time  from  page  two  in  the  Al- 
manac also,  and  correct  it  in  the  same  manner  as  the  declination; 
but  when  applying  it  to  the  apparent  time  at  ship,  always  go  by  the 
rule  at  top  of  page  one  of  the  month  in  the  Nautical  Almanac. 

Third.  If  the  declination  and  latitude  are  both  north  or  both  south, 
the  declination  is  to  be  taken  from  90°  for  the  polar  distance;  but  if 
one  is  north  and  the  other  south,  the  declination  must  be  added  to 
90°  for  the  polar  distance. 

Fourth.  Correct  the  sun's  altitude  in  the  same  way  as  for  the 
meridian  altitude,  first  for  index  error  (if  any,)  next  the  dip  of  the 
horizon  (Table  VII,)  then  the  correction  from  (Table  XIII),  and  sun's 
semi-diameter  from  the  Nautical  Almanac. 

Fifth.  Add  together  the  true  altitude,  the  latitude,  and  polar  dis- 
tance, divide  this  sum  by  2,  and  call  it  the  half  sum,  then  take  the 
true  altitude  from  this  half  sum  and  call  it  ths  remainder. 

NOTE.— If  the  polar  distance  exceeds  90°,  take  the  secant  of  the  corrected  declination,  in 
place  of  the  co-secant  of  the  polar  distance. 


Sixth. 


Add  together.  * 


Secant  of  the  latitude. 
Co-secant  of  the  polar  distance. 
Co-sine  of  the  half  sum. 
Sine  of  the  remainder. 


H  To  seconds. 


Seventh.  The  sum  of  these  four  logs,  rejecting  10  in  their  index, 
being  added  together  will  give  the  apparent  time  at  ship  in  (Table 
XVIII),  when  a  P.M.  sight,  and  of  the  same  date  as  the  question; 
but  if  the  sight  be  A.M.,  the  time  thus  found  is  to  be  taken  from  24 
hours  for  the  apparent  time  at  ship,  which  date  one  day  back  of  the 
date  at  the  head  of  the  question. 


76  PKACTICAL   NAVIGATION. 

Eighth.  To  the  apparent  time  at  ship  apply  the  equation  of  time 
(according  to  the  rule  found  at  the  top  of  page  one,  Nautical  Al- 
manac), and  this  will  give  the  mean  time  a,u  ship. 

Ninth.  If  the  mean  lime  at  Greenwich  is  of  the  same  date  as  mean 
time  at  ship,  subtract  the  less  from  the  greater,  and  that  will  be  the 
longitude  in  time;  but  should  either  of  the  two  times  be  of  different 
dates,  add  24  hours  to  whichever^  is  the  greatest  date  before  sub- 
tracting, then  turn  the  time  into  degrees  by  Td*ble  XI,  and  name 
the  longitude  east,  if  Greenwich  time  is  least ;  and  west,  if  Green- 
wich time  is  best. 

Tenth.  Should  the  longitude  in  time  exceed  12  hours,  take  it  from  24 
hours,  before  turning  it  into  degrees;  do  not  forget  to  change  its  name. 

Ex.  1.  H.  M.  s. 

Mean  time  at  ship.  March  5th 20  14  36 

Mean  time  at  Greenwich,  March  5th.     7  13  36 

13  01  00 
24  00  00 


Longitude  in  time . . 10  59  00= 164°  45'  00"  W. 

.  Eleventh.  To  find  the  logs,  for  seconds,  take  the  difference  be- 
tween the  logs,  for  the  given  minutes,  and  the  next  higher  number 
of  minutes;  multiply  this  difference  by  given  number  of  seconds, 
and  divide  by  GO;  add  the'  quotient  to  the  log.  found  for  degrees 
and  minutes,  in  the  case  of  sine  and  secant;  subtract  it  in  the  case 
of  co-sine  and  co-secant.  (See  explanation  of  Table  II.) 

Twelfth.  To  reduce  the  latitude  to  the  time  of  observation.  Remem- 
ber the  latitude  must  always  be  reduced  to  the  time  of  observation, 
and  the  usual  method  of  doing  this  at  sea,  is  to  find  the  difference 
of  latitude  the  ship  has  made  in  the  interval  between  the  time  the 
sights  were  taken  and  the  correct  latitude  obtained  by  observation 
at  noon.  With  the  course  and  distance  sailed  from  time  of  sights 
enter  (Table  III)  and  find  the  difference  of  latitude  in  the  latitude 
column,  this  difference  is  to  be  applied  according  to  the  course  the 
ship  has  been  steering;  viz:  "When  the  sights  are  taken  in  the  after- 
noon, and  in  north  latitude,  and  sailing  north,  add  the  difference  of 
latitude;  when  sailing  south,  subtract  the  difference  of  latitude.  Thus 
you  will  have  the  correct  latitude  of  the  ship  at  the  time  of  sights. 
To  apply  this  rule  in  south  latitude  simply  substitute  south  for  north. 

Thirteenth.  To  reduce  the  longitude  by  chronometer  at  time  of  sights 
to  noon.  Take  the  latitude  in  as  a  course,  and  the  departure  made 
in  the  interval,  in  the  latitude  column,  the  difference  of  longitude 
is  found  in  the  distance  column.  Apply  this  as  follows: 

Observation  taken  in  the  morning,  in  west  longitude.    |  g*|ifo|  ^^'  subtract. 
Observation  taken  in  the  afternoon,  in  west  longitude.      |^|l}uf  ^J*'  J^rf*""5*' 

To  or  from  the  longitude  by  chronometer,  will  give  the  longitude  in  at  noon. 
By  substituting  east  for  west,  the  same  rule  may  be  applied  in  east  longitude. 


RULES  FOR  FINDING  THE  LONGITUDE. 


77 


Fourteenth.  When  the  latitude  arid  declination  is  0°  0'  0"t  take 
the  true  altitude  from  90°,  and  the  zenith  distance  turned  into  time 
is  the  apparent  time  at  ship  if  P.M.,  or  taken  from  24  hours  for  the 
apparent  time  if  A.M.  sights. 

Ex.  1.  1878,  January  28th,  P.M.,  at  ship  in  latitude  32°  44' 34"  N.  The  ob- 
served altitude  of  the  sun's  lower  limb  was  22°  3'  20";  index  error+1'  02".  Eye 
20  feet  Time  by  chronometer,  2Sd:3h:27m:  18s.,  which  was  slow  for  mean 
noon  at  Greenwich,  lh: 25m:  55s.,  January  1st.;  and  on  January  llth  was  elow 
for  mean  noon  at  Greenwich  lh:  25m:  20s.  Required  the  longitude  by  chronom- 
eter. 


H 

H.  8. 

H.  M.  8. 

Sun's  dec 

..  18° 

9'  V  S. 

H.  dif  .  3U".76 

January 
Slow  Jan 

28th.... 
llth... 

3 

1 

27  18 
25  20 

Slow  Jan.  Ift.. 
blow  Jan.  llth 

.  1  2:>  Co 
..  1  25  20 

Cor 
4k: 

for  ] 
52iu.  J 

- 

313       . 

4.8G 

4  52  38 

Gain  10  days... 

..    =     35 

Cor 

dec.. 

...  18 

f.  50  S. 

3  18<  JO 

—  a  K 

M  T  G 

Jan  28 

.| 

51  38 

Jan.  llth  to  28th.     —17.2 

Pol 

dis... 

.  .  108°  fi'  RC" 

6  0)193"  1850 

7.0 

'-     S.13 

245 

35 

6.0)6.0.?0 

Accumulated  rate,      i.0.2 


Observed  altitude.  22 
Index  error   4- 

,    3,2Q» 
1   02 

Equation  of  time  .  .  . 
Cor.  for  4h:52m  

Cor.  equat'n  of  time. 

Secant  =  0.075149-'' 
Co-sec.  =  0.022038 

Co-sine  =  9.167739 
Sine...=  9.  934430  \ 

M.     S. 
13  14.02" 
+     2.25 

Hr.  dif. 

464 

X 

Cor  
Dif  

4.86 

2784 
3712 
1850 

22 
Dip.  for  2t)feet...    - 

22 
Correction  (table  13)  - 

4 
4 

0 

2 

22 
17 

05 
12 

13  16.27 

075103 
+  46 

,075149 

021999 
+  39 

.2".-25E(.4 

....       85 

Seconds. 

Cor  
Dif.  

34 

324 
243 

6.0)275.4 
45.54 
42 

21 

Sun's  semidiameter  + 

True  altitude  22 
Latitude  32 

57 
16 

14 
44 
05 

53 
16 

09 
34 
5tf  . 

Polar  distance  108 

Sum     163 

04 
32 

18 

39 
19 

10 

Seconds. 

66 

Cor  

Dif  

252 
210 

6.0)235.2 

£  Sum  81 

\  022038 

168008 
\    -   269 

Remainder  59 

H. 

App.  time  at  ship  )     „ 
January  28th.     \     ' 
Equation  of  time.    + 

Bf. 

7 
13 

s. 
32 
16 

i 

9  19936r>  '• 

.  ...  39.12 

'U  67739 

934424 
.     +   12 

649 

Seconds. 

19 

Cor  

Meantime  atshipj      q 
January  28th.     j 
Mean  time  at    j      . 
Green'li  Jan.  28.  f 

20 
51 

48 
38 

7C4 
8491 

6.0)10131 

\934436 

It 

...   268.51 

Lon<ritiule                    1 

30  50=22°  4^  30"  W. 
lepsthan 
therefore 

X.  B.—  Mean  time  at  ship 
nn'.'  n  time  ut  Greenwich, 
longitude  is  west. 

Seconds. 

10 

Cor  

6.0)  75^0 
!•-'  .•!() 

NOTE.— When  P.M.  the  sum  of  the  four  logarithms  gives  (in  Table  18)  the  Apparent  Time  at 
ship  of  the  name  date. 


78 


PRACTICAL  NAVIGATION. 


Ex.  2.  1878,  April  1st,  A.M.,  at  ship,  in  latitude  32°  16'  32"  S.  The  observed 
altitude  of  the  sun's  lower  limb  was  32°  16' 20";  index  error +1' 35".  Eye  18 
feet.  Time  by  chronometer,  March  31st,  Sh:30:32s.,  which  was  slow  for  mean 
noon  at  Greenwich  lh:  24m:  12s.,  January  14th;  and  on  February  13th,  was  slow 
Ih:  20m:  27s.  for  mean  noon  at  Greenwich.  Required  the  longitude  by  chronom- 
eter. 


H.  M.    S. 

March  31st,  chronometer  8  30  32 
Slow 1  20  27 


Gain  in  46. 4  days  x  7.5  s.  -     5  48 
M.  T.  G.,  March  31st. . .   9  45  11 


Declination.  4  13  03 N. 
Correction . .  +    9  26 


Hr.  dif..  ..  58.03 
9h:  45m.  =9 .75 


90 


N. 


Sun's  P.  D.94  22  29 


H.  M.    S. 

Jan.  14th,  slow..   1  24  12 
Feb.  13th.  slow..   1  20  27 


6.0)56.5.7925 


9.26 


Chr.  gained  in  30  dys  3.45 
60 


Divide  by  days,     30)225(7.5  gaining  daily. 
210 

M.     S. 

150  Eq.  of  time  ____  4  14.00    Hr.  dif..  ..  0.757 

Cor.  for  9h:  45m-     7.38          9h:45m=9.75 


0    , 
Obs.  altitude  ..........  32  16  20 


Cor.  eq.  time...  4    6.62 


7.38075 


32  28  31 


Secant    0. 
Co-Sec.  0. 


Logarithms  to  Seconds. 


"   "    "     Co-sine.  9 

47  05  15    Sine..  .  0 


H.  M.  S.      Log....   9.196961 
3    6  59  = 

24 


A.  T.  ship,  March  31st.  20  53  01 


«     <c     « 


Longitude 11  11  57=167°  59'  15"  E.  because  Greenwich  time  is  least. 


NOTE. — When  A.M.  sights,  take  the  time  (the  four  logarithms  gives)  from  24  hours  for  the 
apparent  time  at  ship,  and  date  it  one  day  less  than  the  date  at  head  of  question. 


RULES  FOK  FINDING  THE  LONGITUDE. 


79 


Ex.  3.  1878,  December  10th,  P.M.,  at  ship  in  latitude  40°20'S.  The  observed 
altitude  of  the  sun's  upper  limb  was  28°  45'  20";  index  error,  +  2'  10".  Eye  20 
feet.  Time  by  the  chronometer,  December  9th,  19h:52m:31s:  which  was  fast  for 
mean  noon  at  Greenwich  23m:OOs:  September  30th,  and  October  20th  was  fast 
for  mean  noon  at  Greenwich  25m  :30s :  Required  the  longitude  by  chronometer. 


II.   M.  S. 

Dec.  9th,  time  by  chron. . .   19  52  31 
—  25  30 


50.8days  x  7.5s.  perday  =  — 


Mean  time  at  Green.  Dec.  9,  192040 


Sun's  dec.  22  56  43S.    Hourly  diff.      13*32 
—    102       Cor.for4h:39m:  4.G5 


if       « 

90 


Pol.  dist. 


60)6,1,9380 

1  .02 

Obs.  alt.  sun's   )      „     ,     „                                 M.     s.  „ 

upper  limb. .  j  28  45  20     Equat'n  of  time  6  59.31     Hourly  diff. 1.139 


Correction 


4.65 


7.  04.60 


28  25  20 

40  20  00     Secant 0.- 

67  04  19     Co-secant 0.- 


Logarithms  to  Seconds. 


"    "    "      Co-sine 9.- 

39  29  29     Sine 9. 

H.  M.  s. 


A.T.S.  Dec.  10th    4  45  38     Logarithm. . . .   9.532246 
*24  = 


A.  T.  S.  Dec.  9th .  28  45  38     because  the  mean  time  at  Greenwich  is  the  9th. 
—    7  05 


M.T.S.  Dec.  9th.    "    "   " 
M. T.G.Dec. 9th.    "    "   " 


Longitude . .     9  17  53  =  139°  28'  15"  E. 


*  When  the  ship's  date  Is  one  day  more  than  the  Greenwich  date,  you  will  add  24  hours  to  the 
hour  angle,  and  call  that  the  apparent  time  at  ship  on  the  day  before  ;  next  apply  the  equation 
of  time,  and  you  will  have  the  mean  time  at  ship  and  mean  time  at  Greenwich  reckoned  from 
the  same  noon. 


80 


PRACTICAL   NAVIGATION. 


Ex  4.  1878,  April  20th,  A.M.,  at  ship  in  latitude  46°  15'  N.  The  observed 
altitude  of  the  sun's  lower  limb  was  29°  8'  20";  index  error  -  1'  22".  Eye  20  feet. 
Time  by  chronometer,  April  20th,  Oh: 50m: 55s:  which  was  fast  for  mean  noon  at 
Greenwich  50m:  25s:  February  21st  and  on  March  3d  was  50m:  OOs:  fast  for  mean 
noon  at  Greenwich.  Required  the  longitude  by  chronometer. 


H.  M.  s. 

April  20th,  time  by  chron . .  0  50  55 
—  50  00 


48  days  x  2.5s.  per  day  =+20 
Mean  time  at  Green.  Apr. 20,  0    2  55 


Sun's  dec..  11  34  14 N.    Hrly.  diff.  51.31 
Cor.  for  3m:        +3  0.05 


11  34  17  N.    Correction  2  5655 

90  == 


Polar  Dist.  78  25  43 


Obs.  alt.  sun's 
lower  limb . . 


29 


8  20 

1  22 


M.  s. 

Equation  of  time     1  8.47 
Correction +    .02 


Hourly  difference 


.539 
.05 


Eedcd.  eq.  time  -1  8.49     Correction ,02695 


29  17  03 

46  15  00  —  0.- 

78  25  43  —  0.- 


"  "  "  —  9.- 
47  41  50  —  9.- 
H.  M.  S. 


Logarithms  to  Seconds, 


3  57  50  =  9.390813 

24  == 


A. T.S.Apr.  19th,  20  02  10 
—    1    8 


M. T.G.Apr.  19th  24    2  55 


When  the  mean  time  at  ship  and  mean  time  at  Green- 
wich are  different  dates,  add  24  hours  to  the  greater 
date  before  getting  their  difference  for  the  longitude. 


Longitude 4h:lin:S3s:  =60°  28'  15"  W. 


Ex.  5.  1878,  September  22d,  P.M.,  at  ship  in  latitude  12°  18'  S.  The  observed 
altitude  of  the  sun's  lower  limb  was  35°  38'  50";  index  error+2'  10".  Eye  at  20 
feet.  Time  by  chronometer,  Sept.  21st,  17h:  28m:  30s.,  which  was  slow  for  mean 
noon  at  Greenwhich,  Ih:  12m:  56s.  June  27th,  and  on  July  7th  was  slow  Ih:  14m: 
20s.  for  mean  noon  at  Greenwich.  Required  the  longitude  by  chronometer. 

Accumulated  rate  for  76.8  days +  10m:45s. 

Mean  time  at  Greenwich,  September  21st 18h:53in:  35s. 

Polar  distance 90°  21'  01" 

Sum  of  four  logarithms 9.300063 

Mean  time  at  ship,  September  21st 27h:25m:  Ols. 

^  Longitude 127°  51'  30"  E 


Ans.  - 


CHRONOMETER.  81 

Ex.  6.  1878,  May  20th,  A.M.,  at  ship  in  latitude  56°  50  N.  Jhe  observed  al- 
titude of  the  sun's  upper  limb  was  30C  12'  30";  index  error+2'  40".  Eye  at  20 
feet.  Time  by  chronometer,  May  19th,  22h:  17m:  20s.,  which  was  slow  for  mean 
noon  at  Greenwich,  lh:  21m:  14s.  February  18th,  and  on  March  10th  was  slow 
Ih :  20m :  18s. ,  for  mean  noon  at  Greenwich.  Required  the  longitude  by  chronom- 
eter. 

(  Mean  time  at  Greenwich,  May  19th 23h:34m:  19s. 

j   Polar  distance 69°  59'  23" 

Ans.  -I   Sum  of  four  logarithms 9.468138 

Mean  time  at  ship,  May  19th 19h:33m:41s. 

Longitude 60°  9'  30"  W. 

Ex.  7.  1878,  November  18th,  A.M.,  at  ship  in  latitude  46°  10'  S.  The  observed 
altitude  of  the  sun's  lower  limb  was  39°  7'  40";  index  error+2'  10".  Eye  19 
feet.  Time  by  chronometer,  November  17th,  13h:5m:10s.,  which  was  fast  for 
mean  noon  at  Greenwich,  16m:  35s.  September  4th,  and  on  September  14th  was 
fast  15m:  10s.  for  mean  noon  at  Greenwich.  Required  the  longitude  by  chro- 
nometer. 

(  Mean  time  at  Greenwich,  November  17th 12h:59m:  9s. 

Sum  of  four  logarithms 9.293290 

Axis.  4  jyjean  tjrae  at  Sj1jpj  November  17th . . 20h :  14m :  44s. 

[  Longitude 108°  53'  45"  E. 

Ex.  8.  1878,  April  1st,  A.M.,  at  ship  in  latitude  33°  58'  44"  S.  The  observed 
altitude  of  the  sun's  lower  limb  was  33°  14' 50";  index  error  - 1'  30".  Eye  21 
feet.  Time  by  chronometer,  March  31st,  7h:56m:  20s.  which  was  slow  for  mean 
noon  at  Greenwich,  lh:  15m: 07s.  December  llth,  1877,  and  on  January  10th 
was  slow  lh:  12m:  40s.  for  mean  noon  at  Greenwich.  Required  the  longitude  by 
chronometer. 

(  Mean  time  at  Greenwich,  March  31st 9h:2m:  26s. 

J  Sum  of  four  logarithms 9. 150628 

Ans'  |  Mean  time  at  ship,  March  31st 21h:  7m:22s. 

[_  Longitude 178°  40'  0"  W. 


EXAMINATION  PAPEKS. 

The  following  six  papers  contain  each,  nine  problems,  and  as  the 
learner  is  supposed  to  have  mastered  in  the  foregoing  pages  all  the 
rules  necessary  for  their  solution,  it  is  now  desirable  that  he  work 
out  successively  the  problems  in  these  papers  (calculating  to  within  a 
few  seconds),  as  they  will  be  needed  in  his  examination  for  master 
or  mate. 


82 


PRACTICAL  NAVIGATION. 


Ex.  1. 


No.  1. 


HOUBS.  || 

COURSES. 

1  KNOTS. 

tn 
I 

0 

WINDS. 

LEEWAY. 

DEVIAT'N. 

REMARKS,  ETC. 

1 

S.  by  W. 

4 

5 

West. 

1 

8°E. 

A  point. 

2 

it 

5 

5 

ii 

In  latitude  10°  1'  N 

3 

« 

5 

5 

(i 

. 

In  longitude  9°  40'  W 

4 
5 

S.  byE.fE. 

5 
3 

5 
5 

11 

S.W.  by  W. 

U 

14°15'W 

Bearing  by  Comp.,  N.  by  W. 
HeadatN.N.W.  Dev.8°40'W 

6 

11 

3 

5 

" 

Distance  20  miles. 

7 

<( 

3 

5 

" 

Variation,  6°  E. 

8 

" 

2 

5 

« 

9 

E.JS. 

4 

5 

N.byE.iE. 

1 

17°  8'  W. 

10 

" 

4 

5 

it 

11 

(i 

5 

5 

" 

12 

" 

5 

5 

" 

1 

S.E.iS. 

5 

5 

N.E. 

H 

22°41'W 

2 

" 

5 

5 

" 

3 

" 

5 

5 

(i 

4 

it 

6 

5 

" 

5 

S.JE. 

3 

5 

E.JS. 

li 

3°15'W. 

6 

" 

3 

5 

« 

7 

" 

4 

5 

" 

8 

" 

4 

5 

" 

A  current  set  by  compass  S. 

9 

S.S.E.JE. 

2 

5 

E.JN. 

g 

9°W. 

25°  W.   (correct  magnetic) 

10 

K 

3 

5 

" 

18  miles  from  the  time  the 

11 

" 

4 

5 

" 

departure  Avas  taken  to  the 

12 

It 

4 

5 

end  of  the  day. 

Ans. 


f  Bearing  corrected S.  14°  E. 

Current         "         S.  31    W. 

1st  course      '•         S.  14  W.- 

2d       "  "         '. S.  42   E. 

3d       •'          "         S.  87  E. 

4th     "          "         S.  42  E. 

5th     '•'          "         S.  14  W. 

6th     "          "         S.  20  E. 

Difference  of  latitude..          112.6 

True  course S.  17°  E. 

I  Latitude  in 8°  8'  N. 


-Distance  21  miles 
13 
20 
23 
16 
15 

35.7 

Distance 118  miles 

Longitude  in..  .    9°  04' W. 


Ex.  2.  1878,  March  20th,  in  longitude  148°  45' W.  The  observed  meridian 
altitude  of  the  sun's  upper  limb  Avas  45°  35'  00"  bearing  S. ;  index  error  -  7'  56". 
Height  of  eye  22  feet.  Required  the  latitude. 

Sun's  corrected  declination 0°    4'  16"  N. 


Ans. 


Latitude 44°  58'  37"  N. 


Ex.  3.  In  latitude  36°  17',  the  departure  made  good  Avas  187  miles.     Required 
the  difference  of  longitude  by  parallel  sailing. 

Ans.  Difference  of  longitude  . .  232.0 


Ex.  4.  Required  the  course  and  distance  from  A  to  B  by  calculation  on  Mer- 
cator's  principle. 

(  Latitude  of  A 51°  25'  N.  Longitude 9°  29'  W. 

Latitude  of  B 49°  40'  N.  Longitude 53°  54'  W. 

I   Difference  of  latitude 105 

1   Meridian  difference  latitude 166 

Difference  of  longitude 2665 

I  Course S.  86°  26'  W.          Distance 1687  miles 


Ans. 


EXAMINATION   PAPERS.  83 

Ex.  5.  1878,  June  10th,  6h:30m:  P.M.  apparent  time  at  ship  in  latitude  60°  10' 
N.,  longitude  180°  00'  E.  The  sun's  magnetic  amplitude  was  N.W.  by  "\Y..v\V. 
Required  true  amplitude  and  error  of  the  compass,  and  supposing  the  variation 
to  be  15°  E.,  required  the  deviation  of  the  compass  for  that  position  of  the  ship's 
head. 

f  Sun's  corrected  declination 23°    1'  02"  N. 

j  True  amplitude W.  51°  49'  N. 

'    ]   Compass  correction 26°  30'  E. 

[_  Deviation  of  the  compass 1 1°  30'  E. 


Ex.  6.  1878,  April  1st,  A.M.  at  ship  in  latitude  33°  18'  15"  S.,  the  observed 
altitude  of  the  sun's  lower  limb  was  33°  14'  50",  index  error  -  1'  10".  Eye  at  20 
feet.  Time  by  chronometer  March  31st,  Sh:  30m:  32s:  Avhich  was  slow  for  mean 
noon  at  Greenwich  lh:  14m:  13s:  January  29th,  and  on  February  13th  was  slow 
for  mean  noon  at  Greenwich  lh:12m:25s:  Required  the  longitude  by  chrono- 
meter. 

f  Mean  time  at  Greenwich  March  31st 9h:37m:23: 

Polar  distance 94°  22'  21" 

Ans.  \  Sum  of  four  logarithms 9. 160121 

Mean  time  at  ship  March  31st 21h:5m:20s: 

I  Longitude. .  . .  171°  59'  50"  E. 


Ex.  7.  1878,  November  8th,  2h:4m:  P.M.  mean  time  at  ship  in  latitude  57°  25' 
40"  N.,  longitude  133°  18' W.,  the  sun's  magnetic  azimuth  was  S.W.JS.  Ob- 
served altitude  of  the  sun's  lower  limb  10°  26'  15".  Eye  at  20  feet.  Index  error 
+  2'  50".  Required  the  true  azimuth,  correction  and  deviation  of  the  compass. 
Variation  per  chart  5°  W. 

f  Mean  time' at  Greenwich  November  8th 10h:57m:12s: 

Polar  distance 106°  45'  54" 

.        J  Sum  of  four  logarithms 18.907871 

1  True  azimuth S.  33°  02'  W. 

I  Compass  correction 9°    9'  W. 

v  Deviation  of  the  compass '. 4°    09'  W. 


Ex.  8.  1878,  June  15th,  P.M.  apparent  time  at  ship,  latitude  by  account  59°  10' 
N.,  longitude  20°  00'  W.,  the  observed  altitude  of  the  sun's  lower  limb  bearing 
S.  was  53°  45'  45".  Eye  at  20  feet.  Index  error  -  0'  00".  Time  by  watch  Oh: 
15m: 26s  P.M.,  which  was  found  to  be  slow  4m:  12s  for  apparent  time  at  ship. 
The  difference  of  longitude  made  to  the  east  was  13  miles.  Required  the  latitude 
by  reduction  to  the  meridian. 

Hour  angle 20m:30s: 

.    e      I   Sun's  corrected  declination 23°  19'  55"  N. 

Sun's  true  altitude 53°  56'  38" 

Latitude..  .  59°  12'    0"  N. 


Ex.  9.   1878.     The  observed  meridian  altitude  of  the  star  A.  Geminor  was  70° 
50'  30",  bearing  S.     Index  error  -  3'  10".     Eye  20  feet.     Required  the  latitude. 

Ans    \   Star's  dcclination 32°  09'  17"  N. 

Latitude . .  .51°  26'  32"  N. 


84 


PEACTICAL   NAVIGATION. 


Ex.  1. 


HOUES. 

COURSES. 

KNOTS. 

B 

'WINDS. 

LEEWAY. 

DEVIAT'N 

KEMABKS,  ETC, 

1 

N.E.JN. 

3 

5 

E.S.E. 

S 

8°  E. 

A  point. 

2 

" 

3 

5 

" 

In  latitude  10°  20'  N 

3 

« 

4 

5 

« 

In  longitude  20°  30'  W 

5 

E.fS. 

4 
4 

5 
5 

N.N.W. 

i 

25°  E. 

Bearing  by  Comp.  W.  by  S.  |S. 
Head  N.fE.    Deviat'n  3£°  W. 

6 

" 

4 

5 

" 

Distance  25  miles. 

7 

" 

4 

5 

" 

Variation  3J  E. 

8 

" 

4 

5 

" 

9 

E.  by  S. 

4 

5 

S.JW. 

1 

22°  E. 

10 

" 

4 

5 

" 

11 

" 

4 

5 

" 

12 

" 

4 

5 

" 

1 

N.W.fcW. 

3 

5 

S.W4W. 

H 

28^oW 

2 

" 

3 

5 

" 

3 

" 

3 

5 

" 

4 

" 

3 

5 

" 

5 

South. 

3 

5 

E4S. 

1| 

0° 

6 

« 

4 

5 

' 

7 

« 

4 

5 

< 

8 

" 

4 

5 

' 

A  current    set    by  compass 

9 

N.fE. 

4 

5 

E.  JN. 

1 

3i°W. 

south  (correct  magnetic)  10 

10 

" 

4 

5 

1 

miles  from  the  time  the  de- 

11 

" 

4 

5 

' 

parture  was  taken  to  the  end 

12 

4 

5 

of  the  day. 

f  Bearing  corrected N.  70°  E. 


Ans.  •{ 


Current 

1st  course     "         .............. 

2nd  "         .............. 

3rd  "         .............. 

4th  "        .............. 

5th  "         .............. 

6th  "         .............. 

Difference  of  latitude.  .  0'.2 

True  courses  ..........  S.  89°  E. 

I  Latitude  in  ...........  10°  20'  N. 


.S.  3  W. 
.N.  42  E.- 
.S.  48  E. 
.S.  65  E. 
.N.  59  W. 
.S.  17  W. 
.N.  3W. 
Departure . 


-  Distance  16  miles. 
18 
18 
14 
17 
18 

45'.5 

Distance 46  miles. 

Longitude  in 19°  44' W. 


Ex.  2.  1878,  March  30th,  in  longitude  155°  45'  E.,  the  observed  meridian  alti- 
tude of  the  sun's  upper  limb  was  69°  27'  00",  bearing  south.  Index  error  -  5'  24". 
Height  of  the  eye  19  feet.  Required  the  latitude. 

\  Sun's  corrected  declination. .  3°  39'  47"  N. 


Ans. 


|  Latitude 24°  38'  43"  N. 


Ex.  3.  In  latitude  53°  52'  the  departure  made  good  was  6'.  75  miles, 
the  difference  of  longitude  by  parallel  sailing. 
Ans.    Difference  of  longitude 


Required 


ir.44 


Ex.  4.  Required  the  course  and  distance  from  A.  to  B.,  by  calculation  ou 
Mercator's  principle. 

f  Latitude  of  A 12°  46'  N.  Longitude 45°  10'  E. 

:     T_^.:O.__J__J:    T>  1000,4'  XT 


Ans. 


Latitude  of  B 18°  34'  N.  Longitude 72°  53'  E. 

Difference  of  latitude 348 

Meridian  difference  latitude 362 

Difference  of  longitude 1663 

Course N.  77°  43'  E.          Distance 1636  miles. 


EXAMINATION  PAPERS.  85 

Ex.  5.  1878,  May  29th,  6h:30m:  A.M.,  apparent  time  at  ship,  in  latitude  29" 
46'  N.,  longitude  0°  15'  40"  E.  The  sun's  magnetic  amplitude  was  E.fS.  Re- 
quired the  true  amplitu.de,  and  error  of  the  compass,  and  supposing  the  variation 
to  be  19"  W.,  required  the  deviation  of  the  compass  for  that  position  of  the  ship's 
head. 

C  Sun's  corrected  declination 21°  36'  45"  N. 

True  amplitude '.  E.  25°    7'  N. 

Aus>    ]   Compass  correction 33°33'W. 

[  Deviation  of  the  compass 14°  33'W. 


Ex.  G.  1878,  August  25th,  A.M.,  at  ship  in  latitude  9°  50'  15"  S.,  the  observed 
altitude  of  the  sun's  lower  limb  was  32°  15'  20",  index  error-f  3'  40".  Eye  at  20 
feet.  Time  by  chronometer,  24d:  18h:58m:20s.,  which  was  slow  for  mean  noon 
at  Greenwich  2h:7m:33s.  May  llth,  and  on  June  10th  was  slow  for  mean  noon 
at  Greenwich  2h :  5m :  48s.  Required  the  longitude  by  chronometer. 

C  Mean  time  at  Greenwich,  August  24th 20h:59m:43s. 

Polar  distance 100°  46'  30" 

Ans.   •<   Sum  of  four  logarithms 9.313965 

Mean  time  at  ship,  August  24th 20h:26m: Ols. 

I  Longitude 8°  25'  30"  W. 


Ex.  7.  1878,  April  15th,  7h:21m:  A.M.,  mean  time  at  ship,  in  latitude  24°  44' 
N.,  longitude  91°  00'  W.,  the  sun's  magnetic  azimuth  was  E.fN.,  observed  alti- 
tude of  the  sun's  lower  limb  was  22°  10'  40".  Eye  at  20  feet.  Index  error — 
0'  00".  Required  the  true  azimuth,  correction,  and  deviation  of  the  compass. 
Variation  per  chart,  9°  east. 


Ans.   - 


'  Mean  timejat  Greenwich,  April  15th Hi :  25m. 

Polar  distance 80°  09'  24" 

Sum  of  four  logarithms 19. 705025 

True  azimuth S.  90°  48'  E. 

Compass  correction 7°  38'  E. 

Deviation  of  the  compass 1°  22'  W. 


Ex.  8.  1878,  January  1st,  A.M.,  apparent  time  at  ship,  latitude  by  account 
6°  10'  N.,  longitude  87°45'W.,the  observed  altitude  of  the  sun 'slower  limb  bear- 
ing south  was  GO0  20'  10".  Eye  at  16  feet.  Index  error— 0'  00".  Time  by 
watch,  lib: 38m: 20s:  A.M.,  which  was  found  to  be  slow  1m: 20s.  for  apparent 
time  at  ship.  The  difference  of  longitude  made  since  to  the  west  was  2  miles. 
Required  the  latitude  by  reduction  to  the  meridian. 


Ans. 


f  Hour  angle 20m :  28s. 

Sun's  corrected  declination 22°  58'  53"  S. 

I  Sun's  true  altitude 60°  32'  10" 

[Latitude 6°    3'    0"  N. 


Ex.  9.  1878,  the  observed  meridian  altitude  of  the  star  B.  Geminor  was  33° 
30'  20",  bearing  north.  Index  crror+0'  0".  Eye  at  18  feet.  Required  the 
latitude. 

.  j  Star's  declination 28°  19'  10"  N. 

Ans<  1  Latitude. .  . .  28°  16'  10"  S. 


86 


PRACTICAL  NAVIGATION. 


Ex.  1. 


No.  3. 


HOUBS.  1  1 

COTIESES. 

KNOTS. 

1 

WINDS. 

LEEWAY. 

DEVIAT'N. 

KEMABES,  ETC. 

1 

w.s.w. 

6 

N.W.  byN. 

i 

17°W. 

A  point. 

2 

« 

6 

" 

In  latitude  48°  25'  N 

3 

II 

6 

(< 

In  longitude  57°  19'  W. 

4 
5 

E.JN. 

6 

8 

9 

« 

N.fE. 

i 

174°E. 

Bearing  by  Comp.  ,  W.fN. 
Head  N.W.    Dev  .54°  E. 

6 

" 

9 

7 

" 

Distance  19  miles. 

7 

" 

9 

7 

" 

Variation,  20°  W. 

8 

" 

9 

"7 

(i 

9 

E.S.E.!S. 

9 

9 

S.byW.4W. 

i 

14°  E. 

10 

" 

9 

7 

" 

11 

" 

9 

7 

" 

12 

" 

9 

7 

tf  ' 

1 

N.E. 

10 

8 

X.W.  byN. 

H 

17°  E. 

2 

" 

10 

8 

" 

3 

" 

10 

7 

" 

4 

a 

10 

7 

" 

5 

N.E.4E. 

7 

5 

N.E.  by  E. 

1 

20°  E. 

6 

" 

7 

5 

« 

7 

ti 

7 

it 

8 

i< 

7 

" 

A    current   set   by  compass 

9 

W.18. 

6 

S.fW. 

i 

14°W. 

N.  22°  W.  (corr't  magnetic) 

10 

v 

4 

it 

26  miles  from  the  time  the 

11 

(i 

3 

" 

departure  was  taken  to  the 

12 

3 

, 

end  of  the  day. 

Ans. 


corrected N.  84°  E. 

..N.  42   W. 


(  Bearin 

Current          "         

1st  course      '*         

2d       "  "         

3d       •'          "         

4th     "  "         

5th     "  "         

6th     "  "         

Difference  of  latitude..          27'. 0 

True  course N.  76°  E. 

I  Latitude  in 48°  52'  N. 


.S.   22   W— Distance  24  miles 


S.  84  E. 
.S.  82  E. 
.N.  56  E. 
.N.  42  E. 
.S.  59  W. 
Departure 


38 
39 
43 
29 
16 


110'.  2 

Distance 113  miles 

Longitude  in 54°  31'  W. 


Ex.  2.  1878,  December  1st,  in  longitude  114°45'E.  The  observed  .meridian 
altitude  of  the  sun's  upper  limb  was  69°  26'  40"  bearing  S. ;  index  error  -  5'  43". 
Height  of  eye  21  feet.  Required  the  latitude. 

Sun's  corrected  declination 21°  47'  50"  S. 

Latitude  . .  0°  47'  49"  S. 


Ans. 


Re- 


Ex.  3.  In  latitude  69°  11'  S.  the  departure  made  good  was  64.75  miles. 
quired  the  difference  of  longitude  by  parallel  sailing. 

Ans.  Difference  of  longitude 182.2 

Ex.  4.  Required  the  course  and  distance  from  A  to  B  by  calculation  on  Mer- 
cator's  principle. 

(  Latitude  of  A 17°  36'  N.          Longitude 146°    5'  E. 

Latitude  of  B 23°  46'  N.  Longitude 121°  55'  W. 

A         J  Difference  of  latitude , 370 

'    I   Meridian  difference  latitude 396 

Difference  of  longitude 5520 

I  Course  . .  .   N.  85J  54'  E.  Distance 5175  miles 


EXAMINATION  PAPERS.  87 

Ex.  5.  1878,  October  21st,  5h:23m:  A.M.  apparent  time  at  ship  in  latitude  47°  51' 
S.,  longitude  30°  17'  E.  The  sun's  magnetic  amplitude  was  S.E.JE.  Required 
true  amplitude  and  error  of  the  compass,  and  supposing  the  variation  to  be 
32°  W.,  required  the  deviation  of  the  compass  for  that  position  of  the  ship's 
head. 

C  Sun's  corrected  declination 10°  37'  39"  S. 

I  True  amplitude E.  15°  58'  S. 

s<  I   Compass  correction 23°  13'  W. 

[_  Deviation  of  the  compass 5°  47'  E. 


Ex.  6.  1878,  December  28th,  A.M.  at  ship  in  latitude  50Q  55'  N.,  the  observed 
altitude  of  the  sun's  lower  limb  was  10°  58'  30",  index  error  -  1'  20".  Eye  at  20 
feet.  Time  by  chronometer  27d:20h:10m:54s:,  which  was  slow  for  mean  noon 
noon  at  Greenwich  2h:35m:53s:  October  3d,  and  on  October  21st  Avas  slow 
for  mean  noon  at  Greenwich  2h  :34m:  50s:  Required  the  longitude  by  chrono- 
meter. 

f  Mean  time  at  Greenwich  December  27th 22h:41m:46s: 

j   Polar  distance 113°  17'  25" 

Ans.  -I  Sum  of  four  logarithms 8.835525 

I  Mean  time  at  ship  December  27th 22h:00m:27s: 

I  Longitude 10°  19'  45"  W. 


Ex.  7.  1878,  November  4th,  2h:46m:  P.M.  mean  time  at  ship  in  latitude  53° 55' 
15"  N.,  longitude  163°  49'  30" E.,  the  sun's  magnetic  azimuth  was  S.W.fS.  Ob- 
served altitude  of  the  sun's  lower  limb  11°  13'  10".  Eye  at  18  feet.  Index  error 
—  1'  20".  Required  the  true  azimuth,  correction  and  deviation  of  the  compass. 
Variation  of  the  compass  8°  E. 

Mean  time  at  Greenwich  November  3d 15h:50m:42s: 

Polar  distance 105°  19'  54" 

Sum  of  four  logarithms 19.126310 

True  azimuth S.  42°  54'  W. 

Compass  correction 6°  20'  E. 

^  Deviation  of  the  compass 1°    40'  W. 


Ans.  - 


Ex.  8.  1878,  June  21st,  P.M.  apparent  time  at  ship,  latitude  by  account  8°  10' 
N.,  longitude  100°  33'  E.,  the  observed  altitude  of  the  sun's  lower  limb  bearing 
N.  was  73°  45' 30".  Eye  at  12  feet.  Index  error  -  0' 00".  Time  by  watch  llh: 
54m:  10s  P.M.,  which  was  found  to  be  slow  26m:46s  for  apparent  time  at  ship. 
The  difference  of  longitude  made  to  the  west  was  20  miles.  Required  the  latitude 
by  reduction  to  the  meridian. 

"]   Hour  angle 19m:36s: 

Ans.    1  Sun's  corrected  declination 23°  27'  30"  N. 

j  Sun's  true  altitude 73"  57'  43" 

)  Latitude 8°  07'  30"  N. 

Ex.  9.     1878,  the  observed  meridian  altitude  of  thu  star  A.  Aquiloa  was  673  42 
30",  bearing  S.     Index  error— 3'  10".     Eye  20  feet.     Required  the  latitude. 

A   0   j  Star's  declination 8°  32'  45"  N. 

AnSl  I  Latitude 30°  58'  42"  N. 


88 


PEACTICAL  NAVIGATION. 


Ex.  1. 


No.  4. 


HotTES.  |  1 

COURSES. 

» 

W 

w 

M 
O 

WINDS. 

LEEWAY. 

DEVIAT'N 

HEMAKKS,  ETC, 

1 

S.byW.fSV. 

3 

9 

West. 

J1 

3°26'  w 

A  point. 

2 

" 

3 

8 

" 

In  latitude  49°  3'  S 

3 

« 

4 

3 

" 

In  longitude  166°  12'  E. 

4 

5 

South 

4 
5 

3 

W.byS. 

s 

5°20'  E. 

Bearing  by  comp.  SWby  W£W 
Head  S.  by  E.    Deviat'n  8U  E. 

6 

" 

fi 

7 

" 

Distance  21  miles. 

7 

" 

5 

4 

" 

Variation  20°  E. 

8 

" 

G 

G 

" 

9 

N.  by  E. 

8 

3 

East, 

i 

5'°  E. 

10 

" 

8 

9 

" 

11 

" 

8 

9 

" 

12 

" 

8 

9 

" 

1 

W.byN.^N. 

9 

9 

s.s.w.nv. 

ii 

26°  W. 

2 

" 

10 

3 

.     " 

3 

'• 

10 

4 

" 

4 

" 

10 

4 

" 

5 

W.byN. 

10 

4 

North. 

i 

22°30'w 

6 

" 

10 

4 

" 

7 

" 

10 

3 

" 

8 
9 

W.N.W. 

9 
9 

9 
9 

S.  W.byS. 

i 

23°  W. 

A  current    set    by  compass 
N.393E.  (correct  magnetic  )S 

10 

" 

9 

9 

" 

miles  from  the  time  the  de- 

11 

" 

10 

1 

" 

parture  was  taken  to  the  end 

12 

10 

1 

of  the  day. 

f  Bearing  corrected S.  87°  E. 

Current         "         N.  59   E. 

1st  course      "          S.  25  W. 

2nd     "          " S.   17  W. 

3rd      "          "         N.  25  E. 

Ans.  •{  4th     "          "         N.  G5  W. 

5th     "          "         N.  84  W. 

6th     "          "         N.62W. 

D  ifference  of  latitude . .         38'.  6 

True  courses N .65°  W. 

I  Latitude  in 48°  24'  S. 


-  Distance  16  miles. 
23 
35 

41 
41 
40 

84'.  1 


Distance 93  miles. 

Longitude  in. .  . .  164° 4'  E. 


Ex.  2.  1878,  November  IGth,  in  longitude  171°14'E.,  the  observed  meridian  alti- 
tude of  the  sun's  lower  limb  was  71°  43'  20",  bearing  south.  Index  error  -  1'  30". 
Height  of  the  eye  24  feet.  Required  the  latitude. 

\  Sun's  corrected  declination 18°  40'  22"  S. 


Ans. 


1  Latitude 0°  33'  27"  S. 


Ex.  3.  In  latitude  68°  49'  N.  the  departure  made  good  was  677  miles, 
the  difference  of  longitude  by  parallel  sailing. 
Ans.    Difference  of  longitude 


Required 


1873 


Ex.4.  Required  the  course  and  distance  from  A.  to  B.,  by  calculation  on 
Mercator's  principle. 

f  Latitude  of  A 4°  22'  S.  Longitude 18°  21'  E. 

I   Latitude  of  B 68°  20'  S.  Longitude 142°  15'  E 

Difference  of  latitude 3S38 

Meridian  difference  latitude 5423 

Difference  of  longitude 7434 

Course S.  53°  53'  E.  Distance 651 1  miles. 


Ans. 


EXAMINATION  PAPERS.  89 

Ex.  5.  1878,  March  21st,  9li:  10m:  A.M.,  apparent  time  at  ship,  in  latitude  10° 
10'  N.,  longitude  118°  10' E.  The  sun's  magnetic  amplitude  was  E.£N.  Re- 
quired the  true  amplitude,  and  error  of  the  compass,  and  supposing  the  variation 
to  be  2"  E.,  required  the  deviation  of  the  compass  for  that  position  of  the  ship's 

head. 

r  Sun's  corrected  declination 0°  7'  36"  N. 

j  True  amplitude E.  0°    8'  N. 

Ans>   ^   Compass  correction 2°  41'  E. 

Deviation  of  the  compass 0°  41'  E. 


Ex.  6.  1878,  March  21st,  A.M.,  at  ship  in  latitude  0°  0' 0"  S.,  the  observed 
altitude  of  the  sun's  lower  limb  \?a3  36°  15'  10".  Index  error-j-2'  38".  Eye  at  20 
feet.  Time  by  chronometer,  20d:  13h:21ui:50s.,  which  was  fast  for  mean  noon 
at  Greenwich  7m:  03.7s:  January  llth,  and  January  20th  was  fast  for  mean  noon 
at  Greenwich  Gm :  25s.  Required  the  longitude  by  chronometer. 

f  Mean  time  at  Greenwich,  March  20th 13h:19m:41s. 

I   Polar  distance 89°  52'  30" 

Ans.   -I   Sum  of  four  logarithms 9.307006 

Mean  time  at  ship,  March  20th 20h:33m:  20s. 

I  Longitude 108°  24'  45"  E. 


Ex.  7.  1878,  March  30th,  3h: 40m: 46s:  P.M.,  meaji  time  at  ship,  in  latitude 
28°  30'  15"  S.,  longitude  174°  20'  W.,  the  sun's  magnetic  azimuth  was  N.  80° 
52'  50"  W.,  observed  altitude  of  the  sun's  lower  limb  was  28°  23'  40".  Eye  at 
18  feet.  Index  error+5'  10".  Required  the  true  azimuth,  correction,  and  de- 
viation of  the  compass.  Variation  per  chart,  12°  10'  east. 

f  Mean  time  at  Greenwich,  March  30th 15h:  18m:  6s. 

Polar  distance 94°  4'  37" 

Ans    -I  ^um  °^  *our  l°oaritnms 19.485071 

I   True  azimuth N.  67°  06'  W. 

Compass  correction 13°  46'  50"  E. 

*•  Deviation  of  the  compass 1°  36'  50"  E. 


Ex.  8.  1878,  November  16th,  P.M.,  apparent  time  at  ship,  latitude  by  account 
1°  20'  30"  S.,  longitude  171°  00'  E.,  the  observed  altitude  of  the  sun's  lower  limb 
bearing  south  was  71°  43'  20".  Eye  at  24  feet.  Index  error — 1'  30".  Time  by 
watch  on  the  16th,  10h:31m:8s:  P.M.,  which  was  fast  lOh:  10m:  12s.  for  apparent 
time  at  ship.  The  difference  of  longitude  made  since  to  the  east  was  10  miles. 
Required  the  latitude  by  reduction  to  the  meridian. 

(Hour  angle 21m :  36s. 
Sun's  corrected  declination 18°  40'  37"  S. 
Sun's  true  altitude 71"  53'  05" 
Latitude 1°  22'  00"  S. 


Ex.  9.  1878,  the  observed  meridian  altitude  of  the  star  A.  Spica  \vas  31° 
27'  40",  bearing  north.  Index  error+5'  20".  Eye  at  20  feet.  Required  the 
latitude. 

A         j  Star's  declination 10°  31'  25"  S. 

Ans<     I  Latitude 48J  01'  25"  N. 


90 
Ex.  1. 


PRACTICAL  NAVIGATION. 


No.  5. 


Hotms. 

COUESES. 

KNOTS. 

8 

H 

0 

l-t 

WINDS. 

LEEWAY. 

DEVIAT'N. 

EEMAEKS,  ETC. 

1 

S.W.fS. 

5 

5 

S.E. 

1 

G°  30'  W 

A  point. 

2 

« 

5 

5 

'< 

In  latitude  34°  28'  S. 

3 

(1 

5 

11 

In  longitude  18°  28'  E. 

4 
5 

N.byKfE. 

6 

6 

5 

E.  by  S. 

1* 

12°30'  E 

Bearing  byComp.,  S.E.-|E. 
HeadS.E.    Dev.  4°  30'  E. 

6 

" 

7 

5 

(3 

Distance  10  miles. 

7 

" 

7 

" 

Variation,  24°  W. 

8 

a 

7 

" 

9 

KJS. 

7 

N.byE.JE. 

1 

15°  E. 

10 

" 

4 

5 

« 

11 

" 

4 

5 

" 

12 

" 

4 

" 

1 

N.E.JN. 

6 

5 

S.E.JS. 

1 

13°  E. 

2 

" 

6 

5 

" 

3 

" 

G 

" 

4 

" 

6 

" 

5 

SAY.  IS. 

G 

5 

S.E.4E. 

i 

3°45'W 

6 

" 

G 

5 

" 

7 

(i 

-6 

5 

it 

8 

" 

G 

5 

" 

A    current   set   by  compass 

9 

S.E.JE. 

9 

9 

S.W.  byW. 

i 

7°25/E. 

S.  46°  E.  (corr  t  magnetic) 

10 

" 

9 

8 

" 

10  miles  from  the  time  the 

11 

" 

9 

7 

" 

departure  was  taken  to  the 

12 

9 

G 

end  of  the  day. 

f  Bearing  corrected N.  70°  W. 


Ans. 


Current 

1st  course 

2d       ' 

3d       • 

4th     ' 

5th     ' 

6th     ' 

Difference  of  latitude..          10'.2 

True  course  ..........   S.  78°  E. 

I  Latitude  in  ..........  34°  38'  S. 


S.   70  E. 

S.   17  W— Distance  22  miles 

...  N.    6  W.           <  28 

....S.   82   E.             '  20 

.  ...N.  20  E.             '  25 

....S.   20  W.            '  26 

. ...S.   70  E.             '  39 

Departure 4G'.8 

Distance 48  miles 

Longitude  in 19°  25'  E. 


Ex.  2.  1878,  June  10th,  in  longitude  30°  30'  W.  The  observed  meridian  alti- 
tude of  the  sun's  lower  limb  was  78°  19'  40"  bearing  N.;  index  error -4' 30". 
Height  of  eye  20  feet.  Required  the  latitude. 

Sun's  corrected  declination  . .  .  23°    2'  28"  N. 


Ans. 


Latitude 11°  28'  58"  N. 


Re- 


Ex.  3.  In  latitude  48°  28'  N.,  the  departure  made  good  was  187  miles, 
quired  the  difference  of  longitude  by  parallel  sailing. 

Ans.  Difference  of  longitude 282' 

Ex.  4.  Required  the  course  and  distance  from  A  to  B  by  calculation  on  Mer- 
cator's  principle. 

Latitude  of  A 30°  00'  N.  Longitude 30°  00'  E. 

Latitude  of  B 60°  00'  S.  Longitude 150°  00'  W. 

A         j  Difference  of  latitude 5400 

/ins.   4   Meridian  diffcrence  latitude 6415 

Difference  of  longitude 10800 

I  Course  . .  .    S.  59°  17'  E.          Distance 10571  miles 


EXAMINATION   PAPERS.  91 

Ex.  5.  1878,  January  1st,  6h:40m:  A.M.  apparent  time  at  ship  in  latitude  30°  10' 
S.,  longitude  100°  10'  W.  The  sun's  magnetic  amplitude  was  E.fS.  Required 
true  amplitude  and  error  of  the  compass,  and  supposing  the  variation  to  be 
12°  E.,  required  the  deviation  of  the  compass  for  that  position  of  the  ship's 
head. 

f  Sun's  corrected  declination 22°  59'  45"  S. 

J  True  amplitude E.  26°  52'  S. 

ns'  I  Compass  correction 18°  26'  E. 

(_  Deviation  of  the  compass 6°  26'  E. 


Ex.  6.  1878,  March  29th,  P.M.  at  ship  in  latitude  33°  8'  15"  K,  the  observed 
altitude  of  the  sun's  lower  limb  was  27U  58'  15",  index  error  2'  45"  to  subtract. 
Eye  at  20  feet.  Time  by  chronometer  28d:17h:16m:28s:,  which  was  slow  for 
mean  noon  noon  at  Greenwich  lh:32m:17s:  November  30,  1877,  and  on  Decem- 
ber 30th,  1877,  was  slow  for  mean  noon  at  Greenwich  lh:28m:56s:  Required 
the  longitude  by  chronometer.  , 

f  Mean  time  at  Greenwich  March  28th 18h:35m:29s: 

Polar  distance 86°  38'  48" 

Ans.  -    Sum  of  four  logarithms 9.375588 

Mean  time  at  ship  March  29th 3h:  58m:  13s: 

Longitude..  ..140°  41' 00"   E. 


Ex.  7.  1878,  April  llth,  2h:7m:25s:  P.M.  mean  time  at  ship  in  latitude  55° 27' 
45"  S.,  longitude  52°  OG'  E.,  the  sun's  magnetic  azimuth  was  N.JE.  Observed 
altitude  of  the  sun's  lower  limb  20°  56' 45".  Eye  at  20  feet.  Index  error — 3''40". 
Required  the  true  azimuth,  correction  and  deviation  of  the  compass.  Variation 
of  the  compass  36°  W. 

("  Mean  time  at  Greenwich  April  10th 22h:39m:01s: 

Polar  distance 98°  21'  16" 

Sum  of  four  logarithms 18.919596 

True  azimuth N.  33°  30'  W. 

Compass  correction 39°  07'  W. 

^  Deviation  of  the  compass 3°  07'  W. 


Ans. 


Ex.  8.  1878,  March  20th,  P.M.  apparent  time  at  ship,  latitude  by  accoimt44° 
30'  N.,  longitude  119°  00'  W.,  the  observed  altitude  of  the  sun's  lower  limb 
bearing  S.  was  45°  2'  50".  Eye  at  22  feet.  Index  error-  7'  55".  Time  by  watch 
Oh:29m:58s:  P.M.,  which  was  found  to  be  fast  3m: 30s:  for  apparent  time  at  ship. 
The  difference  of  longitude  made  to  the  east  was  24  miles.  Required  the  latitude 
by  reduction  to  the  meridian.  * 

Hour  angle 28m:04s: 

.         i    Sun's  corrected  declination 0°    2'  46"  N. 

Sun's  true  altitude 45°    5'  39" 

Latitude..  .    44°  31' 00"  N. 


Ex.  9.  1878,  January  1st,  the  observed  meridian  altitude  of  the  star  A.  Regulus 
was  84'J  47' 20"  bearing  N.  Index  error +4' 20".  Eye  11  feet.  Required  the  lat- 
itude. 

Ans    \   Star's  declination • 12°  33'  40"  N. 

Latitude..  7°  22'  11"N. 


92 


PRACTICAL   NAVIGATION. 


Ex.  1. 


No.  6. 


HOURS. 

COUBSES. 

KNOTS. 

n 
| 

WINDS. 

LEE.WAT. 

DEVIAT'N 

REMABKS,  ETC. 

1 

NEbyNiN. 

4 

8 

S.E.  byE. 

li 

12°  E. 

A  point. 

2 

" 

4 

9 

" 

In  latitude  30°  15'    S. 

3 

ci 

4 

8 

it 

In  longitude  40°  20'  W. 

4 
5 

N.N.W.JW. 

5 
5 

5 
5 

W.  by  S. 

2 

7°30'W. 

Bearing  by  compass  S.  S.  E. 
Head  N.W.     Dev.  4°  30'  W. 

6 

" 

5 

3 

" 

Distance  10  miles. 

7 

" 

5 

3 

" 

Variation  10°  E. 

8 

" 

5 

3 

" 

9 

N.E.JE. 

4 

S.E4E. 

2* 

12°15'  E 

10 

a 

3 

" 

11 

" 

3 

" 

12 

" 

3 

<( 

1 

N.JW. 

4 

9 

W.  by  N. 

2| 

2°  E. 

2 

" 

5 

8 

" 

3 

" 

6 

8 

" 

4 

" 

7 

5 

" 

5 

N.fE. 

7 

1 

E.  by  N. 

2i 

13°  W. 

6 

" 

6 

3 

" 

7 

" 

6 

3 

" 

8 

" 

6 

3 

" 

A  current  set  by  compass  N. 

9 

N.E. 

5 

4 

N.W.  by  N. 

1 

7°  E. 

25°  W.  (correct  magnetic)  48 

10 

" 

4 

8 

it 

miles  from  the  time  the  de- 

11 

a 

4 

9 

" 

parture  was  taken  to  the  end 

12 

4 

9 

u 

of  the  day. 

Aus. 


f  Bearing  corr 
Current 
1st  course 
2nd     " 
3rd     " 
4th      " 
5th     " 
6th      " 
Difference  of 
True  courses 

ected  N.  17°W. 

-  Distan 

« 

ii 

ce  20  miles. 
21.4  ' 
13      ' 
25      ' 
26      ' 
20      ' 
30'.  1 
156  miles. 

N.  15  W. 

N.  39  E. 

N.    3  W. 

N.42    E. 

N.  37    E. 

N.  20  W. 

N.  73    E. 

latitude..        152'.  8          Departure. 

..N.  11°E.           Distance.. 

Latitude  in 27°  42'  S. 


Longitude  in 39°  46'  W. 


Ex.  2.  1878,  January  14th,  in  longitude  51°  54'  W.,  the  observed  meridian  alti- 
tude of  the  sitn's  upper  limb  Avas  78°  35'  00",  bearing  south.  Index  error +5'  55". 
Height  of  the  eye  18  feet.  Required  the  latitude. 

\  Sun's  corrected  declination 21°  15'  08"  S. 


Ans. 


I  Latitude 9°  35'  32"  S. 


Ex.  3.  In  latitude  66°  40'  S.  the  departure  made  good  was  387  miles, 
the  difference  of  longitude  by  parallel  sailing. 
Ans.    Difference  of  longitude 


Required 


977.1 


Ex.4.  Required  the  course  and  distance  from  A.  to  B.,  by  calculation  on 
Mercator's  principle. 

f  Latitude  of  A 52°  30'  S.  Longitude 167°  30'  E. 

Latitude  of  B 12°  20'  N.  Longitude 92°  32'  W. 

Difference  of  latitude , 3890 

Meridian  difference  latitude 4460 

Difference  of  longitude 5998 

Course. .  .  N.  53°  22'  E.          Distance 6519  miles. 


Ans. 


EXAMINATION  PAPERS.  93 

Ex.  5.  1878,  September  6th,  6h: 40m:  A.M.  apparent  time  at  ship  in  latitude 
38"  40'  N.,  longitude  25°  45'  E.  The  sun's  magnetic  amplitude  was  E.  by  N. 
Required  the  true  amplitude  and  error  of  the  compass  and  supposing  the  varia- 
tion to  be  8°  \V.,  required  the  deviation  of  the  compass  for  that  position  of  the 
ship's  head. 

r  Sun's  corrected  declination 6°  30'  46"  N. 

I  True  amplitude. .  .  .E.  8°  21'  N. 

A  YIQ         J 

|  Compass  correction 2°  54'  E. 

(_  Deviation  of  the  compass 10°  54'  E. 


Ex.  6.  1878,  August  20th,  P.M.  at  ship  in  latitude  36°  41'  20"  N.,  the  ob- 
served altitude  of  the  sun's  lower  limb  was  23°  27'  30",  index  error -3'  10". 
Eye  at  19  feet.  Time  by  chronometer  19d:  18h:10m:20s.,  which  was  slow  for 
mean  noon  at  Greenwich  24m:  46s:  June  12th,  and  on  June  20th,  was  slow  for 
mean  noon  at  Greenwich  25m :  30s.  Required  the  longitude  by  chronometer. 

f  Mean  time  at  Greenwich,  August  19th 18h:41m:24s: 

Polar  distance 77°  30'  10" 

Ans.  -I   Sum  of  four  logarithms 9.514859 

Mean  time  at  ship,  August  20th 4h:  42m :  24s: 

I  Longitude . .  150°  15'  0"  E. 


Ex.  7.  1878,  June  4th,  6h:  8m:  P.M.  mean  time  at  ship,  in  latitude  47°  30'  N., 
longitude  16°  20'  W.,  the  sun's  magnetic  azimuth  was  W.JN.  Observed  alti- 
tude of  the  sun's  lower  limb  Avas  33°  44'  40".  Eye  at  19  feet.  Index  error -2' 
20".  Required  the  true  azimuth,  correction  and  deviation  of  the  compass. 
Variation  per  chart,  32J  W. 

f  Mean  time  at  Greenwich,  June  4th 7h:  13m:  20s: 

Polar  distance 67°  30'  22" 

Sum  of  four  logarithms 19.676223 

True  azimuth S.  87°  04'  W. 

Compass  correction » .  5°  45'  W. 

Deviation  of  the  compass 26°  15'  E. 


Ans. 


Ex.  8.  1878,  November  23d,  P.M.  apparent  time  at  ship,  latitude  by  account 
50°  30'  N.,  longitude  38°  30'  W.,  the  observed  altitude  of  the  sun's  lower  limb 
bearing  S.  was  18°  49'  14".  Eye  at  20  feet.  Index  error  -  4'  19".  Time  by  watch 
Oh: 26m:  12s:  P.M.,  which  was  found  to  be  slow  2m: 20s:  for  apparent  time  at 
ship.  The  difference  of  longitude  made  since  to  the  west  was  18  miles.  Re- 
quired the  latitude  by  reduction  to  the  meridian. 

r  Hour  angle 27m :  20s : 

Sun's  corrected  declination 20°  25'  11"  S. 

Ans>   |  Sun's  true  altitude 18°  54'  13" 

Latitude 50D  26'  00"  N. 


Ex.  9.  1878,  the  observed  meridian  altitude  of  the  star  A  Taurus  was  50° 
17' 20"  bearingS.     Index  error +  3' 10".     Eye  20  feet.     Required  the  latitude. 

.        (  Star's  declination 16°  15'  54"  N. 

'  <  Latitude . .  .56°  00'  20"  N. 


94:  PKACTICAL  NAVIGATION. 


TO  FIND  THE  LATITUDE  AND  LONGITUDE  BY  TWO  OB- 
SERVED ALTITUDES,  THE  RESULT  OF  EACH  COMPU- 
TATION BEING  AT  THE  TIME  AND  PLACE  WHERE 
THE  GREATER  ALTITUDE  WAS  TAKEN. 

The  system  of  double  altitudes  herein  introduced  lias  not  heretofore  been  pub- 
lished in  any  American  work,  and  its  great  advantage  is  that  both  latitude  and 
longitude  are  thereby  obtained  simultaneously. 

First.  Be  careful  to  note  the  times  by  the  same  chronometer  at 
each  observation,  and  apply  its  error  to  the  time  shown  when  the 
greater  altitude  was  taken,  to  obtain  the  mean  time  at  Greenwich. 

Second.  Take  out  the  sun's  declination  on  the  given  day  from 
page  two  of  the  month  of  the  nautical  almanac,  and  correct  it  for 
Greenwich  mean  time  by  the  hourly  difference;  the  correction  thus 
obtained  is  to  be  added  when  declination  is  increasing,  but  sub- 
tracted if  decreasing. 

Third.  Then  ascertain  the  angle  between  the  ship's  course  and 
sun's  bearing  at  the  time  of  taking  the  least  altitude,  with  which, 
and  the  ship's  run  between  the  observations,  find  the  correction  for 
change  of  position,  and  apply  the  same,  if  any,  to  the  least  altitude. 

Fourth.  If  the  less  altitude  be  observed  in  the  forenoon,  add  the 
correction  thus  found;  if  the  angle  is  less  than  eight  points,  but  if 
more,  then  subtract  it. 

Fifth.  If  the  less  altitude  is  taken  in  the  afternoon,  then  subtract 
the  correction,  if  the  angle  is  less  than  eight  points;  but  if  greater, 
then  add  it. 

Sixth.  Should  the  angle  between  the  ship's  course  and  sun's 
bearing  be  equal  to  eight  points  or  90°  degrees,  then  there  is  no 
correction  to  apply,  because  the  lesser  altitude  is  neither  raised  nor 
depressed. 

Seventh.  In  sailing  directly  towards  or  from  the  sun,  apply  the 
correction  for  the  change  of  position  in  the  following  manner,  viz: 

Eighth.  When  the  lesser  altitude  is  observed  in  the  forenoon  and 
sailing  towards  the  sun,  add  the  correction  to  the  lesser  altitude; 
but  when  sailing  from  the  sun  then  subtract  the  correction  from  the 
lesser  altitude. 


DOUBLE  ALTITUDE.  95 

Ninth.  When  the  less  altitude  is  taken  in  the  afternoon  and  sailing 
but  toward  the  sun,  subtract  the  correction  from  the  least  altitude; 
when  sailing  from  the  sun,  then  add  the  correction  to  the  least  alti- 
tude. 

Tenth.  Correct  each  of  the  altitudes  for  index  error,  if  any;  dip  of 
the  horizon,  (Table  VII,  Kefraction  Table  VI,  Parallax  Table  VIII), 
and  sun's  semi-diameter,  Page  1  Nautical  Almanac,)  to  be  added  to 
the  sun's  lower  limb,  but  subtracted  from  the  sun's  upper  limb  to 
obtain  the  true  altitude.  Then  proceed  to  find  the  latitude  and  lon- 
gitude of  the  ship  when  the  greater  altitude  was  observed,  by  the 
following  rules : 

Eleventh.  Add  together  the  true  altitudes  and  take  half  their 
sum;  subtract  the  less  altitude  from  the  greater,  and  take  half  their 
difference. 

Twelfth.  Find  the  interval  between  the  times  of  observing  the  two 
altitudes,  which  call  elapsed  time;  take  half  of  the  elapsed  time 
and  reduce  it  to  degrees,  by  Table  XI. 

Thirteenth.  Add  together  the  co-secant  (Table  II)  of  half  the 
elapsed  time,  reduced  as  before,  and  the  secant  of  the  declination; 
their  sum  will  be  the  co-secant  of  arc  first. 

Fourteenth.  Add  together  the  co-secant  of  arc  first,  the  co-sine 
of  half  the  sum  of  the  altitudes  and  the  sine  of  half  their  difference; 
the  sum  of  these  logarithms  will  be  the  sine  of  arc  second. 

Fifteenth.  Add  together  the  secant  of  arc  first,  the  sine  of  half  the 
sum  of  the  altitudes,  and  the  co-sine  of  half  their  difference,  and 
the  secant  of  arc  second;  their  sum  will  be  the  co-sine  of  arc  third. 

Sixteenth.  Add  together  the  secant  of  arc  first,  already  found, 
and  the  sine  of  the  declination;  their  sum  will  be  the  co-sine  of  arc 
fourth,  when  the  latitude  and  declination  are  of  the  same  name; 
but  when  they  are  of  contrary  names  take  the  supplement  for  arc 
fourth,  that  is  from  180°. 

Seventeenth.  Take  the  sum  or  difference  of  arcs  third  and  fourth, 
for  arc  fifth.  (See  rule  20.) 

Eighteenth.  Add  together  the  secants  of  arc  second  (already 
found)  and  arc  fifth,  their  sum  will  be  the  co-secant  of  the  latitude 
when  the  greater  altitude  was  observed,  and  the  nearer  it  is  taken 
to  noon,  the  better.  Having  obtained  the  true  latitude  of  the  ship 
when  the  greater  altitude  was  observed,  proceed  in  the  following 
manner  to  ascertain  the  longitude  at  the  same  instant. 


96  PBACTICAL  NAVIGATION. 

Nineteenth.  To  the  co-secant  of  arc  second  add  the  co-nine  of  the 
latitude  just  found,  their  sum  will  give  the  co-secant  of  an  arc  in  de- 
grees and  minutes,  which,  converted  into  time  by  Table  XI,  produces 
arc  A ;  the  difference  between  it  and  the  half  elapsed  time  will  give 
the  apparent  time  at  ship  when  the  greater  altitude  is  taken  in  "the 
afternoon;  but,  should  the  greater  altitude  be  observed  in  the  fore- 
noon, then  subtract  it  from  24  hours  to  obtain  the  apparent  time 
past  the  preceding  noon,  to  which  apply  the  corrected  equation  for 
the  mean  time  at  ship;  the  difference  between  it  and  the  mean  time 
at  Greenwich  by  the  chronometer  will  be  the  longitude  in  time  when 
the  greater  altitude  was  observed,  which  being  converted  into  de- 
grees and  minutes  by  Table  XI,  will  produce  the  east  longitude  of 
the  ship,  if  the  time  at  ship  be  greater  than  Greenwich,  but  west,  if 
less. 

Twentieth.  When  the  sum  of  arcs  third  and  fourth  is  equal  to,  or 
greater  than  90°,  their  difference  is  always  arc  fifth;  bxit  when  their 
sum  is  less  than  90°,  which  will  rarely  happen,  it  may  be  doubtful 
whether  their  sum  or  difference  ought  to  be  taken  for  arc  fifth,  but 
the  computation  is  soon  made  on  both  suppositions,  for  the  secant 
of  arc  fifth  is  the  last  logarithm  which  is  taken  from  the  table,  and 
the  other  parts  of  the  calculation  are  therefore  not  affected  by  the 
change;  one  of  the  results  must  certainly  be  the  required  latitude, 
and  the  latitude  by  account  will  generally  be  sufficient  to  determine 
which  of  them  ought  to  be  taken. 

It  may  be  useful  to  remark,  the  preceding  not  only  applies  to  cases 
when  the  latitude  and  declination  are  of  the  same  name,  and  very 
nearly  alike  in  amount,  in  which  case  it  becomes  doubtful  whether 
the  sum  or  difference  of  arcs  third  and  fourth  shduld  be  taken  to 
obtain  arc  fifth;  hence  it  follows,  such  instances  only  occur  between 
the  tropics  where  the  latitude  by  double  altitudes  is  rarely  observed, 
but  should  this  method  of  ascertaining  the  ship's  position  be  prac- 
ticed when  the  sun  is  vertical,  or  nearly  so,  then  it  becomes  abso- 
lutely requisite  to  work  the  arcs  very  rigidly  to  the  nearest  second, 
on  account  of  the  difference  of  the  sines  answering  to  small  arcs^ 
and  co-sines  of  large  ones  varying  so  considerably;  hence  it  is 
deemed  advisable  not  to  practice  this  method  when  the  sun  is  within 
5°  of  being  vertical. 


DOUBLE  ALTITUDE. 


97 


Ex.  1.  April  13th,  1878,  P.M.,  ship  time  at  both  observations  in  latitude  by 
account  9°  50'  S.,  and  longitude  10°  24'  W.  Suppose  the  following  true  altitudes 
and  times  by  chronometer  were  taken,  to  find  the  true  latitude  and  longitude  of 
the  ship,  the  chronometer  being  12m:  36s.  slow  of  Greenwich  time. 


H.  M.   S. 


Time  by  chron.  at  greater  alt.   1  13  30 
Chronometer  slow +  12  36 

Mean  time  at  Green.  April  13.   1  26  06 


1st  true  alt. .  67  58 
2nd  true  alt.  42  20 


Sum 110  18.  .Half  sum.  55°  09' 


Difference  . .  25  38.  .Half  dif . .  12°  49' 


Sun's  dec. 
Apr.  13th. 


9  06  13  N.  Hr.  dif.  54.30 
+    1  16  1.4 


Cor.  dec 9  07  29  N. 


21720 
5430 

6,0)76.  "020 

rie* 


H.  M.  S. 

Timebychr.  Istobs.  1  13  30 
2d    "    3  24  20 


Elapsed  time 2)2  10  50 

Half  elapsed  time . .   1     5  25. .  16°  21'  15" 


Half  el ap.  time  16  21  15 
Sun's  dec 90729 

1st  arc 16  08  00 

Half  eum 550900 

Half  difference  12  49  00 
2darc 27  08  00 


..Co-secant..  0.550515 

..Secant 0.0055-21 Sine 9.200666 


..Co-secant..  0.556036 Secant  .. 

. .  Co-sine 9.75GU03 Sine 

. . Sine 9.34W24 Co-sine . . 


3d  arc 20  36  00 


••Sine 9.659023 Secant  .. 

...Co  sine.. 


0.017449. . . .Secant  ....  0.017449 

9.914158 

9.989042 

0.050C36 


80  29 9.218115 

180  00        


4th  arc 99  31  00 Co-sine..  99  31 


5th  arc 78  55  00 

Marc 27  08  00.. 


..Secant 0.716164 

..Secant 0.05063S....  Co-secant..  0.340975 


Latitudein  ...    9  51  00  8.  .Co-sec 0.7C6800...  .Co-sine 9.993550 

Co-secant..  C.334525....Arc  A  27°  34' 


H.  M.  S. 

Arc  A  in  time 1  50  16 

Half  elapsed  time 1  05  25 

Apparent  time  at  ship 0  44  51 

Equation  time +        31 

Mean  time  at  ship 0  45  22 

Greenwich  mean  time. . .  .  1  26  06 


Longitude  in  time 0  40  44=10°  11' 


98  PRACTICAL  NAVIGATION. 

Ex.  2.  April  11,  1878,  A.M.  ship  time  at  both  observations,  in  latitude  by 
account  43 J 10'  N.,  and  longitude  G '  32'  W.,  when  a  chronometer  showed  9h: 
5S:n:36s.  A.M.  being  10m: 42s.  slow  of  Greenwich  mean  time,  the  altitude  of  the 
sun's  lower  limb  39 J  45' 50",  and  at  llh:4Sm:34s.  A.M.  By  the  same  chronom- 
eter, the  altitude  of  the  sun's  lower  limb  was  48J  15'  25",  the  sun  bearing  at  least 
altitude  S. E.|E.,  and  the  ship's  course  between  the  observations  Avas  N.E.^N, 
The  distance  run  being  14  miles;  the  height  of  the  eye  18  feet,  and  index  error 
2'  10"  to  subtract.  Required  the  true  latitude  and  longitude  of  the  ship,  at  the 
time  of  taking  the  greater  altitude. 

H.  M.  S.  „     ,     „ 

Apr.  11,  time  by  chr.  at  greater  alt .  11  48  34  A.M.     Sun's  dec.  Apr.  llth  8  22  29  N. 

120000  Cor.  for  G.  T..         0000 


Astronomical  time,  April  10th ....  23  48  34  Dec.  for  April  llth  8  22  29 

Chronometer  slow -f  10  42 

Taken  out  for  the  11  as  it  wants 

Mean  time  at  Greemvich  Apr.  10th  23  59  16  &««  «  minute  from  noon   of  tUat 

•  date. 

Sun's  bearing  Avhen  least  altitude  Avas  taken S.  E.  £  E  =  S    4  £  points  E. 

Ship's  course  between  the  observation N.  E.  £  N  =  S  12  £  points  E. 

Angle  between  the  ship's  course  and  sun's  bearing 8 ....  points. 

Distance  run  14  miles,  •with  angle  at  8  points,  heuce,  no  correction  for  change  of  position. 

First  observed  altitude 39  45  50     Second  observed  altitude 4°8  15  23 

Index  error —    2  10    Index  error —    2  10 

39  43  40  48  13  15 

Dip,  Table  VH ,  —  04  04    Dip —  04  C4 


39  39  36  48  09  1 1 

Refraction,  Table  VI —    108    Refraction —       51 

39  38  28  48  08  20 

Semi-diameter +  1550    Semi-diameter -f  1553 

True  altitude...                                   ..  39  f,4  27  Sun's  second  true  altitude...             ..482419 


o    /  //  &•  M.  s. 

First  true  alt. . .  39  54  27  Time  by  chr.  at  1st  alt.  9  5*  ?6  A.M. 

Second  true  alt.  48  24  19  Time  by  chr.  at  2nd  alt.  11  43  31  A.M. 

Sum 83  1846— Half  sum.  44°  09' 23"  Elapsed  time 1  4'J  54 

Half  elapsed  time 0  54  69=13°  44' 45" 

Difference 829  r,2-Half  dif.  4°  14' 56"  "'  - 


Half  elapsed  time..  13  44  45 Co-secant.  O.C23997 

Sun's  declination...    8  22  29. ...Secant ..  .  0.004666 Sine.  ..  9.162885 

Firstarc 133500 Co-secant.  0.6286H3...  Secant...  0.019351... . Secant.  0.012351 

Half  sum 440023 Co-sine.  .  9.855833 Sine 9.842946 

Half  difference 4  14  56 Sine 8 . 8(59863 Co-sine ..  9 . 998804 


Second  arc 13  04  00 Sine 9.354364 Secant...  0.011393 


Third  arc  42  48  CO Co-sine..  9.865494  

Fourtharc 812300 ...  Co-sine.  9.1752*5 


Fifth  arc 38  35  00.  ...Secant .  ..  0.106959.... 

Second  arc 13  04  00 Secant.  ..  0.011393 Co-secant  0.645729 


Latitude  In 49  35  N...... Co-secant.  0.118352.... Co-sine..  9.811655 


Co-secant  0 . 457384. . . .  20°^5/  arc  A. 


H.  M.   S. 

Arc  A  in  time 1  21  40 

Half  elapsed  time 0  54  59 


Time  from  noon,  April  llth 0  26  41 

24  00  00 


Apparent  time  at  ship,  April  10th 23  33  19 

Equation  of  time +     103 

Mean  time  at  sMp,  April  10th 23  34  22 

Mean  time  at  Greenwich,  April  ICth...  23  59  16 

Longitude  in  time 0  24  54.. Long.,  G°  13' 30"  W. 

NOTE.— Take  out  the  equation  for  the  llth  of  April.    NameUie  latitude  same  namt  as  latiwde 
ly  account, 


DOUBLE  ALTITUDE. 


99 


Ex.  3.  April  23,  1878,  A. M.  ship  time  at  greater,  and  P.M.  at  lesser  altitude, 
in  latitude  by  account  39°  30'  S.,  and  longitude  30°  12'  \V.  Time  by  chronom- 
eter, Hi:  36m:  15s.  P.M.,  which  was  fast  for  Greenwich  mean  time  7m:  15s.  when 
first' altitude  of  the  sun's  upper  limb  was  observed  to  be  38°  10'  30",  and  at  Gli: 
3m:36s.  P.M.  the  second  altitude  of  the  sun's  lower  limb  was  36°  20'  45".  Sun's 
bearing  N.  byW.f.  Ship's  course  between  the  observations  N.N.E.-iE.  Dis- 
tance rim  during  the  interval  10  miles.  Index  error  2'  30"  to  subtract.  Height 
cf  the  eye  22  feet.  Kequired  the  latitude  of  the  ship  at  the  time  of  taking  the 
greater  altitude. 


H.  M.  8. 

April  23,  chr. showed...  1  3G  15 
Fast  for  G.  M.  time —    1  15 

1  29  00 
24  00  00 


Sun's  dec.  April  23.... 12  34  56 
1  H 


Hourly  diff 


Correct  declination....  12  36  10 


49.85 
1,5 


24925 
4985 


G.  M.  time,  April  22.... 2.)  29  00 


6.0)7.4.775 
1'  14" 


Sun's  bearing  when  last  observation  was  taken _.N.byW.  %  W.=N.  1%  points  W. 

Ship's  course  during  the  elapsed  time N.N.E.  J$  E.=N.  2M  points  E. 

Angle  between  the  ship's  course  and  sun's  bearing 4^ 

The  angle  between  the  ship's  course  and  sun's  bearing  4?4  points  is  to  be  taken  as  a  course  in  Table 
III.,  and  the  distance  run  during  tlie  elapsed  time  (10  miles),  as  a  distance,  gi»es  in  the  latitude 
column,  C'  7"=6'  42,  whicliis  to  be  subtracted  from  the  less  altitude,  the  angle  being  less  than  eiyfit 
points,  and  the  less  altitude  having  been  taken  in  the  afternoon. 

UPPER  LIMB,  o      <•     ,//  LOWER    LIMB.  o      ,      „ 

First  obs.  alt 38103)  Second  obs.  alt b6  20  45 

Index  error —  ,2  30  Index  error —    2  30 

33  03  00  36  18  15 

Dip —    430  Dip —    430 

33  <  3  30  30  13  45 

Kef —    113  Kef —    118 

33  02  17  3(5  12  27 

Parallax +        08  Parallax +         8 

38  02  25  36  12  35 

Semi-diameter —1356  Semi-diameter +  1556 

True  altitude. ^..»^.^-^..—^ 37  46  29  True  altitude  sun's  center 3628  31 

.  Correct.on  for  change  of  position . .  —    6  42 

Sun's  correct  altitude 36  2)  49 

ALTITUDES.  TIMES. 

o     /   //  H.  M.  s. 

First  alt 37  40  29  1  3<>  15  P.M.    Greater  alt.  obs. 

Second  alt  ...  .3(5  21  49  3  03  36  P.M.    Less  alt.  obs. 

Sum 74  08  18— Half  sum.  37°  04' 09"      1  27  21 Elapsed  time. 

Difference 1  24  40— Half  diff. ..  0°  42' 20"      °  43  40 Half  elapsed  time ..10°  55' 

Half  elapsed  time fo  55 Co-secant..  0.7226G3 

Jjeclmatiou 1236 Secant 0.010587 Sine 9.338742 

Arc  first 1039 Co-secant..  0. 733250....  Secant. ..  0.007546...  Secant...  0.00734C 

Hulf  sum  of  alt 3704 Co-sine 9.9011)67 Sine 9.780133 

Half  diff.  of  alt 0  42 Sine 8.08<i9G5.  ...Co-sine..  9.9999C6 

Arc  second...  .    301 Sine 8.722182 Secant...  0.000009 


Arc  third 52  07 Co-sine..  9.788254 


Arcfourth 102  50  . . . = (180°    —   77°  10') Co-Bine,.  9,34(>288 

Arc  fifth 50  43.... Secant 0.19R489 

Arc  second 301 Secaut 0.000009 


LATITUDE  IN 39  13  S.. Co-secant. .  0.199098 


100 


PRACTICAL  "NAVIGATION. 


Ex.  4.  September  8,  1878,  A.M.,  at  ship  in  latitude  GO0  10'  S.  by  account,  and 
longitude  178°  45'  E.,  the  altitude  of  the  sun's  lower  limb  was  observed  to  be 
19°  42'  at  10h:04m:20s:  apparent  time,  the  sun's  center  bearing  N.N.E.  by  com- 
pass, and  at  Ih:  32m:  36s:  P.M.  by  same  chronometer,  the  second  altitude  was 
21°  08'  10"  (being  the  greater).  The  ship's  course  during  the  elapsed  time  was 
S.W.  by  S.,  and  the  distance  run  in  the  interval  was  31  miles.  Height  of  the 
eye  16  feet.  Required  the  latitude  of  the  ship  at  the  time  of  taking  the  greater 
altitude. 

H.  M.  8.  0    ,  „ 

Ap.  time  at  ship  at  greater  altitude.  13236P.M.    Sun's  dec.  Sept.  7th.  6  01  44     Hourly  dif.  56.23 
Long.  178°  45' E.  24  00  00  Correction —  1245  13.6 

253236  Correct  declin 5  48  59  N.  33738 

60)71500       Long,  in  time...  11  5500  E.  " 


=11   55        G.  M.T.  Sept.  7..13S736 


3G8G9 
5623 


bhip's  course  during  the  elapsed 
Angle  between  the  ship's  course 

To  be  taken  out  as  a  course,  Tab 

First  observed  altitude  (least)  .  . 
Dip  

time  was 

{ 

5."W.  by  S.=N!  13  points^ 

15  points. 
16 

1  point. 

and  sun's  be: 
le  II,  (and  di 

.  194200 
.  —   3  50 

iring  

[stance  31  miles)  

Second  observed  alt. 
Dip  , 

(greatest)..  .  .  2°1  08  10 
—   350 

Refraction  

Refraction  

It)  38  10 
.  —    2  40 

21  04  20 
—    2  27 

19  35  30 

.    +         8 

21  01  53 
-|-         8 

19  35  38 
Semi-diameter +1555 


21  02  01 
Semi-diameter +  15  55 


True  altitude 195133 

Correction  for  change  of  position.  —  30  24 

Correct  altitude ...  . .  1 9  21  09  A.M. 


True  altitude.... 21  17  56  P.M. 


NOTE. —  The  observation  being  in  the  forenoon, 
and  angle,  more  than  8  points,  subtract  the  correc- 
tion, 3U°  24'. 

TRUE  ALTITUDES. 

First  obs.  alt..l°9  2'l  09 
Sec'd  obs.  alt.. 21  17  56 


Sum 40  39  05— Half  Bum.  20°  19'  32" 

Difference...    .  1  56  57— Half  dif ..    0  58' 33" 


TIMES. 
E.  M.  s. 

10  04  20  A.M.  less  altitude  observed. 
(Add  12  hours..)  1  32  3G  P.M.  greater  altitude  obs. 

3 28  16.. Elapsed  time. 

1  44  08.  .Half  elap.  time,  26°  02'. 


Half  clapped  time..  2602 Co-secant .  0.357640 

Correct  declination.    549 Secant....  0.002242 


..Sine 9.C05805 


Arc  first 

Half  Burn  of  alt.. 
Half  dif.  of  ait... 

Arc  second... 


2554 Co-secant.  0. 353882.... Secant ..  0.045971 Secant..  0.045971 


20  19j£....Co-sine..  .  9.972081        Sine  .... 
0  58J$ Sine 8.230029 Co-sine 


9.540772 
9.999937 


205 Sine 8. 561992.... Secant ..  0.000287 


Arcthird 6716 Co-sine.  9.586967 

Arc  fourth 96  28= (180°— 83°  32') X3o-sine 

Arc  fifth 2912 Secant....  0.059025 

Arc  second ...    205 Secant 0.000287 

LATTTCDEIN 60  44  S.... Co-secant .  0.059312 


9.051776 


DOUBLE"  ALTITUDE. 


101 


Ex.  5.  September  9,  1878,  A.M.  at  ship  in  latitude  by  account  6°30'N.,  at 
ISh:  16m:  20s:  by  a  chronometer  showing  Greenwich  mean  time,  the  altitude  of 
the  sun's  lower  limb  was  35°  10'  30",  and  at  20h:  36:  20s:  by  the  same  chronom- 
eter the  altitude  was  69°  49'  30" ;  the  height  of  the  observer's  eye  18  feet.  Re- 
quired the  latitude  at  the  time  of  taking  the  greater  altitude. 

H.  M.   8.  o    /    //  // 

Gr.  mean  time  Sept  8.  .20  80  20  (at  greater  alt.)     Sun's  dec.  Sept.  9. .  6  16  33     Hourly  dif .  60.70 
=^=.  Cor.  for  ah: 24m 313  3.4 


Corrected  declin. . .  6  19  46  N. 


22G80 
17010 


60)19.2.780 


3f   -I  t\ff    I-OA 
la      .  I oU 

Correction  for  Zh.-llm:  from  noon  of  the  9th  to 
be  added,  as  the  declination  is  decreasing from  noon 
of  the  Stk,  ana  therefore  we  correct  for  the  nearest 
noon. 


First  obs.  alt.  Bun's  lower  limb 35  10  30  Second  observed  altitude 6°9  49  'M 

Dip —     404  Dip —    404 

35  06  26  69  45  26 

Refraction —    121  Refraction —       21 


Parallax. 


35  05  05  69  45  05 
+        08    Parallax +        03 

35  05  13  69  45  08 

Semi-diameter +  1555    Semi-diameter -f  1565 

Sun's  true  altitude  at  first  obs 35  21  C8  Second  true  altitude....                     ..  7001  03 


TEOE  ALTITUDES. 


First  iiltitude...  35  21 
Second  altitude.  70  01 


TIME  BY  CHHOXOMETEB. 
H.  M.  s. 
18  16  20 
20  36  20 


Sum 105  22— Half  sum  alt..  52°  41'      2  20  CO— Elapsed  time. 

1  10  Ou— Half  elap.  time=17°  SO' 
Difference 34  40— Half  dif.  alt..  17° 20' 


Half  elapsed  time. 
Sun's  declination  . 

Arcfir=t 

Half  sum  of  ait 

Half  dif.  of  alt... 


17  30 Co-secant .  0 . 521858 

5  20 Secant 0  001884 .Sine  ....  8.968249 

17  25 .Co-secant.  0  523742 Secant..  0. 020382....  Secant ..  0.020382 

6241 Co-sine..  .  9.782630 Sine 9.900529 

17  2i» Sine 9. 474115... .Co-sine  .  9.979816 


Arc  second. 
Arc  third... 


37  OCJj.... Sine 9. 780487.... Secant ..  0.098271 


3  54 Co-sine  .  9.998998 

When  latitude  and  declination  of  same  name,  '\ 
take  the  difference  between  third  and  fourth  [ 
arcs  for  fifth  arc.  ) 


Arc  fourth 84  24. 


.Co-Bine  .  8.988G31 


Arc  fifth 

Arc  second 


8020 Secant....  0.782391 

37  06 Secant....  0.098224 


Latitude  in 7  S4N....Co-sccaut .  0.880615 


XOTE.— The  sum  of  the  third  and  fourth  arcs  being  less  than  90°,  thisexample  admits  of  two 
answers.    Read  carefully  the  note  in  rules. 


102 


PRACTICAL  NAVIGATION. 


Ex.  6.  November  10,  1878,  in  latitude  by  account  32°  32'  K,  at  9h:  30m.  A.M. 
the  altitude  of  the  sun's  lower  limb  was  28°  14',  the  bearing  of  its  center  by  com- 
pass being  S.E4E.;  and  at  the  llh:  17m:  42s.  A.M.  the  altitude  of  the  upper  limb 
was  39°  08',  the  height  of  the  observer's  eye  being  18  feet,  and  the  ship's  course 
between  the  observations  S.  by  E.,  running  7  knots  per  hour;  required  the  lati- 
tude of  the  ship  at  the  time  of  the  greater  altitude. 


H.  M.  S.  0     ,    „ 

Timebychro 11  17  42A.M.    Sun's  declination  Nov.  10....  17  12  11.. S.  hourly  diff.  42" .08 

120000  Correction  for  42m:  18s —       29"  7 

M.  T.  G.  Nov.  9  ...  23  17  42  Correct  declination  Nov.  9 17  11  42  S.  ly'AoC, 

Sun's  bearing  at  first  observation S.E.^E.  or  S.4J6  points  E. 

Ship's  course  during  the  elapsed  time S.  by  E.  or  S.  1  point  E. 

Angle  between  the  ship's  course  and  sun's  bearing 33^  points. 

The  elapsed  time  between  the  observation  is  1?£  hours  nearly,  and  the  rate  of  sailing  7  miles 
per  hour;  that  will  give  the  distance  run  12  miles,  to  be  taken  out  as  in  example  3. 

First  obs.  alt.  sun's  lower  limb 2°8  14  00    Second  obs.  alt.  of  sun's  upper  limb. . .  39  08  66 

Dip  of  the  horizon —    4    4    Dip  of  horizon ,t.  4    4 

28  09  56  3D  03  50 

Refraction 147    Eefraction 110 

28  08  09  39  02  46 

Parallax 8    Parallax 7 

28  08  17  39  02  53 

Semi-diameter +1612    Semi-diameter —  1012 

True  alt.  sun's  center 28  24  29    True  alt.  sun's  center ~ . .  38  40  41 

Correction  for  change  of  position +918  irzzzzz: 

Sun's  corrected  alt ..  28  33  47 


TKUE  ALTITUDES. 


First  alt  .....  28  33  47..  Less  altitude. 
Second  alt..  38  46  41..  Greater  altitude. 


Sum  .........  67  20  28  ..  Half  sum  alt  .  33°40/24 


Difference...  10  12  54..  Half  diff.  alt..  5°  6'  27" 


TIMES. 
a.  M.  B. 

9  30  00  AM. 
11  17  42A.M. 

1  47  42  .  .  Elapsed  time. 

0  53  51..  Half  elapsed  time  =13°  27'  45" 


Half  elapsed  time..  1328 Co-secant..  0.632869.... 

Sun's  declination. ..  17  12 Secant 0.019870 Sine 9.470S63 

Arcfirst 12  51}$ Co-secant..  0.652739.... Secant...  0.011044.... Secant...  0.011044 

Half  sum  of  alt 3340 Co-sine....  9.920268....  Sine 9.743792 

Half  difference  alt.    506 Sine 8.949509.  ...Co-sine..  9.998277 


Arc  second 1927 Sine 9.522516 Secant...  0.025519 


Arcthird 5305 Co-sine..  9.778G32  

Arcfourth 10739 .=  (180°    —   72°  21') Co-sine..  9.481907 

Arc  fifth fi4  34 Secant 0.236755 

Arc  second 19  27 Secant 0.025519 

Latitude  in 33  09  N.. . .  Co-secant. .  0.262274 


DOUBLE  ALTITUDE.  103 

Ex.  7.  JulyTth,  1878,  in  latitude  by  account  58°  25'  N.  and  longitude  122° 
30'  W.  at  llh:02m:OOs:  A.M.  per  watch,  the  altitude  of  the  sun's  loM'er  limb  was 
52°  53',  and  at  lh:25m:OOs:  r.M.  the  altitude  was  52°  44',  the  sun  at  that  time 
bearing  S.W.  by  W.  by  compass;  height  of  the  observer's  eye  being  20  feet, 
and  the  ship's  course  during  the  elapsed  time  S.S.W.^W.,  the  distance  made  in 
the  interval  was  18  miles;  required  the  ship's  true  latitude  at  the  time  the 
greater  altitude  was  observed. 

,        j  Declination 22°  33' 36"  N. 

1  I  Latitude  in 57°  22'  N. 

Ex.  8.  August  30th,  1878,  in  latitude  12°  43'  S.  by  account,  and  longitude  24° 
15'  E.  time  by  watch,  lh:J3m:30s:  P.M.,  the  altitude  of  the  sun's  lower  limb  was 
66°  09'  30",  and  at  3h:15m:12s:  r.M  it  was  62°  00'  15",  bearing  at  that  time  N.  W. 
$W. ;  course  during  the  elapsed  time  S.W.  by  W.  and  distance  sailed  being  8 
miles;  height  of  the  observer's  eye,  28  feet;  required  the  true  latitude  at  the 
time  of  taking  the  greater  altitude. 

.        j  Declination 8°  58'  28"  N. 

Ans'  1  Latitude  in 11°  37'  S. 

Ex.  9.  November  llth,  1878,  in  latitude  by  account  32°  34'  N.  at  9h:30m:  A. 
M.,  the  altitude  of  the  sun's  lower  limb  was  28°  18',  bearing  by  compass  S.E.,  and 
at  llh:17m:42s:  A.M.,  the  second  altitude  of  the  sun's  tipper  limb  was  39°  10'; 
height  of  the  observer's  eye,  18  feet;  and  the  ship's  course  between  the  observa- 
tions was  S.  byE.;  distance  run  during  the  interval,  12  miles.  Required  the 
latitude  and  longitude  of  the  ship  at  the  time  of  taking  the  greater  altitude. 

(  Declination 17°  28'  24"  S. 

Ans.  \  Latitude  in 32J  51' N. 

(  Longitude  in. 3°  10°  15' W. 

Ex.  10.  February  25th,  1878,  latitude  in  by  account  49°  3G'  N.;  time  by  chro- 
nometer Oh:33m:OOs:  P.M.,  the  observed  altitude  of  the  sun's  lower  limb  was 28° 
53',  and  at  2h:43m:OOs:  P.M.,  by  the  same  chronometer,  the  second  altitude  was 
19°  14',  the  height  of  the  observer's  eye  being  14  feet.  Required  the  latitude 
and  longitude  in  at  the  time  of  taking  the  greater  altitude. 

(Declination 9°  01'  02"  S. 

Ans.  \  Latitude  in 51°  17'  N. 

( Longitude  in o}  12'  45"  E. 


104:      ,  PRACTICAL   NAVIGATION. 


TO  FIND  THE  LATITUDE  BY  THE  POLE  STAE. 

The  latitude  by  the  meridian  altitude  of  the  pole  star  can  be 
found  at  any  time  on  a  clear  night  in  the  northern  hemisphere,  by 
the  following  rules: 

First.  Correct  the  altitude  for  index  error,  if  any,  dip  of  the 
horizon  and  refraction;  after  being  thus  corrected,  the  altitude  is 
increased  if  the  star  is  below  the  pole,  or  decreased  if  the  star  is 
above  the  pole.  This  correction  is  found  in  Table  XV,  and  applied 
thus: 

Second.  Find  the  sun's  right  ascension  for  the  given  day  in  the 
Nautical  Almanac,  to  which  add  the  apparent  time  at  ship;  if  the 
sum  of  these  exceeds  24  houre,  reject  24  hours,  and  that  will  be  the 
right  ascension  of  the  meridian. 

Third.  Enter  Table  XV,  and  in  one  of  the  side  columns,  opposite 
in  the  center  column,  will  be  found  the  correction  in  degrees  and 
minutes. 

Fourth.  If  the  right  ascension  of  the  meridian  is  found  in  one  of 
the  right-hand  columns,  add  the  correction  to  the  altitude;  but  if 
found  in  one  of  the  left-hand  columns,  subtract  the  correction,  and 
you  have  the  latitude  to  be  named  North,  always. 

Ex.  1.  December  31,  1878,  mean  time  at  ship  lOh:  50m:  OOs.  P.M.,  in  longitude 
323  30'  \V.  The  observed  altitude  of  the  Pole  star  out  of  the  meridian  was 
40°  20'  10".  Index  error,  +  1'  10",  eye  20  feet.  Required  the  latitude  in. 

H.  M.  s.  0     /    // 

Sun's  right  ascen.,  Dec.  10. . .   18  42  49    Obs.  alt , 40  20  10 

Time  of  observation..  .  105000    Index  error. ..  +     1  10 


29  32  49  40  21  20 

24  00  00    Dip -  -    417 

Right  ascension  of  meridian .     5  32  49  40  17  13 

=   Ref —    1  08 

Stars  true  alt 40  1C  05 

Correction  for  table  XV —  36  00 


Latitude  in . .  39  40  05N. 


Ex.  2.  February  12,  1878,  mean  time  at  ship,  at  llh:09:OOs.  P.M.  in  longi- 
tude 35°  12'  W.  The  observed  altitude  of  the  Pole  star  was  41°  12'.  Required 
the  latitude.  Eye  17  feet. 

H.    M.   S.  0     ,     „ 

Sun's  right  ascension 21  44  07    Obs.  alt 41  12  00 

Time  of  obs 11  09  00  Dip —    3  57 

32  53  07  41  08  03 

24  00  00   Ref. .  —     1  05 


R.  A.  of  Meridian 8  53  07  41  06  58 

=    Correction +  36  00 

Latitude  in..  ..41  42  58N. 


LATITUDE  BY  THE  POLE  STAB. 


105 


Ex.  3.  September  10,  1878,  mean  time  at  ship  at  2h:30m:  los.  A.M.  in  longi- 
tude 30°  17'  W.  The  observed  altitude  of  the  Pole  star,  out  of  the  meridian 
was  54°  Off  30";  eye  18  feet;  required  the  latitude  in. 

H.  M.  S. 

Time  of  observation 2  30  15A.M.    Obs.  alt 64  00  30 

(Add  12  hours) 120000  Dip —    4    4 


14  30  15 
Sun's  R.  Ascension +11  14  42 


Ref 


53  56  26 
—        41 


25  44  57 
—24  00  00 


53  55  45 
Correction..  ,..—12300 


R.  A.  of  Meridian. .  1  44  57 


Latitude. . .  .52  32  45N. 


Ex.  4.  July  16,  1878,  mean  time  at  ship  at  4h:37m:  11s.  A.M.— longitude  18° 
30'  W.  The  observed  altitude  of  the  Pole  star  out  of  the  meridian  was  39°  54" 
20";  eye  at  16  feet;  index  error  +  5'  10";  required  the  latitude  in. 


Time  of  observation . , 


Sun's  R.  Ascension  . . , 


H.    M.    S. 

.     4  37  11A.M. 
+  12  00  00 


Obs.  alt 39  54  20 

Index  error +     510 


16  37  11 
+  7  42  33 


24  19  44 
—24  00  00 


Dip. 
Ref. 


39  59  30 
—    3  50 


39  55  40 
—     1  08 


R.  A.  of  Meridian..  0  19  44 


39  54  32 
Correction 1  29  00 

Latitude  in..  .  38  25  32X. 


Ex.  5.  August  31,  1878,  mean  time  at  2h:40in:20s:  A.M.  in  longitude  85° 
30'  E.;  the  observed  altitude  of  the  Pole  star  off  the  meridian  was  20°  10'  40". 
Index  error— 1' 10".  Eye  20  feet.  Required  the  latitude  in. 

Ahs.  Latitude  in,  18°  38'  38"  N. 

Ex.  6.  December  10,  1878,  mean  time  at  ship  at  2h:16:04s:  A.M.  in  longi- 
tude 76°  12'  E. ;  the  observed  altitude  of  the  Pole  star  off  the  meridian  was  47° 
50'  20".  Index  error -4'  05".  Eye  13  feet.  Required  the  latitude  in. 

Ans.  Latitude  in,  47°  48'  57"  N. 

Ex.  7.  March  6,  1878,  mean  time  at  ship  at  7h: 43m: 40s:  P.M.  in  longitude 
36°  58'  45"  W. ;  the  observed  altitude  of  the  Pole  star  off  the  meridian  was  44° 
30'  30".  Eye  20  feet.  Required  the  latitude  in. 

Ans.  Latitude  in,  44°  08'  14"  N. 

Ex.  8.  January  16,  1878,  mean  time  at  ship  at  9h:38m:OOs:  P.M.  in  longitude 
59°  15'  E.;  the  observed  altitude  of  the  Pole  star  off  the  meridian  was  67°  30'  22". 
Eye  20  feet.  Required  the  latitude  in. 

Ans.  Latitude  in,  66°  49'  41"  N. 


106  PRACTICAL  NAVIGATION. 


TO  FIND  THE  TIME  OF  A  STAR'S  PASSING  THE  MERIDIAN, 
ALSO,  ITS  APPROXIMATE  ALTITUDE. 

First.  Find  the  star's  right  ascension  as  given  in  pages  242  to 
245  in  the  American  Nautical  Almanac,  nest  the  sun's  right  ascen- 
sion in  page  one  for  the  month  in  the  Almanac. 

Second.  Subtract  the  sun's  right  ascension  from  the  star's  right 
ascension,  increasing  the  star's  right  ascension  by  24  hours  when 
the  sun's  right  ascension  is  greater  than  the  star's  right  ascension. 

Ex.  At  what  time  will  Arcturus  be  on  the  meridian  on  April  27,  1878. 

H.   M.    S. 

Right  ascension  of  Arcturus,  April  27 14  10  05 

Sun's  right  ascension,  April  27 2  15  06 


Time  of  Arcturus'  meridian  passage 11  54  59 

By  this  method  the  time  of  any  particular  star  passing  the  meridian 
can  be  found,  and  knowing  at  what  time  a  star  will  pass  the  me- 
ridian, and  having  its  approximate  altitude  at  that  time  (as  shown 
in  the  following  example)  there  will  be  no  difficulty  in  determining 
the  latitude. 

Third.  To  find  the  approximate  altitude  of  a  star,  subtract  the  lati- 
tude in  by  account  at  the  time  of  observation,  from  90°  which  will 
give  the  co-latitude  of  the  place  of  observation,  find  the  star's  de- 
clination in  Nautical  Almanac,  as  per  rule,  and  remember  that  the 
sign  thus  —  placed  before  the  declination  stands  for  south  declina- 
tion, and  thus  -f  stands  for  north  declination. 

Fourth.  If  the  co-latitude  and  the  star's  declination  are  of  the 
same  name,  take  their  sum,  but  if  contrary  names  take  their  differ- 
ence, for  the  altitude;  the  star  will  be  found  in  the  south  part  of  Ihe 
Heavens  when  the  latitude  is  north,  and  in  the  north  part  when  the 
latitude  is  south.  When  the  sum  of  the  co-latitude  and  the  star's 
declination  exceed  90°,  subtract  it  from  180°  and  the  remainder  will 
be  the  altitude,  but  in  this  case  the  star  will  be  found  in  the  north 
part  of  the  Heavens  in  north  latitude  and  in  the  south  part  when 
the  latitude  is  »;outh. 

Fifth.  To  find  the  star  from  its  approximate  altitude  and  meridian 
passage,  set  the  index  of  the  sextant  to  the  approximate  altitude, 
and  a  few  minutes  before  the  time  of  its  meridian  passage,  direct 
the  sight  towards  the  north  or  south  points  of  the  horizon  and  the 
reflected  image  of  the  star  will  be  perceived  in  the  horizon  glass, 
upon  or  near  the  horizon,  the  star  then  being  brought  in  contact 
•with  the  horizon  and  kept  so  until  it  arrives  at  its  greatest  or 


TIME  OF  A  STAIl'S  PASSING  THE  MEKIDIAN.  107 

meridian  altitude.  There  is  not  the  least  danger  of  mistaking  the 
star  as  no  two  stars  will  have  the  same  meridian  altitude  at  the  same 
time. 

NOTE. — The  best  time  for  obtaining  a  correct  altitude  of  a  star  is  at  twilight,  for  the  horizon 
Is  then  distinctly  visible,  and  the  latitude  thus  found  is  nearly  cs  true  as  that  obtained  by  an 
altitude  of  the  sun,  in  dark  nights,  and  in  consequence  of  the  obscurity  of  the  horizon  a  Isrge 
errcr  may  be  found  in  the  altitude;  to  counteract  this  the  latitude  should  be  found  from  an 
altitude  of  a  star  to  the  southward,  end  another  to  the  northward,  and  half  the  sum  of  the  two 
latitudes  thus  found  will  be  the  correct  latitude, 

Ex.  1.  February  27,  1878,  at  ship  in  latitude  by  account,  40°  50'  10"  N.,  re- 
quired the  time  of  the  meridian  passage  of  the  star  Aldebaran,  and  its  approxi- 
mate altitude. 

February  27.  Right  ascension  of  Aldebaran  from  page  242  Nauti-  IT.  M.  s. 

cal  Almanac 4  28  55 

Add  24  hours  as  the  snn?s  right  ascension  is  greater 24  00  00 


28  28  55 
Sun's  right  ascension  (page  1,  Nautical  Almanac) 22  41  41 


Time  of  Aldebaran  meridian  passage 5  47  14p.ai. 


Latitude  by  account 40  50  ION. 

90  00  00 


Co-latitude 49  09  50  N. 

Star's  declination,  Nautical  Almanac  page  242 16  05  45  + N. 


Approximate  altitude 65  15  35 

Set  the  index  of  the  sextant  to  this  altitude  and  sweep  the  horizon  to  the  southward, 
as  the  latitude  is  north,  and  the  star  will  be  distinctly  seen  near  the  horizon;  watch  it 
closely,  and  when  it  has  ceased  to  rise,  it  is  on  its  meridian,  then  apply  the  usual  rules 
to  find  the  latitude. 

Ex.  2.  March  21,  at  ship,  in  latitude  by  account,  1°  30'  25"  S.,  at  what  time 
will  the  star  Sirius  pass  the  meridian,  and  what  will  be  its  approximate  alti- 
tude ? 

H.  M.  s. 
March  21.  Sirius'  right  ascension 6  39  46 

Sun's  right  ascension 0    2  47 


Time  of  Sirius'  meridian  passage 6  36  59P.M. 


Latitude  in  by  account 1  30  25  S. 

90  00  00 


Co-latitude 88  29  35  S. 

Star's  declination 16  32  59— S. 


105  02  34 
180  00  00 

Approximate  altitude 74  57  26  Toward 

the  south 
KOTK.— See  page  71  for  finding  the  latitude  by  a  star. 


108  PBACTICAL  NAVIGATION. 

Ex.  3.  May  1,  1878,  at  ship,  in  latitude  by  account,  20°  00' 00"  N.,  required 
the  meridian  passage  of  the  star,  Vega,  and  its  approximate  altitude. 

May  21.  Vega  right  ascension 18  32  48 

Sun's  right  ascension 2  34  06 


15  58  43 
12  00  00 


Time  of  Vega  meridian  passage 3  58  43  A.M. 


Latitude  in  by  account 20  00  00  N. 

90  00  00 


Co-latitude 70  00  00  N. 

Star's  declination 38  40  16  +  N. 


108  40  16 
180  00  00 


Approximate  altitude  .................................  71  19 


TO  FIND  THE  TIME  AT  ANY  GIVEN  MERIDIAN  BY  THE 
SUN'S  ALTITUDE. 

Take  any  number  of  altitudes  with  their  corresponding  times  by 
watch,  or  chronometer,  when  the  sun  bears  as  nearly  east  or  west  as 
possible,  of  which  take  the  "  means,"  add  them  all  together  and  divide 
the  number  of  observations. 

To  these  means  of  the  altitudes  apply  the  corrections,  as  usual,  and 
get  the  true  altitude  of  the  sun's  centre. 

Take  the  sun's  declination  (page  2,  Nautical  Almanac),  and  cor- 
rect it  by  the  hourly  difference  for  the  mean  time  at  Greenwich,  and 
get  the  sun's  polar  distance,  adding  the  declination  to  90°  when 
the  latitude  and  declination  are  of  contrary  names;  subtracting  it 
from  90°  when  they  are  of  the  same  name,  N.  or  S. 

Correct  the  equation  (page  1,  Nautical  Almanac)  for  the  mean 
time  at  Greenwich. 

Add  together  the  sun's  polar  distance,  ship's  latitude  and  sun's 
true  altitude;  take  half  the  sum,  and,  lastly,  the  difference  between^ 
that  and  the  true  altitude;  call  this  the  remainder. 

Add  together  the  secant  of  the  latitude;  co-secant  of  the  polar  dis- 
tance; co-sine  of  the  half  sum;  sine  of  the  remainder;  and  the  sum, 
rejecting  tens  in  the  index,  will  be  the  log.  (Table  XVIII.)  answer- 
ing to  the  hour  angle  or  apparent  time,  from  noon,  at  which  the  ob- 
servation was  taken. 

If  the  observations  be  made  in  the  morning,  the  time  thus  found 


TO   FIND   THE   TIME  BY  THE   SUN7S  ALTITUDE. 


109 


must  be  taken  from  24  hours  to  obtain  the  apparent  time  from  the 
preceding  noon. 

To  ,the  apparent  time  thus  found,  apply  the  reduced  equation  of 
time,  by  addition  or  subtraction,  as  directed  at  the  head  of  its  column 
on  page  1  of  the  Nautical  Almanac,  and  the  sum  or  remainder  will 
be  the  mean  time  at  the  ship  or  place  of  observation.  Hence,  the 
error  of  the  watch  at  the  meridian  of  the  place  may  be  found  for 
both  apparent  and  mean  time. 

Ex.  1.  August  16th,  apparent  time  at  ship  4h:  42m:  06s:  in  latitude  36°  31'  N. 
and  longitude  by  account  152°  00'  E.,  the  observed  altitude  of  the  sun's  lower 
limb  was  23a  50'  24";  height  of  the  observer's  eye  being  18  feet.  Required  the 
true,  apparent  and  mean  time  at  ship,  and  the  error  of  the  watch. 


Apparent  time  at  ship,  August  16....    4  42  00 


Longitude 


152°  00' 
4 


6.0)60.8  00 


10h:08m. 


Longitude  in  time. 

Greenwich  apparent  time,  Aug.  15. 


24  00  00 
28  42  00 


10  03  00 


Sun's  dec.  Aug.  16..  13  43  02 
Cor.  for  5h :  26m 4  1C 


Hr.  dif.  47.46 
54 


Dec.  at  Gr.  M.  T...  IS  47  18 N. 
90  00  00 

Sun's  polar  distance  76  1 2  42 


18984 
2:i730 

6.0)25.6.281 
4'  16" 


Talce  the  declination  out  for  the  IGth  of  Autjwt, 
and  correct  it  for  5h:  Wm  ;  from  the  noon  of  the 
Kith,  towards  the  \5tli,  tht  Jint  beintj  the  nearest 
noon,  and  add  the  correction  as  the  declination  is 
decreasing,  tliat  will  give  the  declination  at  Green- 
wich mean  time  on  Auyust  15th. 


Observed  altitude  .....  23  50  24 
Dip  ..................  —    4  17 

23  46  07 
Correction  Table  XHI.  —    2  00 

23  44  07 
Sun's  semi-diameter.  .  .        15  50 


Sun's  true  altitude....  23  59  57 

Latitude  .............  36  31  00.  ...Secant 

Polar  distance  ........  761242  ____  Co-secant 

Sum  ................  2)136  43  39 

Half  sum  .............  68  21  49....  Co-sine 

Eemaiuder  ............  44  21  52.  ...Bine 


M.    s. 

Equation  of  time ..    4  05 . 56 
2.74 


4  03.30 


0.094915 
0.012699 


9.566691 
9.8446U 


Hourly  dif.  509 
54 

2036 
2545 


2". 7486 


H.  M.  S.  B.  It.  8. 

Apparent  time  at  Bhip.    44039  ____  Log.  Table  XVIII.  9.518919  ........................  44039 

Equation  of  time  ......          408  Time  by  watch  .............  44206 


Mean  time  at  ship  .....    44447 
Time  bywatch  ........    44206 

Watch  slow  for  M.  T.  .  .    0    2  41 


Watch  fatt  for  app.  time...  0    127 


110 


PRACTICAL  NAVIGATION. 


Ex.  2.  March  15,  1878,  A.M.  at  ship,  when  a  watch  showed  6h: 44m: 49s:  lati- 
tude in  at  time  of  observation  16°  29'  N.,  and  longitude  99°  30'  W.,  the  observed 
altitude  of  the  sun's  lower  limb  was  10°  36'  10";  the  error  of  the  sextant  was 
2'  50"  to  subtract;  eye  22  feet.  Required  the  apparent  and  mean  time  at  the 
meridian  of  ship,  and  the  error  of  the  watch. 


II.  M.  s. 

Time  by  watch  . .  G  44  49  A.  M. 
12  00  00 

Apparent  time  at 

ship,  March  14.184449 
Long,  in  time..    .   G  38  00  W. 


25  22  49 
24  00  00 

Apparent  time  at 

Greenwich  . ,    .   1  22  49 


Sun's  dec.  March  15. .     2  04  07    Hr.  dif.  59.18 


Correction  for  lh:  23m  —     1  17 


1.3 


Sun's    declination    at 
Green,  mean  time .     2  02  50  S. 
90  00  00 


17754 
5918 


Sun's  polar  distance..  92  02  50 


60)7.6.934 
1'16"934 


—    2  50 


—       .93 


10  33  20    Correct  equation.  9  03.62 

—    4  30  == 


10  28  50 
—    4  53 


10  23  57 
Sun's  semi-diameter. . +   1606 


10  40  03 


13 


Observed  altitude 10  36  10    Equation  of  time.  9  04.55  H.  dif.  717 

Index  error , 

Dip 

Correction  Table  XIII.. 


2151 
717 

9321 


Sun's  true  altitude 10  40  03 

Latitude 16  29  00 Secant 0.018226 

Polar  distance 92  02  50 Co-secant 0.00027S 

Sum 2)119  11  53 

Half  sum 59  35  56. . .  .Co-sine 9.704179 

Remainder 485553 Sine 9.877340 


H.  M.  S.    . 

Appparent  time  from  noon ...     5  12  59 ....  Log.  Table  XVIII 9 . 600023 

24  00  00  ===== 

H.  M.  s. 


Apparent  time  at  ship 18  47  01 18  47  01 

Equation  of  time +     9  03 Time  by  watch 18  44  49 

Mean  time  at  ship 18  56  04 Watch  slow  for  app.  time.     0    2  12 

Time  by  watch 18  44  49 

Watch  slow  for  mean  time  ..  „     0  11  15 


TO  FIND  THE  ERKOB  OF  A  WATCH.  Ill 


TO  FIND  THE  ERROR  OF  A  WATCH  OR  CHRONOMETER 
BY  EQUAL  ALTITUDES  OF  THE  SUN. 

Subtract  the  first  time  from  the  second,  for  the  interval. 

Add  the  two  times,  and  divide  the  sum  by  2,  for  the  middle  time 
by  chronometer.  Get  the  difference  between  the  declination  of  the 
day  before  and  day  after,  for  the  change  of  declination  in  two  days, 
and  multiply  the  difference  by  GO,  which  will  give  seconds. 

Correct  the  sun's  declination  for  the  Greenwich  time  and  date, 
and  the  longitude  in  time,  if  west,  it  is  the  Greenwich  time;  but  if 
east,  take  the  longitude  in  time  from  24  hours,  and  call  the  day  one 
back. 

Correct  the  equation  of  time  for  the  Greenwich  time,  as  usual; 
taking  it  out  of  page  2,  Nautical  Almanac.  From  Table  XVI.  take 
out  log.  A.  and  B.  for  the  interval,  and  place  the  log.  of  natural 
number  (Table  I.),  for  the  change  of  declination  in  two  days  under 
both  log.  A.  and  B.  The  log.  tangent  (Table  II.)  of  the  latitude  un- 
der log.  A.  and  log.  tangent  of  the  declination  under  log.  B. 

*See  note  for  Table  XVI. 

The  sum  of  the  first  three  logs,  is  the  log.  in  logarithms  of  num- 
bers (Table  I.)  of  the  first  part  of  the  equation  of  equal  altitudes, 
and  the  sum  of  the  last  three  logs.,  that  is,  log.  B.,  log.  of  change  of 
declination,  and  log.  tangent  (Table  II.)  of  the  corrected  declination, 
will  bo  the  second  part  of  the  equation  of  equal  altitudes. 

The  first  part  of  the  equation  is  additive  when  the  declination  is 
decreasing,  and  of  the  same  name  with  the  latitude,  or  increasing', 
and  of  a  different  name  from  the  latitude;  but  subtractive  when  the 
declination  is  increasing,  and  of  the  same  name  with  the  latitude, 
or  decreasing,  and  of  a  different  name  from  the  latitude. 

The  second  part  of  the  equation  is  additive  when  the  declination 
is  increasing,  but  subtractive  when  the  declination  is  decreasing. 

"When  both  parts  are  additive  or  subtractive,  get  the  sum  of  them 
and  apply  them  to  the  middle  time  by  chronometer  (according  to 
the  sign  -f  or  — ).  But  if  one  is  additive  and  the  other  subtractive, 
take  their  difference  and  apply  it  to  the  middle  time  by  chronometer, 
according  to  the  sign  of  the  greater. 

Apply  the  equation  of  time  corrected  for  longikide  to  the  apparent 
noon  at  place,  as  directed  at  head  of  column,  page  1  of  the  month 
Nautical  Almanac,  for  the  mean  time  at  place  of  observation. 

Get  the  difference  between  the  time  by  chronometer  at  apparent 
noon  and  mean  time  at  place,  and  call  the  chronometer  fast  or  slow, 
as  shown  by  the  times. 

NOTE.— Table  XVI.  contains  but  four  place  of  figures,  besides  the  index  figures;  therefore, 
In  taking  out  tlie  logarithms  from  Table  I.,  only  take  out  the  first  four  figures,  increasing  the 
fourth  figure  by  one  when  the  remaining  figures  exceed  CO.  Do  the  game  with  the  log.  taugeut. 


112 


PRACTICAL  NAVIGATION. 


EQUATIONS  OF  EQUAL  ALTITUDES. 

Ex.  1.  August  5,  1878,  in  latitude  37°  35' N.  and  longitude  60°00'"W.,  the 
following  times  were  noted  down  when  the  sun  had  equal  altitudes.     Requhed 
the  error  of  the  watch  for  mean  time  at  place  of  observation. 
A.M.  P.M. 

H.  M.  S.  H.  M.  S. 

7  25  40 1  33  06 

7  26  23 1  32  23 

7  27  06 1  31  40 


3)97  09 

Means 1  32  23 

Add  24  hours.. 24  00  00 


3)79  09 

jjeang  7  26  23 

Add  12  hours 12  00  00  

August  4 19  26  23  August  5 25  32  23 

H.  M.   S.  H.  M.  S. 

25  32  23  P.  M 25  32  23 

19  26  23  A.M 19  26  23 


Interval . . .     6  06  00 


Sum  of  times 2)44  58  46 

Middle  time  by  chronometer.  22  29  23 


Sun's  declination  August  4 17  13  41  N. 

Sun's  declination  August  6 16  41  08  N. 

Difference  of  declinations  in  two  days.     0  32  33 

x   CO 

In  seconds 1953 


Dec.  Aug.  5.  16  57  33  N.    H.  dif.  40."70 
Cor.  for  long.  —    2  40 

Reduced  dec.  16  54  53  N.          6)162"SO 


2'  40" 


M.      S. 

Eq.  of  time  Aug.  5.  5  46.73  H.  dif.  248 
Cor.  for  Ion.  in  time —    .99  4 


Red'd  eq.  of  time. .  5  45.74 


99.2 


Longitude 60°  00' 

4 

60)240   00 

4h:OOW. 

Interval  of  time  (Table  XVI).  Gh:06m:.  .Log.  A.  7.7719.. Opp.  Log.  B..  7.6156 
Change  of  declination  for  two 

days,  log.  of  numbers  Ta.  I.  1953.  .Log.  . .  3.2907.  .Same  Log. . .  .  3.2907 

Latitude  (Tangent  Table  II).       37° 35' 9.8863.  .Dec.  tan.  T. II.  9.4831 


+  S".S9 0.9489  

-2".45 Log.  0.3894 


First  part 

Second  part 

Equation  of  equal  altitudes. .         6". 44 

H.  M.     S.  H.   M.   S. 

Middle  time  by  chron 22  29  23.0.  .Middle  app.  time  at  ship.  . .  24  00  00 

Equation  of  equal  altitudes.  +          6.5.  .Equation  of  time -f-    545 

Time  by  chron.  at  ap.  noon.  22  29  29.5.  .Mean  middle  time  at  ship.  .  24    5  45 
Mean  middle  time  at  ship.  24  05  45 

Chron.  slow  for  mean  time .     1  36  16    at  place  of  observation. 


EQUATIONS  OP  EQUAL  ALTITUDES. 


113 


Ex.  2.  October  4,  1878,  in  latitude  39°  19'  S.  and  longitude  90''  00'  E.,  the 
following  times  were  noted  when  the  sun  had  equal  altitudes.  Required  the 
error  of  the  watch  for  mean  time  at  place  of  observation. 

A.M.  P.M. 

H.  M.  S.  H.  M.  S. 

7  00  05 11  50  03 

7  00  55 11  50  53 

7  01  30 11  51  34 


Add  12  hours.  . 
Octobers 


3)2  30 

7  00  50 
...12  00  00 


19  00  50 


3)152  30 

11  50  50 
Add  12  hours..  12  00  00 

October  3..     .  23  50  50 


H.  M.  S.  H.  M.  S. 

23  50  50  Second  time 23  50  50  A.M. 

19  00  50  First  time 19  00  50  A.M. 


Interval ...     4  50  00 


Sum  of  times 2)42  51  40 

Middle  time  by  chronometer.  21  25  50 


Declination  October  3 4  01  Ob*  S. 

Declination  October  5 4  47  27  S, 


Change  of  declination  in  two  days 4G  21 

x     60 


In  seconds. 


2781 


Declin.  Oct.  3. .  4  01  98   Hr.  dif.  58.06 
Cor.  for  18h.  ..+  1725  18 

Reduced  dec...  4  18  31 


46448 
5806 


90°  00' 
4 

)3GO 

Long,  in  time.    6h:00m. 
24h:00in, 


6,0)1045,08 
17'  25" 


18h:00m. 


M.    S. 

Equation  of  time.  10  57.41    Hr.  dif.  770 
+  13.86  v.  IS 

Correct  equation.  11  11.27  6]t>0 

770 

\60)13".860 

Take  the  longitude  in  time  from  24 
hours  as  the  ship  is  to  the  east  of  Green- 
wich, and  take  the  decimation  out  for  the 
3rd  of  October. 


Interval 4h: 50m:.  .Log .A. .  7.7541.  .Log.  B 7.C60f> 

Change  of  declin.  in  2  days. .  2781 .  .Log S.4442 .  3.4442 

Latitude 36"  19' S. .. Tangent  9.8663.  .Dea  T't  4°  19'  sisTTS 

First  part —  11". 60.. Leg 1.0646 

Second  part -f-    0".96 .   0.9P2G 

Equation  equal  altitudes. .  ..       10". 64 


H.  M.    s. 


H.  M.   S. 


11.  jYi  •   *3. 

Middle  time  by  chron 21  25  50.0.  .Mid.  ap.  time  at  ship  noon.  .  240000.0 

Equation  of  equal  altitudes.  -          10.6.  .Equation  of  time —  11  27.2 

Time  by  chron.  at  ap.  noon.  21  25  39.4.  .Mean  middle  time  at  ship.  .  23  48  32.S 
Mean  middle  time  at  ship,  23  48  32.8  — 


Chr.  slow  for  M.  T.  at  place.    2  22  53.4 
Nav.— 8 


114 


PRACTICAL  NAVIGATION. 


Ex.  3.  April  6,  1878,  in  latitude  32°  40'  S.  and  longitude  153"  00'  E.,  the  fol- 
lowing times  were  noted  when  the  sun  had  equal  altitudes.  Required  the  error 
of  the  watch  for  mean  time  at  place  of  observation. 

A.M.  P.M. 

H.  M.  S.  H.  M.  S. 

9  28  20 2  33  43 

9  29  01 2  33  02 

9  29  58 2  32  05 

9  30  56 2  31  07 

9  31  44 .  2  32  39 


Means 

Add  12  hours .  . 


5)149  59 

. . .  9  29  59 
. . . 12  00  00 

21  29  59  A.M. 


5)160  36 

Means 2  32  07 

Add  24  hours  ..24  00  00 


2G  32  07  P.M. 


II.  M.  S. 

First  time. .  2G  32  07  P.  M 

Second  time  21  29  59A.M... 


H.  M.  S. 
26  32  07 
21  29  59 


Interval . .       5  02  08 


Sum  of  times 2)48  0?  OG 

Middle  time  by  chronometer.  24  01  03 


Declination  April  5 6  08  03  N. 

Declination  April  7 6  53  21 

Difference  of  declination  in  two  days ....       45  18 

x   60 


In  seconds 2718 


Dec.  Aril  5.  G  08  03  N.  Hr.  dif.  56.89 


Cor.  13h:48m+  1305 
Reduced  dec.  6  21  08  N. 


13.8 


Longitude....  153°  00' E. 
4 


6,0)61,2   00 


45512 
170G7 
5689 

6,0)78,5,082 
13'  05" 


Long,  in  time  10h:12m: 
From  24  hours  24h:00m: 


Gr.  time  5th.  13h:48m: 


M.     S. 

Equation  of  time.  2  44  05    Hr.  dif.  728 
—  10  04  138 


Correct-equation.  23461 


5824 
2184 
728 

6,0)10,0464 


Interval  of  time  ........  .5h:02m:OSs:  .Log.  A  .  .  7.7566.  .Log.  B  ......  7.6546 

Change  of  dec.  in  2  days.  2718.Log.of  No.3.4342  ..............  3.4342 

Latitude  ...............         32°  40'  S.  .  Tangent  .   9.  8070  .  .  Dec.  tan.  6°  21'  9.  04(J4 


First  part 

Second  part 

Equation  of  equal  alt .... 


+  9".  95.  Log  .....  0.9978 
+  1".36.  .  .  .. 


H.    M.     S.  H.  M.    S. 

Middle  time  by  chron 24  0 1  03. 0 .  Mid.  ap .  time  at  ship  noon.  ..  24  00  00. 0 

Equation  of  equal  altitudes.   4-     0  11. 3.  Equation  of  time ..  +    234.6 

Time  by  chron.  at  ap.  noon.  24  01  14. 3. Mean  middle  time  at  ship.  . .  24  02  34.6 
Mean  middle  time  at  place.  24  02  34. 6 

Chronometer  slow..       ....     0    120.3 


SHIP'S  POSITION  FROM  TWO  BEARINGS.  115 


TO  FIND  THE  SHIP'S   POSITION  FKOM  TWO  BEAKINGS 
OF  THE  SAME  OBJECT. 

This  method  of  finding  the  position  of  the  ship  when  in  sight  of 
land,  by  two  bearings  of  the  same  object,  will  be  found  of  great 
value  when  a  cross-bearing  cannot  be  obtained: 

Select  an  object,  the  latitude  and  longitude  of  which  is  known; 
take  a  correct  bearing  of  it  by  the  compass  (apply  the  variation  and 
deviation  due  the  compass  bearing),  and  note  the  time  by  watch. 
After  the  bearing  has  altered  not  less  than  three  points,  take  a  sec- 
ond bearing,  and  note  the  time  by  watch.  Having  the  interval  of 
time  between  the  first  and  second  bearings,  and  the  rate  of  sailing 
per  hour,  the  distance  sailed  in  the  interval  of  time  between  the  first 
and  second  bearings,  and  the  rate  of  sailing  per  hour,  the  distance 
sailed  in  the  interval  may  easily  be  obtained,  and  the  ship's  correct 
latitude  and  longitude  found,  as  explained  in  the  following  example 
and  table: 

Ex.  1.  April  15.  at  8h.  P.M.,  a  light-house  bore  by  compass  N.\V.  ^  N.;  ship's 
course,  W. ;  sailing  at  the  rate  of  7  miles  per  hour  till  lOh:  P.M.,  when  the  same 
light  bore  N.N.E.  ^  E.     Required  her  distance  at  both  places: 
First  bear.,  N.W.  JN.  )  Second  bear.  N.N.E.  JE.  ) 

Course  west >  Angle  4J  pts.  Course  west >  Angle  10£  pts. 

Found  at  top  of  table.  }  Found  .at  side  of  the  table.  } 

With  4J  pts.  at  the  top  of  table,  and  10J  pts.  at  the  side  of  table, 

give  the  tabular  number 0  84 

Distance  sailed  in  2  hours +  14 


11  76 

The  tabular  number  multiplied  by  14,  the  distance  run  in  two  hours,  and  the 
two  right-hand  figures  struck  off  (being  .decimals)  gives  the  distance  off  at  lOh: 
P.M.,  11 J  miles. 

To  find  the  distance : 

The  first  angle  being..  4 ?3  pts    The  second  angle..  10 J$  pts.    The  tabular  number  Is ..    095 
Subtracted  f rom 16      „      Subtracted  from...  16       „       Distance  made — 14 


Taken  from  Bide  table. .  11 M          Taken  at  the  top . . .  6  M  380 


1330 

Gives  the  distance  at  8h:  P.M.,  13^  miles. 

Ex.  2.  At  5  o'clock  A.M.,  a  light-house  bore  by  compass  W.  by  S.  J  S.  Ship 
then  sailed  on  a  S.  \  W.  course,  at  the  rate  of  5J  knots  an  hour,  until  7  A.M., 
when  the  same  object  bore  N.W.  by  N.,  variation  \  point  west.  Required  the 
ship's  latitude  and  longitude  at  the  time  of  each  bearing. 

1st  bearing  W.  by  S.  %  S.  by  compass.  2d  bearing  N.W.  by  N.  by  compass. 

Corr.  for  M  pt.  W.  var.  is  W.S.W.)  Anc]efiTlts  Corr.  for  M  pt.  var.  N.  W.  M  N.)  ,„„,„  19V5  „,„ 

Course  S.  M  W.          „        South,    }  Ang]e6Pts-  Course true  S.  \  Angle  12M  pts' 

Tabular  number 97 

2  hours  and  5%  knots=  Distance  Bailed 11 

Distance  off  at  time  of  second  bearing  at  7  A.M 10  07  miles. 

Theop.  pt.to2dbear.  is  S.E.&S..dtet.lOJ<SmB.,  D.Lat..   0    8  S.  Dep.  6.7=D.  Long.  0    8  45  E. 
Latitude  of  light-house.  . .  40  24  N.  Loug  of  light 73  58  48  W, 

At  7  A.M.  the  latitude  of  the  ship  was 401GN.  Long 73  60    3  W. 


116  PEACTICAL  NAVIGATION. 

To  Find  the  Position  of  the  Ship  at  5  A.M.,  or  Time  of  First  Bearing. 

1st  Angle  was 6  points.    2 d  Angle  was 12  J$  points. 

Subtract  from 16       „        Subtract  from 16         „ 

Look  for 10  points  at  the  side  of  the  table,  and 3J£  at  top. 

Tabular  number 66 

Distance  Bailed 11 

Dist.  >lf  at  time  of  1st  bear.  5  A.M 7.26',  or  7!4  miles,  nearly. 

Theop.  pt.  to  1st  bear.  isE.N.E.,dist.  7%  gives  Dif.  Lat.  .  0    3  N.  Dep.6.7=D.  Long.    0    8  45  E. 
Latitude  of  light-house 40  24  N.  Lon. .  73  58  48  W. 


At  5  A.M.  the  latitude  of  the  ship  was 40  27  N.  Lon.. 73  56    8  W. 


The  ship  having  made  her  true  south  course,  she  has  sailed  on  the  meridian  of 
73°  50'  3"  west,  and  was  in  the  same  longitude  at  7  A.M.  as  at  5  A.M.  and  her 
difference  of  latitude  is  equal  to  the  distance  sailed. 

Ex.  3.  At  noon  a  point  of  land  bore  SE.  by  E.  by  compass.  Ship  then  sailed 
on  a  south  course,  at  the  rate  of  10  knots  an  hour,  until  4  P.M.,  at  which  time 
the  same  point  of  land  bore  N.  E.  by  E.  %  E. ,  the  magnetic  variation  here  being 
1^  points  westerly.  Required  the  latitude  and  longitude  of  the  ship  at  the  time 
of  each  bearing. 

The  1st  Bear.  SE.  by  E.  by  compass.  2d  Bear.  N.E.  by  E.  %  E.  by  compass. 

Cor.forl^pts.  W.var.=E.byS.J$S.l   .        -    t    Cor.  forlJS  pts.  var.=N.E.       )   .      ,     -   ^     . 
Course  south,  corr.=S.  by  E.  %  E.     }  Ang'5  pts'True  course. . .  .8.  by  E.  K  E.  j  Angle  10^  Pts' 

Tabular  number 0.94 

4  hours  at  10  knots 40 

Dist.  off  at  the  time  of  the  2d  bearing,  at  4  P.M 37.CO  miles. 

Theop. pt. to 2dbear.isS.W.dis.37J<s  mis.,  givesD.Lat.  0  2'e  SoS.Dep.  26.5=D.Long.  °0  27  40W. 
Latitude  of  NW.  point  of  land 1712    0  N.  and  Lon 2519    OW. 


At  4  P.M.  latitude  of  the  ship  was 16  45  SON.  and  Lon 23  46  50W. 


To  Find  the  Position  of  Shi})  af  Noon,  or  Time  of  First  Bearing. 

Thelst  Angle  was...  5  points.        2d  Angle  was....  10%  points. 

Subtract  from 16      ;<  Subtract  from.  ..16         "  )  Tabular  No...  1.00 

}  Dist.  Bailed...      40 
11  pts.  at  the  side  of  table,  and.  5%  at  the  top.) 

Dist  off  at  the  time  of  1st  bearing,  or  noon 40.00  miles. 

Theop.  pt.  tolstbear.isW.byN.JSN.,  dist.  40=D.Lat..  0  11  3'<3N.  Dep.  38.3W.  D.Lon.  0  40  W. 
Lat.  N.W.  point  of  land  is 1712    ON.  Lon..2519W. 


Lat.  of  the  ship  at  noou  was 17  23  36  N.  Lon..2359W. 


SHIP'S  POSITION  FEOM  TWO  BEARINGS. 


117 


TABLE  FOR  FINDING  THE  DISTANCE  OF  AN  OBJECT 
BY  TWO  BEARINGS,  AND  THE  DISTANCE  BETWEEN 
THEM. 

First.  To  find  the  distance  of  the  object  when  the  last  bearing  was 
taken,  enter  the  table  with  the  number  of  points  at  the  top,  con- 
tained between  the  first  bearing  and  the  ship's  head,  and  the  num- 
ber of  pointsat  the  side  contained  between  the  second  bearing  and 
the  ship's  head.  At  the  angle  of  meeting  take  out  the  tabular  num- 
ber which  multiply  by  the  number  of  miles  of  distance  made  good  by 
the  ship.  The  result  is  the  distance  in  miles  off  shore  at  the  time  the 
last  bearing  was  taken. 

Second.  To  find  the  distance  when  the  first  bearing  was  observed, 
enter  the  table  with  the  difference  between  these  bearings  and  1 6 
points;  the  second  bearing  in  this  case  must  be  taken  from  the  top, 
and  the  first  bearing  from  the  side  column.  Take  out  the  tabular 
number  corresponding  and  multiply  it  by  thje  number  of  miles  of 
distance  made  good  by  the  ship.  The  result  is  the  distance  of  the 
ship  off  shore  at  the  time  of  the  first  bearing. 


Difference 

DIFFERENCE  BETWEEN  THE  COURSE  AND  THE  FIRsr  BEARING. 

between  the 

course  and 

2nd  bearing. 

POINTS  OF  THE  COMPASS. 

POINTS. 

2 

2% 

3 

3% 

4 

4}* 

5 

5H 

6 

6J$ 

7 

7H 

8 

8J$ 

9 

9)3 

10 

3% 

1.00 

4 

1.1(1 

4J$ 

0.81 

1.23 

5 

0.69 

1.00 

1.45 

5% 

0.00 

0.85 

1.17 

1.C6 

6 

0.54 

0.74 

1.00 

1.35 

1.85 

6* 

0.49 

0.67 

0.88 

1.14  l.EO 

2.02 

7 

0  4fi 

0  61 

0  79 

1.00 

1  «7 

1  ,64 

2,17 

7* 

0.43 

0.57 

0.72 

0.90ll.ll 

1.39 

1.77 

2.30 

8 

0.41 

0.53 

0.67 

0.82 

1.00 

1.22 

1.50 

1  87 

2.41 

SJ$* 

0.40 

0.51 

0.63 

0.7fi 

0  92 

1.09 

1.31 

1.58 

1.96 

2.50 

9 

0  39 

0  49 

0  f.O 

0.79 

0.85 

1  ,01) 

1.18 

1  39 

1.662.03 

2.66 

9& 

0.38 

0.48 

0.58 

0.69 

0.800.93 

1.08 

1.25 

1.461.72 

2.08 

2.60 

10 

0.3ft 

(i.47 

01.67 

11.66 

0.76 

O.S)- 

1.00 

1   14 

1.31  1.51 

1.76 

2.11  2.61 

10% 

0.38 

0.47 

0.56 

0.65 

0.74,0  84 

0.94 

1.06 

1.191.35 

1.53 

1.792.12 

2.60 

11 

0.39 

0.47 

o.ro  0.  r.4 

0.720.81 

0.90 

1.00 

1.11  1.24 

1.39 

1.571.80 

2.11 

2.66 

11M 
19 

0.40 
0.41 

0.48 
0.49 

0.560.63 
0.570.64 

0.710.79 

0.71  0.78 

0.87 
0.85 

0.95 
0.92 

1.05  1.15 
1.001.08 

1.27 
1.18 

1.41  1.58 
1.291.41 

1.792.08 
1.57  1.76 

2.50 
2.03 

2.41 

1254 

0.43 

0.51 

0.58 

0.650.71 

0.77 

0.83 

0.90 

0.97 

1.03 

1.11 

1.29 

1.29 

1.41 

1.35 

1.72 

1.96 

118  PRACTICAL  NAVIGATION. 


EXPLANATIONS  OF  THE  TABLES. 

TABLE  I. — Logarithms  of  numbers. 

The  decimal  point  separates  the  two  parts  of  a  logarithm,  the  in- 
teger before  it,  called  the  index,  and  the  decimal  part  after  it. 

The  index  is  governed  by  the  number  of  figures  in  the  whole 
number,  being  always  one  less  than  this  number.  The  index  of  12 
is  1;  of  999,  it  is  2;  1999,  it  is  3. 

If  the  number  is  a  mixed  decimal,  the  decimal  is  not  taken  into 
account  in  finding  the  index,  the  whole  part  only  being  used.  In- 
dex of  23.45  is  one;  of  235.507  is  2.  If  the  number  consists  of  a 
decimal  only,  count  the  number  of  ciphers  before  the  first  figure, 
and  then  subtract  this  number  from  9  for  the  index.  The  index  of 
.45  is  7;  of  .045  is  8;  of  .000045  is  5. 

To  find  the  logarithm  of  a  natural  number,  If  the  number  has 
only  one  or  two  places  of  figures  in  the  whole  part,  look  in  the  first 
page  of  logarithms,  and  in  the  column  marked  "  No."  at  the  top, 
until  the  required  number  is  found;  the  corresponding  logarithm, 
with  its  index,  will  be  found  in  the  first  column  on  the  right,  and 
opposite  the  number.  The  log  of  75  is  1.875061;  of  99  is  1.905635. 

If  the  number  is  of  three  figures,  look  in  the  column  of  numbers 
for  it,  and  then  under  the  column  marked  "  0  "  at  the  top  will  be 
the  required  logarithm.  The  log.  of  158  is  2.198657. 

If  the  number  is  of  four  figures,  find  the  first  three  in  the  left- 
hand  column,  and  the  fourth  at  the  top  of  the  page.  Under  the 
fourth  and  opposite  the  first  three  figures  will  be  the  required  loga- 
rithm. The  logarithm  of  158.4  is  3.200029. 

If  ihe  number  is  of  more  figures  than  four,  find  the  log.  of  the 
first  four,  then  multiply  the  difference,  opposite  in  the  column 
marked  "  Dif./'  by  the  figures  which  follow  the  first  four,  point  off 
as  many  places  from  the  right  as  there  were  figures  in  the  multiplier, 
add  the  remaining  figures  to  tlie  log.  first  found;  this  will  give  the 
true  logarithm. 

Find  the  log  of  519468:  log  of  first  four  figures  is 5.715502 

The  difference,is  84,  which,  multiplied  by  68,  gives 57 

Log  of  519468 5.715559 

84 
G8 

672 
504 

57.12  Cor. 


EXPLANATIONS  OF  THE  TABLES.  119 

Find  the  log  of  4496345:  log  of  first  four  figures  is 6.652826 

Difference,  97,  multiplied  by  345,  gives 33 

Log  of  4496345  is G.652859 

345 

97 

2415 
3105 


33.467  Cor. 

If  the  number  is  a  mixed  decimal,  find  same  as  if  it  was  a  whole 
number,  and  point  off  for  the  whole  part  only,  Log.  of  51.94  is 
1.715502;  of  4496343,  is  2.652859. 

If  the  number  is  a  decimal  only,  find  the  decimal  part  of  the  loga- 
rithm in  the  same  way  as  if  it  was  a  whole  number;  then  prefix  the 
index,  which  is  9  less  the  number  of  ciphers  before  the  first  figure. 
The  log.  of  .2641  is  9.421768;  the  log.  of  .002641  is  7.421768;  the 
log  of  .00002641  is  5.421768. 

To  find  the  natural  number  corresponding  to  any  logarithm: 

If  the  index  is  3 ,  the  required  number  will  have  four  figures  in  its 
whole  part.  Look  in  the  columns  of  logarithms  for  the  decimal 
part  of  the  logarithm,  and  find  the  logarithm  that  is  nearest  to  the 
given  logarithm;  take  the  three  figures  in  the  column  of  numbers 
opposite,  and  the  figure  at  the  top  of  the  column  in  which  the  loga- 
rithm lies.  This  will  be  the  required  number. 

Find  the  number  corresponding  to  log.  3.421770.  Opposite  to 
421768  (the  nearest  log.)  is  264,  and  over  it  is  1.  The  number  cor- 
responding to  3.421770  is  2641. 

If  the  index  is1 4  or  over,  find  the  log.  which  is  next  less  than  the 
given  log;  take  the  three  figures  opposite  and  the  one  over,  as  the 
first  four  figures  of  the  required  number.  Then  take  the  difference 
between  that  log.  nearest  the  given  log.  and  the  given  log. ,  annex  as 
many  ciphers  as  there  are  figures  required  in  the  number  to  be 
found,  and  divide  by  the  difference  opposite  in  the  "Dif."  column. 

From  the  logarithm  5.879242  find  the  number  corresponding.  The  first  four 
figures  are  7572;  the  difference  between  the  given  and  required  log.  is  31;  the 
difference  from  the  "Dif."  column  is  57. 

57)3100(54    The  number,  then,  is  757254. 

285 

250 

228 

If  the  log.  is  that  of  a  decimal,  such  as  9.681241,  find  the  num- 
ber just  as  if  were  a  whole  number,  480,  and  point  off  for  the  index 
9,  the  whole  as  a  decimal;  for  the  index  8,  prefix  0  and  point>off  the 
whole  as  a  decimal. 

f9.G81241 480^1 

T  8.681241 0480    XT      ,        ~  ,. 

Logs..  •(  7  (;81.24i  .00480  (  Numlt)crs  Corresponding. 

1 6.681241 !!  !  .000480 J 


120  PRACTICAL  NAVIGATION. 

TABLE  II.  —  To  find  the  log.  sine,  tangent,  etc.,  of  any  arc  or  angle,  in 
degrees  and  minutes. 

If  the  number  of  degrees  is  under  45,  they  will  be  found  at  the 
top  of  the  page,  and  the  minutes  in  the  left-hand  column  of  the 
page,  marked  "  M."  at  the  top  and  bottom;  the  required  logarithm 
•will  be  found  opposite  the  minutes,  and  in  the  column  with  the 
name  of  the  function  that  you  want  to  find  at  the  top.  But  if  the 
number  of  degrees  is  over  45,  they  will  be  found  at  the  bottom  of 
the  page,  with  the  minutes  in  the  right-hand  side  column  of  the  page, 
marked  "  M."  at  bottom  and  top;  opposite  the  minutes,  and  in  the 
column  with  the  name  of  the  required  function  at  the  bottom,  will 
be  found  the  required  logarithm.  If  it  is  required  to  find  the  log. 
co-sine  of  9°  51',  look  for  the  page  marked  with  9°  at  the  top,  and 
then  down  the  side  column  for  51';  opposite  to  this,  and  in  the 
column  marked  "  Co-sine  "  at  the  top,  will  be  found  9.993550,  which 
is  the  log.  co-sine  of  9°  51'.  The  log.  tangent  of  80°  IT  is  found  in 
the  same  way,  with  the  80  degrees  at  the  bottom  of  the  page,  the 
minutes  in  the  right-hand  side  column,  and  in  the  column  marked 
""Tang."  at  the  bottom;  it  is  10.761880. 

When  the  given  degrees  exceed  90,  they  are  to  be  subtracted  from 
180  degrees,  and  the  logarithm  of  the  remainder  taken  out,  as  before. 
Or  the  logarithmic  sine,  tangent,  etc.,  of  an  arc  more  than  90  is  the 
logarithmic  co-sine,  co-tangent,  etc.,  of  its  excess  above  90  degrees. 

Examples: 


.  .  .  36° 

Log.  to  6  places.         Log.  to  r-  places. 
32'     97.74729         9.77473 
18      9.681443         9.68144 
17       10.143263          lO.mQfi 

co-sine  of  

...61 

...54 

co-taugent  of  .  .. 
secant  of  

...42 
...  19 

50       

10.032877 

10.03288 

27       
33      
36) 
21       

36) 

10.025519 
10.025519 

9.976702 

lu.02552 
10.02S52 

9.97670 

co-secant  of.  ... 

...70 

sine,  of  

.  .  .  108 

...71 

..  18 

To  find  the  log.  ,  sine,  co-sine,  secant,  etc.  ,  of  any  arc  or  angle,  in  de- 

grees, minutes  and  seconds. 

Take  the  difference  between  the  logs,  for  the  given  minutes  and 
the  next  higher  number  of  minutes;  multiply  this  difference  by  the 
given  number  of  seconds,  and  divide  by  GO;  add  the  quotient  to  the 
log.  found  for  degrees  and  minutes,  in  the  case  of  sines,  tangents 
and  secants;  subtract  it  in  the  case  of  co-sines,  co-secant  and  co- 
tangent. For  example. 


EXPLANATIONS  OF  THE  TABLES.  121 

Required  the  log.  secant  for  32°  44'  34". 

The  log.  secant  for  32°  44'  is 10.075103  10.075103 

And  for  32J  45' is 10.075184  +  46 

Difference 81  Correct  log.  .10.075149 

x  34"  ' 


324 


60)275.4 
Correction 45.54 


Call  the  correction  46,  as  there  is  54  over,  and  add  it  to  the  log.  secant  of 
32°  44'  and  the  correct  log.  secant  will  be  for  32°  44'  34" 10.075149. 

Required  the  log.  co-sine  to  seconds  for  81°  32'  19". 

The  co-sine  for  81°  32'  is 9.168008  9.168008 

And  for  81°  33'  is 9. 167159    Correction  . .          269 

Difference 849    Correct  log.  .9.167739 

x   19  

7641 
849 


60)1613.1 
Correction.,  268.51 


To  find  the  arc  or  angle,  in  degrees  and  minutes,  which  corres- 
ponds the  nearest  to  any  given  logarithmic  sine,  tangent,  secant,  etc. : 

Look  in  the  column  marked  at  the  top  or  bottom  with  the  name 
of  the  given  logarithm,  and  find  the  logarithm  which  agrees  the 
nearest  with  the  given  logarithm;  then,  if  the  name  at  the  top 
of  the  column  corresponds  with  the  name  of  the  given  logarithm, 
take  the  degrees  from  the  top  of  the  page  and  the  minutes  (opposite 
the  nearest  logarithm)  in  the  left-hand  side  column;  but  if  the  name 
at  the  bottom  of  the  page  corresponds  with  that  of  the  given  log., 
take  the  degrees  from  the  bottom  of  the  page,  and  the  minutes  (op- 
posite the  nearest  logarithm)  in  the  right-hand  side  column. 

Required  the  arc  corresponding  to  log.  sine  9.595435.  The  near- 
est log.  is  9.595432;  the  arc  23°  at  the  top  of  the  page,  and  12"in 
the  left-hand  side  column.  Log.  sine  9.595435=23°  12'. 

Required  the  arc  corresponding  to  log.  co-secant,  10.044160.  The 
nearest  logarithm  in  the  co-secant  column  is  10. 044151;  the  arc  is 
64°,  from  the  bottom  of  the  page,  and  36'  from  the  right-hand  side 
column.  Log.  co-secant  10.044161=64°  36'. 

TABLES  III.  AND  IV. — Difference  of  latitude  and  departure  for  })oints 

and  degrees. 

These  tables  are  the  same  except  one  contains  points  and  the  other 
degrees.  The  difference  of  latitude  and  departure  are  in  miles  and 
tenths  for  distances  of  less  than  300  miles.  The  courses  are  set 


122  PRACTICAL  NAVIGATION. 

down  in  points  and  degrees,  at  the  top  of  the  pages,  if  they  are  less 
than  4  pts.  or  45°;  but  the  courses  are  at  the  bottom  of  the  pages 
if  they  are  over  4  pts.  or  45°.  The  distances  are  in  the  column 
marked  "  Dist."  at  the  top  and  bottom;  opposite  to  these  distances, 
and  to  the  right  of  them,  are  the  difference  of  latitude  and  depar- 
ture. If  the  courses  are  under  45°,  the  "Lat."  and  "Dep."  are 
marked  at  the  top  of  the  columns.  But  if  the  courses  are  over  4 pts. 
or  45°,  the  "Lat."  and  "Dep."  are  at  the  bottom  of  the  columns; 
that  is,  if  the  course  is  at  the  bottom,  read  the  column  from  the 
bottom;  but  if  the  course  is  at  the  top,  read  the  columns  from  the 
top. 

TABLE  V. — Table  of  meridional  parts. 

This  table  is  used  in  solving  problems  by  Mercator's  sailing.  The 
meridional  parts  are  found  in  the  columns  with  the  degrees  at  the 
top  and  bottom  of  the  pages,  and  the  minutes  at  the  sides.  It  is 
also  used  in  Mercator's  projections  in  constructing  charts.  The 
meridional  part  corresponding  to  37°  18'  is  2415. 

TABLES  VI. ,  VII. ,  VIII. — Refraction,  dip  and  parallax  tables. 

These  are  to  be  applied  to  all  observed  altitudes.  Kefraction  is 
subtractive  from  the  observed  altitude  and  must  be  taken  out  for  the 
altitude  which  is  nearest  the  given  one.  Dip  is  subtractive  from  a 
fore  observation  and  additive  to  a  back  one.  It  is  given  to  100  feet 
height  of  the  eye.  Parallax  is  always  additive  and  must  be  taken 
out  to  the  nearest  degree. 

TABLE  XI. — For  reducing  longitude  into  time,  and  the  contrary. 

This  table  has"  been  added  to  quicken  the  reduction  of  degrees, 
etc.,  of  longitude  into  time,  or  of  hours,  etc.,  into  longitude.  Now 
suppose  you  want  to  convert  160°  20'  into  time,  first  look  in  the 
column  marked  degrees  until  you  come  to  160°,  then  in  next  column 
on  the  right  hand  and  directly  opposite  1GO°  you  will  see  10h:40m: 
which  is  equal  in  time  to  160°,  then  in  the  seventh  column  marked 
minutes  of  degrees  you  will  find  20  minutes,  and  directly  opposite 
in  the  next  column  on  the  right  hand  you  will  see  1m:  20s:  which 
added  to  1  Oh: 40m:  will  make  10h:41m:20s:  in  time,  which  is  equal 
1GO°  20'  of  longitude. 

Ex.  1.  Required  the  degrees,  etc.,  corresponding  to  8h:32m:45s. 

H.  M.  s.          0      , 

Longitude  answering  to 8  32  45  is  128  00 

Longitude  answering  to 45  is  3 

Hence  the  longitude  answering  to ...  8  32  46  is  128  03 


EXPLANATIONS  OP  THE  TABLES.  123 

TABLE  XII. — For  reducing  the  sun's  declination  to  noon  at  any  given 

meridian,  and  to  any  time  at  the  meridian  of  Greenwich. 
This  table  contains  the  corrections  to  be  applied  to  the  sun's 
declination  as  given  in  the  Nautical  Almanac;  which  is  computed 
for  apparent  or  mean  noon  at  Greenwich;  it  is  to  be  entered  with 
the  declination  for  noon  of  the  given  day  as  found  in  page  one  or 
two  of  the  Nautical  Almanac,  at  the  top,  and  the  longitude  of  the 
place  or  time  at  Greenwich,  in  the  side  columns;  corresponding  to 
these  will  be  found  the  minutes  and  seconds  to  be  applied  to  the 
above  declination  by  addition  or  subtraction,  as  directed  at  the  head 
of  the  column  table;  that  is,  when  the  declination  is  increasing,  the 
correction  to  be  added  in  west  longitude,  but  to  be  subtracted  in  east 
longitude,  or  to  be  added  for  Greenwich  time;  but  when  the  declin- 
ation is  decreasing  the  correction  is  to  be  subtracted  in  west  longi- 
tude but  to  be  added  in  east  longitude,  or  to  be  subtracted  for 
Greenwich  time.  When  the  declination  and  longitude,  or  time  at 
Greenwich,  are  not  nearly  found  in  the  table,  proportional  parts 
may  be  used.  When  the  given  time  at  the  meridian  of  Greenwich 
exceeds  12  hours,  the  correction  must  be  taken  out  twice  as  in  ex- 
ample three.  It  must  be  observed  that  this  table  is  subject  to  an 
error  of  a  few  seconds,  from  the  sun's  unequal  motion  in  the  elliptic; 
but  it  is  nevertheless  in  general,  sufficiently  exact  for  observations 
taken  at  sea. 

Ex.  1.  Required  the  sun's  declination  at  apparent  noon  on  August  17,  1877, 
in  longitude  122°  21'  west. 

Sun's  declination  «at  apparent  noon  by  p.  1  N.  A.  (decreasing) 21  09  38  N. 

Correction  for  longitude  122J  21'  W -     3  44 

Sun's  declination  when  passing  the  meridian  of  the  given  place 21  05  44  N. 

Ex.  2.  Required  the  sun's  declination  on  Juue  12,  1877,  at  Gh:24m:  apparent 
time  at  Greenwich. 

Sun's  dec.  on  June  12th  at  apparent  noon,  p.  1  N.  A.  (increasing). .  23  11  18  N. 
Correction  Gh:  24m:  apparent  time +         54 

Sun's  declination  at  Greenwich  time ' 23  12  12  N. 

TABLE  XIII. — Corrections  for  the  apparent  altitudes  of  sun  and  stars. 
Enter  the  columns  marked  at  the  top  "  App.  Alt.,"  with  the  ap- 
parent altitude  which  you  have,  and  find  the  nearest  arc  to  the  one 
you  have.  Take  the  Correction  opposite.  If  the  sun  was  observed, 
the  correction  is  in  the  first  column  to  the  right  of  the  apparent 
altitude,  but  if  the  altitude  is  that  of  star,  the  correction  is  in  the 
second  column  to  the  right  of  the  app.  altitude.  This  correction  is 
always  subtractive,  and  is  only  the  refraction  and  parallax  combined. 

TABLE  XIV. — Natural  sines  and  co-sines. 

The  degrees  for  the  natural  sine  are  found  at  the  top  of  the  page, 


124  PRACTICAL  NAVIGATION. 

and  the  minutes  in  the  left-hand  column  of  the  page.  But  for  the 
co-sines  the  degrees  are  at  the  bottom  of  the  page,  and  the  minutes 
in  the  right-hand  side  column.  The  sines  are  under  the  degrees  and 
opposite  the  minutes,  while  the  co-sines  are  over  the  degrees  and 
opposite  the  minutes.  The  natural  sine  or  co-sine  of  any  number 
of  degrees  over  90°  is  the  same  as  the  natural  sine  or  co-sine  of  its 
supplement,  that  is,  180° — the  angle. 

If  the  angle  or  arc  is  given  in  degrees,  minutes  and  seconds,  mul- 
tiply the  difference  at  the  bottom  of  the  column  by  the  number  of 
seconds,  point  off  two  places,  and  add  or  subtract  the  quotient,  ac- 
cording as  the  natural  sine  or  natural  co-sine  is  increasing  or  de- 
creasing. 

Required  the  natural  sine  of  9°  30'  10".  Natural  sine  of  9°  30'  is 
165048;  difference  for  100"  is  478,  which,  multiplied  by  10  and 
point  off  two  places=47.80;  165048+47=165095.  Natural  sine  of 
9°  30'  10". 

Arc  corresponding  to  natural  co-sine  032289  is  88°  9'. 

TABLE  XV. — For  finding  the  distance  of  terrestrial  objects  at  sea. 

When  the  eye  is  elevated  above  the  surface  of  the  adjacent  land 
or  water,  we  not  only  see  the  surrounding  objects  more  distinctly, 
but  also  see  those  which  are  more  remote  the  higher  we  advance. 
Now,  although  the  irregularity  of  the  surface  of  the  land  will  not 
admit  of  any  one  rule  that  will  give  the  distance  to  which  objects 
may  be  seen  at  different  elevations,  yet  at  sea,  where  the  curvature 
of  the  water  is  uniform,  those  distances  may  be  easily  computed  by 
means  of  this  table,  in  which  the  distances  are  exhibited  in  nautical 
miles  and  decimal  parts;  answering  to  the  height  of  the  eye,  or  that 
of  the  given  remote  object,  allowance  having  been  made  for  terres- 
trial refraction. 

EXAMPLE.  Being  at  the  mast  head  looking  out  for  land,  and  elevated  130  feet 
above  the  .surface  of  the  sea,  I  discovered  the  top  cf  a  light-house  in  the  horizon, 
whose  height  above  the  level  of  the  sea  is  known  to  he  300  feet :  required  my 
distance  from  the  light-house. 

In  the  tahle  opposite  130  feet  is 13. 1  miles. 

Ditto  300  19.9 


Sum  gives  the  distance  of  the  ship  from  the  light-house 33.0 

TABLE  XVI. — Equations  of  equal  altitudes. 

Observations  of  the  sun,  taken  when  at  equal  altitudes,  afford  an 
easy  and  accurate  method  of  ascertaining  the  time  shown  by  a  chro- 
nometer at  apparent  or  mean  noon;  and  from  thence  its  error;  but 
since  the  sun  changes  his  declination  during  the  interval  between 
the  corresponding  altitudes,  the  middle  of  the  times  by  the  chro- 
nometer when  they  were  taken,  will  not  be  that  shown  by  it  when 
the  sun  passes  the  meridian;  and  hence  it  becomes  necessary  to 
apply  a  correction,  called  the  equation  of  equal  altitudes,  to  the 


EXPLANATIONS  OP  THE  TABLES.  125 

middle  of  the  times,  which  may  be  easily  computed  as  follows,  by 
means  of  this  Table: 

1.  Opposite  the  interval  between  the  observations,  take  out  the  logarithms 
marked  A  and  B  at  the  head  of  the  columns. 

2.  To  log.  A  add  the  log.  (Table  I)  of  the  seconds  in  the  change  of  the  sun's 
declination  between  the  noons  of  the  preceding  and  following  days  (taken  from 
the  Nautical  Almanac),  and  the  log.  tangent  (Table  II)  of  the  given  latitude; 
the  sum  of  these  three  logs,  will  be  the  log.  (Table  I)  of  the  Jlrst  part  of  the 
equation. 

3.  To  log.  B.  add  the  log.  of  the  above  seconds,  and  the  log.  co-tangent  of 
the  sun's  declination  to  the  nearest  minute  of  the  given  day;  their  sum  will  be 
the  log.  of  the  second  part  of  the  equation . 

4.  Tlie/r^part  of  the  equation  additive  when  the  declination  is  decreasing, 
and  of  the  same  name  with  the  latitude;  or  increasing,  and  of  a  different  name 
from  the  latitude;  but  subtractive,  when  the  declination  is  increasing,  and  of  the 
same  name  with  the  latitude;  or  decreasing,  and  of  a  different  name  from  the 
latitude. 

5.  The  second  part  of  the  equation  is  additive  when  the  declination  is  increas- 
ing; but  subtractive  when  the  declination  is  decreasing. 

TABLES  XVII.  AND  XVIII. — Log.  rising  and  horary  angle. 

Enter  this  table  with  the  hours,  minutes  and  seconds.  The  hours 
will  be  found  at  the  head  of  the  page,  the  minutes  in  the  left-hand 
column,  and  the  seconds  at  the  head  of  the  column  of  logarithms. 
In  the  right-hand  column  will  be  found  a  column  of  proportional 
parts,  there  being  five  seconds  of  difference  between  each  column. 

Required  the  log.  rising  corresponding  to  Ih :  55m :  55s. 

Ans.  Index  4.09762=required  the  log.  rising  of  57m:  57s. 

For  57m:  5os:  we  liave.^. -„_ 50190 

For  2s:  we  have x  50 

3.50240 

TABLE  XIX. — Required  the  apparent  time  corresponding  to  8.30270.     The 
angle  corresponding  this  log.  islh:05m:  10s.     Required  the  log.  corresponding 
to  horay  angle  2h:  15m:  36s:    2h:  15ni:  35s:  gives  8.92928;  Is:  gives  10,  additive. 
Log.  8.92928 
+  10 


8.92938 

TABLE  XX. — To  reduce  the  equation  of  time  to  any  time  under  the  me- 
ridian of  Greenwich. 

This  table  is  entered  with  the  daily  variation  or  change  of  the 
equation  of  time  (being  the  difference  of  the  equations  at  the  pre- 
ceding and  the  following  noons,  taken  from  pages  1  or  2  of  the 
month  in  the  Nautical  Almanac,  when  they  are  both  additive  or 
both  subtractive,  but  their  sum  when  one  is  subtractive  and  the 
other  additive)  at  the  top,  and  the  Greenwich  time  in  the  left  side 
column.  The  corresponding  correction  is  then  to  be  applied  to  the 
equation  at  the  preceding  noon,  by  addition  or  subtraction,  accord- 
ing as  the  equation  is  increasing  or  decreasing.  But  should  the 
, 


126  PKACTICAL  NAVIGATION. 

Aquation  be  less  than  the  correction  at  the  preceding  noon,  the 
former  is  to  be  substracted  from  the  correction,  and  the  remainder 
•will  be  the  reduced  equation  of  time,  to  be  applied  in  the  same  way 
as  directed  in  the  Nautical  Almanac,  for  the  equation  at  the  follow- 
ing noon.  When  the  Greenwich  time  exceeds  twelve  hours,  the 
correction  must  be  taken  out  twice,  as  in  second  example. 

Ex.  1.  Required  the  equation  of  time,  August  17,  1877,  at  4  hours  apparent 
time  at  Greenwich. 

M.  S. 

Equation  of  time  at  app.  noon,  Aug.  17,  page  1,  Naiit.  Aim 3  49 

Equation  of  time  at  app.  noon,  Aug.  18,  page  1,  Jfaut.  Aim 3  36 

Daily  change  of  variation  (decreasing) 0  13 

Equation  of  time  (as  above)  Aug.  17 3  49 

Correction  to  difference  13  seconds  and  4  hours -  0  02 


Reduced  equation  time  (to  be  added  to  apparent  time) 3  47 

Hence  the  mean  time  at  4  hours  apparent  time  at  Greenwich  on  August  17, 
1877,  is4h:  3m:  47s. 

Ex.  2.  Required  the  equation  of  time  on  September  17,  1877,  at  16h:  35m: 
mean  time  at  St.  Helena,  in  longitude  5°  45'  "W. 

H.  M. 

Mean  time  at  St.  Helena 16  35 

Longitude  5°  45'  W.  in  time  (Table  IX. ) +  23  W. 

Mean  time  at  Greenwich 16  58 

M.  S. 

Equation  time  at  mean  noon,  Sept.  17,  by  page  2  N.  A 5  40 

Correction  to  daily  Variation  21s:and  J2h:. .  10  5  I  ^   ,. 

Correction  to  daily  variation  4h:  58m: 3  9  j  ' 

Reduced  equation  (to  be  added  to  mean  time) 5  54 

TABLE  XXI. — Amplitude. 

This  table  shows  a  method  of  finding  the  variation  of  the  compass 
by  comparing  the  magnetic  with  the  true  amplitude.  The  true  am- 
plitude is  taken  from  this  table,  which  has  the  declination  at  the  top 
of  the  pages,  and  the  latitude  at  the  left  hand. 

When  the  minutes  of  latitude  or  declination  are  over  20,  the  mean 
of  the  amplitude  for  the  two  nearest  degrees  will  give  the  required 
amplitude,  nearly. 

Required  the  true  amplitude  in  latitude  40°  31'  N.,  when  the  declination  is  16°. 

True  amplitude  for  latitude  40°,  dec.  16° 21  05 

True  amplitude  for  latitude  41°,  dec.  16° 21  25 

2)42  30 
True  amplitude 21  15 

Required  the  true  amplitude  in  latitude  2°50'S.,  declination  10°  25'. 

True  amplitude  in  latitude  3%  dec.  10° 10  01 

True  amplitude  in  latitude  3°,  dec.  11° 11  01 

2)21  09 
True  amplitude  lat.  33  S. ,  dec.  10°  25' 10  30 


TABLES. 


127 

TABLE  I. 

LOGARITHMIC  SINES,  TANGENTS,  and  SECANTS,  to  every  Point  and  Quarter 

Point  of  the  Compass. 

tl 

hj 

o 

o 

p 

sr 

Sine. 

Co-sine. 

Tangent 

Co-tang 

Secant. 

Co-sec. 

5 

0 

0.000000 

10.000000 

0.000000 

Infinite. 

10.000000 

Infinite. 

8 

o  % 

8.690796 

9.999477 

8.691319 

11.308681 

10.000523 

11.309204 

73/ 
/4 

0  % 

8.991302 

9.997904 

8.993398 

11.006602 

10.002096 

11.008698 

7  y* 

0  % 

9.166520 

9.995274 

9.171247 

10.828753 

10.004726 

10.833480 

7  % 

1 

9.290236 

9.991574 

9  298662 

10.701338 

10.008426 

10.709764 

7 

1  % 

9.385571 

9.986786 

9.398785 

10.601215 

10.013214 

10.614429 

6  % 

1   % 

9.462824 

9.980885 

9.481939 

10.518061 

10.019115 

10.537176 

6  % 

1  % 

9.527488 

9.973841 

9.553647 

10.446353 

10.028159 

10.472512 

6  % 

2 

9.582840 

9.965615 

9.617224 

10.382776 

10.034385 

10.417160 

6 

2  Ji 

9.630992 

9.956163 

9.674829 

10.325171 

10.043837 

10.3690C8 

5  % 

2  % 

9  673387 

9.945430 

9.727957 

10.272043 

10.054570 

10.326613 

5  ya 

2  % 

9.711050 

9.933350 

9.777700 

10.222300 

10.066650 

10.288950 

5% 

3 

9.744739 

9.919846 

9.824893 

10.175107 

10.080154 

10.255261 

5 

3  >£• 

9.775027 

9.904828 

9  870199 

10.129801 

10.095172 

10.224973 

4  % 

3  y, 

9.802359 

9.888185 

9.914173 

10.085827 

10  111815 

10.197641 

4  % 

3  % 

9.827084 

9.869790 

9.957295 

10.042705 

10.130210 

10.172916 

4  % 

4 

9  849485 

9.849485 

10.000000 

10.000000 

10.150515 

10.150515 

4 

Co-sine 

Sine. 

Co-tang 

Tangent 

.    Co-sec. 

Secant. 

LOGARITHMS   OF   NUMBERS. 

Ttfn    1 

LOO                      Log.  0.00000 

00 

000000 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

l 

0.000000 

21 

1.322219 

41 

1.612784 

61 

1.785330 

81 

1.908485 

2 

0.301030 

22 

1.342423 

42 

1.623249 

62 

1.792392 

82 

1.913814 

3 

0.477121 

23 

1.361728 

43 

1.633468 

63 

1.799341 

83 

1.919078 

4 

O.G02060 

24 

1.380211 

44 

1.643453 

04 

1.806180 

84 

1.924279 

5 

0.698970 

25 

1.397940 

45 

1.653213 

65 

1.812913 

85 

1.929419 

6 

0.778151 

26 

1.414973 

47 

1.662758 

66 

1.819544 

86 

1.931498 

7 

0.845098 

27 

1.431364 

47 

1.672098 

67 

1.826075 

87 

1.939519 

8 

0.903090 

28 

1.447158 

48 

1.681241 

68 

1.832509 

88 

1.944483 

9 

0.954243 

29 

1.462398 

49 

1.690196 

69 

1.838849 

89 

1.949390 

10 

1.000000 

30 

1.477121 

50 

1.698970 

70 

1.845098 

90 

1  951243 

11 

1.041393 

31 

1.491362 

51 

1.707570 

71 

1.851258 

91 

1.959041 

12 

1.079181 

32 

1.505150 

52 

1  716003 

72 

1.857332 

92 

1.963788 

13 

1.113943 

33 

1.518514 

53 

1.724276 

73 

1.863323 

93 

1.  908483 

14 

1  146128 

34 

1.531479 

54 

1  732394 

74 

1.869232 

94 

1.973128 

15 

1.176091 

35 

1.544068 

55 

I.  740363 

75 

1.875061 

95 

1.977724 

16 

1.204120 

36 

1  556302 

56 

1.748188 

76 

1.880814 

96 

1.982271 

17 

1.230449 

37 

1.5G8202 

57 

1.755875 

77 

1.886491 

97 

1  98G772 

18 

1.255273 

38 

1  579784 

58 

1.763428 

78 

1.892095 

98 

1.991226 

19 

1.278754 

39 

1.591065 

5.9 

1.770852 

79 

1.897627 

99 

1  995635 

20 

1.301030 

40 

1.602060 

60 

1.778151 

80 

1.903090 

100 

2  000000 

128 

TABLE  I. 

LOGARITHMS  OF  NUMBERS. 

No.  1 

000      1 

GOO         Log.  00 

1000 

J04120 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

100 
101 
102 
103 
104 
105 
106 
107 
103 
109 

ooooou 

004321 
008600 
012837 
017033 
021189 
025306 
0293S4 
033424 
037426 

000434 
004751 
:009026 
01325& 
017451 
021603 
025715 
029789 
033826 
037825 

000868001301001734 
005180005609006038 
009451009876010300 
013680014100014520 
017868  018284  01870f 
022016  022428  022841 
026124026533026942 
030195030600031004 
034227  034628  035029 
038223038620039017 

002166 
006466 
010724 
014940 
019116 
023252 
027350 
031408 
035430 
039414 

,002598 
006894 
011147 
015360 
019532 
023664 
027757 
031812 
035830 
039811 

003029 
007321 
011570 
015779 
019947 
024075 
028164 
032216 
036229 
040207 

003460 
007748 
011993 
016197 
020361 
024486 
028571 
032619 
036629 
040602 

OU3891 
008174 
012415 
016615 

020775 
021896 
028978 
033021 
037028 
040998 

432 
428 
424 
420 
416 
412 
408 
404 
400 
397 

110 
111 
112 
113 
—  114 
115 
116 
117 
118 
119 

011393 
045323 
049218 
053078 
056905 
060698 
364458 
038186 
071882 

0417«7 
045714 
049606 
053463 
057286 
061075 
064832 
068557 
072250 

042182 
046105 
049993 
053846 
057666 
061452 
065206 
168928 
072617 

042575 
046495 
050380 
054230 
058046 
061829 
065580 
069298 
072985 

042969 
046885 
050766 
054613 
058426 
062*206 
065953 
069668 
073352 
077004 

043362 
047275 
051152 
054996 
058805 
062582 
066326 
070038 
073718 
07736S 

043755 
047644 
051538 
0.>-j:;7S 
059185 
062958 
066699 
070407 
074085 
077731 

044148 
Oi8053 
051924 
055760 
059563 
063333 
067071 
07077G 
074451 
078094 

044540 
048442 
052309 
056142 
059942 
063709 
067443 
071145 
074816 
o78457 

U44D31 
048830 
052694 
056524 
060320 
064083 
067814 
071514 
075182 
078819 

393 
390 
386 
383 
379 
376 
373 
370 
366 
363 

J7o547  OVoUia  076276:07(5640 

120 
121 
122 
123 
124 
125 
126 
127 
128 
129 

J79181 
082785 
)S6360 
089905 
093422 
J96910 
100370 
103804 
107210 
110590 

079543 
083144 
086716 
09025S 
093772 
097257 
100715 
10414G 
107549 
110926 

071J904'08026G 
083503083861 
087071  087426 
090611090963 
094122  094471 
097604097951 
101059  101403 
104487  104828 
1078S8  108227 
111262  111598 

080626 
084219 
087781 
091315 
094820 
098297 
101747 
105169 
108565 
111934 

080987 
084576 
08813G 
091667 
095169 
098644 
102090 
105510 
108903 
112270 

081347 
084934 
088490 
092018 
095518 
098990 
102434 
105851 
109241 
112605 

081707 
085291 
088845 
092370 
0958G6 
099335 
102777 
106191 
109578 
112940 

082067 
085647 
089198 
092721 
096215 
099681 
103119 
108531 
109916 
113275 

08^42b 
086004 
089552 
093071 
096562 
10002<:i 
103462 
106870 
110253 
113609 

360 
357 
355 
352 
349 
346 
343 
341 
338 
335 

130 
131 
132 
133 
134 
135 
136 
137 
138 
139 

113943 
117271 
120574 
123852 
127105 
130334 
133539 
136721 
139879 
143015 

1142/v 
117603 
120903 
124178 
127429 
130G55 
133858 
137037 
140194 
143327 

114611114944 
117934118265 
121231121560 
124504  124830 
127752123076 
130977  131298 
134177  134496 
137354137670 
140508  140822 
143639  143951 

115278 
118595 
121888 
125156 
128399 
131619 
134814 
137987 
141136 
144263 

115610 
118926 
122216 
125481 
128722 
131939 
135133 
138303 
141450 
144574 

115943 
119256 
122543 
125806 
129645 
132260 
135451 
138618 
141763 
144885 

116276 
119586 
122871 
126131 
129368 
132580 
135768 
138934 
142076 
145196 

116608 
119915 
123198 
12G45G 
129690 
132900 
136086 
139249 
142389 
145507 

116940 
120245 
123525 
126781 
130012 
133219 
136403 
139564 
142702 
145818 

332 
330 
328 
325 
323 
321 
318 
316 
314 
311 

140 
141 
142 
143 
144 
145 
146 
147 
148 
149 

146128  146438 
149219  149527 
152288  152594 
155338  155640 
158362158664 
161368161667 
164353  164650 
1G7317  167613 
170262  170555 
173186173478 

146748 
149835 
152900 
155943 
158965 
161967 
164947 
167908 
170848 
173769 

147058 
150142 
153205 
15624G 
159266 
162266 
165244 
168203 
171141 
174060 

147367 
150449 
15351Q 
156549 
1595G7 
162564 
165541 
168497 
171434 
174351 

147676 
150756 
153815 
156852 
159868 
162863 
165838 
168792 
171726 
174641 

147985 
151063 
154119 
157154 
160168 
163161 
166134 
169086 
172019 
174932 

148294 
151370 
154424 
157457 
160468 
163460 
166430 
169380 
172311 
175222 

148603 
151676 
154728 
157759 
160769 
163757 
166726 
169674 
172603 
175512 

148911 
151982 
155032 
158061 
161088 
.64055 
167022 
1699G8 
172895 
175802 

309 
307 
305 
303 
300 
298 
296 
294 
292 
290 

150 
151 
152 
153 
154 
155 
156 
157 
158 
159 

17609J 

178977 
181844 
1S4691 
187521 
190332 
193125 
195900 
198932 
201397 

176381 
179264 
182129 
184975 
187803 
190612 
193403 
196176 
198392 
201670 

176670 
179552 
182415 
185259 
188084 
190892 
193681 
196452 
199206 
201943 

176959 
179839 
182700 
185542 
188366 
191171 
193959 
196729 
199481 
202216 

177248 
180126 
182985 
185825 
188647 
191451 
194237 
197005 
199755 
202488 

177536 
180413 
183270 
186108 
188928 
191730 
194514 
197281 
200029 
202761 

177825 
180699 
183554 
186391 
189209 
192010 
194792 
197556 
200303 
203033 

178113 
180986 
183839 
186674 
189490 
192289 
195069 
197832 
200577 
203305 

178401 
181272 
184123 

186956 
189771 
192567 
195346 
198107 
200850 
203577 

178689 

181558 
184407 
187239 
190051 
192846 
195623 
198382 
201124 
203848 

288 
287 
285 
283 
281 
279 
278   . 
276 
274 
272 

0 

1  '1  2 

3 

4 

5 

G 

7  |  8 

9 

TABLE  I.                  129 

LOOAKITHMS  OF  NUMBERS. 

No.  1 

ftnn  ...  ,m  ,  -  ° 

200        Log.  20- 

1  1  °0 

!42423 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

160 
161 
162 
1C3 
164 
165 
166 
167 
168 
169 

204120 
206826 
209515 
112188 
214844 
217484 
220108 
2-22716 
225309 
227887 

204391 
207095 
209783 
212454 
215109 
217747 
220370 
222976 
225568 
228144 

•21)4662 
207365 
210051 
212720 
215373 
218010 
220631 
223236 
225826 
228400 

204933 
207634 
210318 
212986 
215638 
218273 
220892 
223496 
226084 
228657 

205204 
207903 
210586 
213252 
215902 
218535 
221153 
223755 
226342 
228913 

205475 
208172 
210853 
213518 
616166 
218798 
221414 
224015 
226600 
229170 

205745 
208441 
211120 
213783 
216430 
219060 
221675 
224274 
226,858 
229426 

206016 
208710 
211388 
214049 
216694 
219322 
221936 
224533 
227115 
229682 

206-280  206556 
208978  209247 
211654211921 
214314214579 
216957217221 
219584219846 
222196222456 
224792  225051 
227372227630 
229938J230193 

2il 
269 
267 
266 
264 
262 
261 
259 
258 
256 

170 
171 
172 
173 
174 
175 
176 
177 
178 
179 

23U449 
232996 
235528 
238046 
240549 
243038 
245513 
247973 
250420 
252853 

230704 
233250 
235781 
138297 
240799 
243286 
245759 
248219 
250664 
253096 

23096U 
233504 
236033 
238548 
241048 
243534 
246006 
248464 
250908 
253338 

231215 
233757 
236285 
238799 
241297 
243782 
246252 
248709 
251151 
253580 

23147U 
234011 
236537 
239049 
241546 
244030 
246499 
248954 
251395 
253822 

231724 
234264 
236789 
239299 
241795 
244277 
246745 
249198 
251638 
254064 

231979 
234517 
237041 
239550 
242044 
244524 
246991 
249443 
•251881 
254306 

232233 
234770 
237292 
239800 
242293 
244772 
247236 
249687 
252125 
254548 

232488 
235023 
237544 
240050 
242541 
245019 
247482 
249932 
252367 
254790 

23274^ 
235276 
237795 
240300 
242790 
245266 
247728 
250176 
252610 
255031 

2>5 
253 
252 
250 
249 
247 
246 
245 
243 
242 

ISO 
181 
182 
183 
184 
185 
186 
187 
183 
189 

255273 
257679 
260071 
262451 
264818 
267172 
269513 
271842 
274158 
276462 

255514 
257918 
260310 
262688 
265054 
267406 
269746 
272074 
274389 
276691 

25575j 
258158 
2B0548 
262925 
265290 
267641 
269980 
272306 
274620 
276921 

255996 
258398 
260787 
•263162 
265525 
267875 
270213 
272538 
274850 
277151 

256236 
258637 
261025 
263399 
265761 
268110 
370446 
272770 
275081 
277380 

256477 
258877 
261263 
263636 
265996 
268344 
270679 
273001 
275311 
277609 

256718 
259116 
261501 
263873 
266232 
268578 
270912 
273233 
275542 
277838 

25695S 
259355 
261738 
264109 
266467 
268812 
271144 
273464 
275772 
278067 

257198 
259594 
261976 
264345 
266702 
269046 
271377 
273696 
276002 
278296 

257439 
259833 
262214 
264582 
266937 
269279 
271609 
273927 
276232 
278525 

241 
239 
238 
237 
235 
234 
233 
232 
230 
229 

190 
191 
192 
193 
194 
195 
196 
197 
198 
199 

•278754 
281033 
283301 
285557 
287802 
290035 
292256 
294466 
;96665 
298853 

27898; 
281261 
283527 
285782 
288025 
290257 
292478 
294687 
296884 
299071 

279210 
281488 
283753 
286007 
288249 
•290480 
292699 
294907 
297104 
299289 

279439 
281715 
283979 
286232 
288473 
290702 
292920 
295127 
297323 
299507 

279667 
281942 
284205 
286456 
288696 
290925 
293141 
295347 
297542 
299725 

279895 
282169 
284431 
286681 
288920 
291147 
263363 
295567 
297761 
299943 

280123 
282395 
284656 
286905 
289143 
291369 
293583 
295787 
297979 
300161 

280351 
282622 
284882 
287130 
289366 
291591 
293804 
296007 
298198 
300378 

280578 
282849 
285107 
287354 
289589 
291813 
294025 
296226 
298416 
300595 

2S0806 
283075 
285332 
287578 
289812 
292034 
294246 
296446 
298635 
300813 

228 
227 
226 
225 
223 
222 
221 
220 
219 
2)8 

•200 
201 
202 
203 
204 
205 
206 
207 
208 
209 

301030 
303196 
305351 
307496 
309630 
311754 
313867 
315970 
318063 
320146 

30  J  247 
303412 
305566 
307710 
309843 
311966 
314078 
316180 
318272 
320354 

301464 
303628 
305781 
307924 
310056 
312177 
314289 
316390 
318481 
320562 

301681 
303844 
305996 
308137 
310268 
312389 
314499 
316599 
318689 
320769 

301898 
304059 
306211 
808351 
310481 
312600 
314710 
316809 
318898 
320977 

302114302331302547 
304275  304491  304706 
306425306639306854 
308564308778308991 
310693310906311118 
312812313023313234 
314920315130315340 
317018317227317436 
319106319314319522 
321184321391321598 

302764 
304921 
307068 
309204 
311330 
313445 
315550 
317645 
319730 
321805 

302980 
305136 
307282 
309417 
311542 
313656 
315760 
317854 
319938 
322012 

217 
216 
214 
213 
212 
211 
210 
208 
208 
207 

210 
211 
212 
213 
214 
215 
216 
217 
218 
219 

322219 
324282 
326336 
328380 
330414 
332438 
334454 
336460 
338456 
340444 

322426 
324488 
326541 
328583 
330617 
332640 
334655 
336660 
338656 
340642 

322633322839 
324694  324899 
326745326950 
328787  328991 
330819331022 
332842  333044 
334856335056 
336860337060 
338855339054 
340841341039 

323046 
325105 
327155 
329194 
331255 
333246 
335257 
337260 
339253 
341237 

323252  323458  323665,323871 
325310  325516  325721  325926 
327359  327563  327767  327972 
329398  329601  329805  330008 
331427  331630  331832  332034 
333447  333649  333850  334051 
335458  335658  335859  336059 
337459  337659  337858  338058 
339451  339650  339849  340047 
341435  341632  341830  342028 

324077 
326131 
328176 
330211 
332236 
334253 
336260 
338257 
340246 
342225 

2U6 
205 
204 
203 
202 
202 
201 
200 
199 
198 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

130                 TABLE  I. 

LOGARITHMS  OF  NUMBEES. 

No.  2i 

•Of)      °£ 

00         Log.  M'2 

•f°M       4 

47158 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Biff. 

!&U 

221  ' 
222 
223 
224 
225 
226 
227 
228 
229 

342423,342620 
344392  344589 
34(5353346549 
348305348500 
350248  350442 
352182352375 
354108354301 
353026356217 
357935358125 
359835360025 

342817 
344785 
346744 
348694 
350636 
352568 
354493 
356408 
358316 
360215 

343014 
3449811 
346939 
348889 
350829 
352761 
354685 
356599 
358506 
360404 

343214 
345178 
347135 
349083 
351023 
352954 
354876 
356790 
358696 
360593 

343409, 
345374 
347330 
349278 
351216 
353147 
355068 
356981 
358886 
360783 

343606 
345570 
347522 
349470 
351410 
353339 
355260 
357172 
359076 
360972 

343802' 
345766 
347720 
349666 
351603 
353532 
355452 
357363 
359266 
361161 

343999 
345962 
347915 
349860 
351796 
353724 
355643 
357554 
359456 
361350 

344196 
346157 
348110 
350054 
351989 
353916 
355834 
357744 
359646 
361539 

197 
196 
195 
194 
193 
193 
192 
191 
190 
189 

230 
231 
232 
233 
234 
235 
236 
237 
238 
239 

361728 
363612 
365488 
367356 
S69216 
371068 
372912 
374748 
376577 
378398 

361917 
363800 
365675 
367542 
369401 
371253 
373096 
374932 
376759 
378580 

362  105 
363988 
365862 
367729 
369587 
371437 
373280 
375115 
376942 
378761 

362294 
364176 
366049 
367915 
369772 
371622 
373464 
375298 
377124 
378943 

362482 
364363 
366236 
368101 
369958 
371806 
373647 
375481 
377306 
379124 

362671362859 
364551  364739 
366423366610 
368287  368473 
370143370328 
371991  372175 
373831374015 
375664  375846 
377488  377670 
379306  379487 

363048 
364926 
366796 
368659 
370513 
372360 
374198 
376029 
377852 
379668 

363236 
365113 
366983 
368844 
370698 
372544 
374382 
376213 
378034 
379849 

363424 
365301 
367169 
369030 
370883 
372728 
374565 
376394 
378216 
380030 

188 
188 
187 
186 
185 
184 
184 
183 
182 
181 

240 
241 
242 
243 
244 
245 
246 
247 
248 
249 

380211 
382017 
383815 
385606 
387390 
3891  6G 
390935 
392697 
394452 
396199 

380392 
382197 
383995 
385785 
387568 
389343 
391112 
392873 
394627 
396374 

380573 
382377 
384174 
385964 
387746 
389520 
391288 
393048 
394802 
396548 

380754 
382557 
384353 
386142 
387923 
389697 
391464 
393224 
394977 
396722 

380934 
382737 
384533 
386321 
388101 
389875 
391641 
393400 
395152 
396896 

3S1115 

382917 
384712 
386499 
388279 
390051 
391817 
393575 
395326 
397071 

381296 
383097 
384891 
386677 
388456 
390228 
391993 
393751 
395501 
397245 

381476 
383277 
385070 
386856 
388634 
390405 
392169 
393926 
395676 
397418 

381656 
383456 
385249 
387034 
388811 
390582 
392345 
894101 
395850 
397592 

381837 
383636 
385428 
387212 
388989 
390759 
392521 
394277 
396025 
397766 

181 
180 
179 
178 
178 
177 
176 
166 
175 
174 

250 
251 
252 
253 
254 
255 
256 
257 
258 
259 

397940 
399674 
401400 
40312I/ 
404834 
406540 
408240 
409933 
111620 
413300 

398114 
399847 
401573 
403292 
405005 
406710 
408410 
410102 
411788 
413467 

398287 
400020 
401745 
403464 
405175 
406881 
408579 
410271 
411956 
413635 

398461 
400192 
401917 
403635 
405346 
407051 
408749 
410410 
412124 
413802 

398634 
400365 
402089 
403807 
405517 
407221 
408918 
410608 
412292 
413970 

398808 
400538 
402261 
403978 
405688 
407391 
409087 
410777 
412460 
414137 

398981 
400711 
402433 
404149 
405858 
407561 
409257 
410946 
412628 
414305 

396154 
400883 
402605 
404320 
406029 
407731 
409426 
411114 
412796 
414472 

399327 
401056 
402777 
404492 
406199 
407900 
409595 
411283 
412964 
414639 

399501 
401228 
402949 
404663 
406370 
408070 
409764 
411451 
413132 
414806 

173 
173 
172 
171 
171 
170 
169 
169 
168 
167 

260 
261 
262 
263 
264 
265 
266 
267 
268 
269 

414973 
416640 
418301 
419956 
421604 
423246 
424882 
426511 
428135 
429752 

415140 
416807 
418467 
420121 
421768 
423410 
425045 
426674 
428297 
429914 

415307 
416973 
418633 
420286 
421933 
423573 
425208 
426836 
428459 
430075 

41U74 
417139 
418798 
420451 
422097 
423737 
42537J 
426999 
428621 
430236 

415641 
417306 
418964 
420616 
422261 
423901 
425534 
427161 
428782 
430398 

415808 
417472 
419129 
420781 
422426 
424064 
425697 
427324 
428944 
430559 

415974 
417638 
419295 
420945 
422590 
424228 
425860 
427486 
429106 
430720 

416141 
417804 
419460 
421110 
422754 
424392 
426023 
427648 
429268 
430881 

416308 
417970 
419625 
421275 
422918 
424555 
426186 
427811 
429429 
431042 

416474 
418135 
319791 
421439 
423082 
424718 
426349 
427973 
429591 
431203 

167  - 
166 
165 
165 
164 
164 
163 
162 
162 
161 

270 
271 
272 
273 
274 
275 
276 
277 
278 
279 

431364 
432969 
134569 
436163 
437751 
439333 
140909 
442480 
414045 
445604 

431525 
433129 
434728 
436322 
437909 
439491 
441066 
442636 
444201 
445760 

431685 
433290 
434888 
436481 
438067 
43864g 
441224 
442793 
444357 
415915 

431846 
423450 
435048 
436640 
438226 
429806 
441381 
442950 
444513 
44C071 

432007 
433610 
435207 
436798 
438384 
439964 
441538 
443106 
444669 
446226 

432167 
433770 
435366 
436957 
438542 
440122 
441695 
443263 
444825 
446382 

432328 
433930 
435526 
437116 
438700 
440279 
441852 
443419 
444981 
446537 

432488 
434090 
435685 
437275 
438859 
440437 
442009 
443576 
445137 
446692 

432649  432809 
434249  434409 
435844436003 
437433437592 
439017439175 
440594  440752 
442166442323 
443732443888 
445293445448 
446848447003 

.160 
160 
159 
159 
158 
158 
157 
157 
156 
155 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLE  I.                  131 

LOGARITHMS  OF  NUMBERS. 

No.  2 

HflO      '-i 

400 

Log.  44 

71  IS 

531479 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

280 
281 
282 
283 
284 
285 
28G 
287 
288 
289 

447156 
44870G 
150249 
151786 
453318 
454845 
15636G 
457882 
459392 
460898 

44731b 
448861 
'450403 
451940 
453471 
454997 
456518 
458033 
459543 
461048 

447466 
149015 
450557 
452093 
45C624 
455149 
45667C 
458184 
459694 
461198 

447023 
44917C 
450711 
352247 
453777 
455302 
456821 
458336 
459845 
461348 

447  778  447933  44808^ 
449324  449478  44963C 
450865  451018  451172 
452400  452553  45270C 
453930  454082  45423c 
455454  455606  455758 
456973457125457276 
458487  458638  45878S 
459995460146460296 
461498  461649  46179S 

44824: 
449787 
451321 
45285£ 
454387 
45591  C 
457428 
45894C 
460447 
46194S 

448397 
449941 
45147£ 
453012 
45454C 
456062 
45757S 
459091 
460597 
462098 

4485o: 
45009c 
45163c 
45316^ 
454692 
456214 
45773C 
459242 
460747 
462248 

165 
154 
154 
153 
158 
152 
152 
151 
151 
150 

290 
291 
292 
293 
294 
295 
29G 
297 
298 
299 

4G23t)b  462548  462(39  1  462847  402997 
463893  464042  464191  464340  464489 
465383  465532  465680  465829  465977 
466868  467016  467164  467312  467460 
468347  168495468643468790468938 
469822  469969  470116  470263  470410 
471292  471438  471585  4717321471878 
472756  472903  473049  473195!473341 
474216  174362474508474653474799 
175671  475816  475962  476107  476252 

463146  463296  463445 
464639464787464936 
466126466274466423 
467C08  467756  467904 
469085469233469380 

463594 
465085 
466571 
468052 
469527 

463744 
465234 
466719 
468200 
469675 
471145 
472610 
474070 
475526 
476976 

150 
149 
149 
148 
148 
147 
147 
146 
146 
145 

470557  470704  470851  470996 
472025  472171  472317  472464 
473487  473633  473779  473925 
474944  475090  475235  475381 
476397  476542  476687  476832 

30J 
301 
302 
303 
304 
305 
3U6 
307 
308 
309 

477121477266477411 
478566  178711  478855 
480007480151480294 
481443481586481729 
482874483016483159 
184300  484442  484584 
185721485863486005 
487138487280487421 
488551  488692  488833 
189958490099490239 

47  7555 
478999 
480438 
481872 
483302 
484727 
48G147 
487563 
488973 
490380 

477700 
479143 
480582 
482016 
483445 
484869 
486289 
487704 
489114 
490520 

477844 
479287 
480725 
482159 
483587 
485011 
486430 
487845 
489255 
490661 

477989478133 
479431  479575 
480869481012 
482302  482445 
483730483872 
485153  485295 
486572486714 
487986488127 
489396489537 
490801  490941 

478278 
479719 
481156 
482588 
484015 
485437 
486855 
488269 
489677 
491081 

478422 
479863 
481299 
482731 
484157 
485579 
486997 
488410 
489818 
491222 

115 
144 
144 
143 
143 
142 
142 
141 
141 
140 

310 
311 
312 
313 
314 
315 
316 
317 
318 
319 

491362 
492760 
494155 
195544 
496930 
498311 
199687 
501059 
502427 
503791 

491502 
492900 
494294 
495683 
497068 
498448 
499824 
501196 
502564 
503927 

491642  491782 
493040493179 
494433494572 
495822  495960 
497206497344 
498586498724 
499962  500099 
501333501470 
502700  502837 
504.063  504199 

491922 
493319 
494711 
496099 
497482 
498862 
500236 
501607 
502973 
504335 

492062 
493458 
494850 
496237 
497621 
498999 
500374 
501744 
503109 
504471 

492201 
493597 
494989 
496376 
497759 
499137 
500511 
501880 
503246 
504607 

492341 
493737 
495128 
496514 
497897 
499275 
500648 
502017 
503382 
504743 

492481 
493876 
495267 
496653 
498035 
499412 
500785 
502154 
503518 
504878 

492621 
494015 
495406 
496791 
498173 
499550 
500922 
502290 
503654 
505014 

140 
139 
139  ' 
139 
138 
108 
137 
137 
136 
136 

320 
321 
322 
323 
324 
325 
32G 
327 
328 
329 

505150 
506515 
507856 
509202 
510545 
511883 
513218 
514548 
515874 
51719G 

•505286 
506640 
507991 
509337 
510679 
512017 
513351 
514680 
516006 
517328 

505421 
506775 
508125 
509471 
510813 
51215C 
513484 
514813 
516139 
517460 

505557 
506911 
508260 
509606 
510947 
512284 
513617 
514946 
516271 
517592 

505692 
507046 
508395 
509740 
511081 
512417 
513750 
515079 
516403 
517724 

505828  505963 
507181507316 
508530508664 
509874510008 
511215511348 
512551512684 
513883514016 
515211  515344 
516535  516668 
517855517987 

506099 
507451 
508799 
510143 
511482 
512818 
514149 
515476 
516800 
518119 

506234 
507586 
508933 
510277 
511616 
512951 
514282 
515609 
516932 
518251 

506370 
507721 
509068 
510411 
511750 
513084 
514415 
515741 
517064 
518382 

136 
135 
135 
134 
134 
133 
133 
133 
132 
132 

330 
331 
332 
333 
334 
335 
33G 
337 
338 
339 

518514518645518777 
519828519959520090 
521138521269521400 
522444522575522705 
523746523876524006 
525045525174525304 
526339526468526598 
527630527759527888 
528917529045529174 
530200530328530456 

518909  519040 
520221  520352 
521530521661 
522835  522966 
524136524266 
525434  525563 
526727  526856 
528016528145 
529302  529430 
530584J530712 

519171  519303 
520483520614 
521792  521922 
523096523226 
524396  524526 
525693  525822 
526985527114 
528274  528402 
529559  529687 
530840  530968 

519434 
520745 
522053 
523356 
524656 
525951 
527243 
528531 
529815 
531095 

519565 
520876 
522183 
523486 
524785 
326081 
527372 
528660 
529943 
531223 

519697 
521007 
522314 
523616 
524915 
526210 
527501 
528788 
530072 
531351 

131 
131 
131 

ISO 

130 
129 
129 
129 
128  < 
128 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

132 

TABLE  I. 

LOGARITHMS  OF  NUMBERS. 

No.  3400— 

4000 

Log.  53J 

470 

02060 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

340 
341 
342 
343 
344 
345 
346 
347 
348 
349 

53147  9  531607  531734  531862 
532745  532882  533009  533136 
534026  534153  534280  534407 
535294  535421  535547  535674 
536558  536685  536811  536937 
537819  537945  538071  538197 
539076  539202  539327  539452 
540329  540455  540580  540705 
541579  541704  541829  541953 
542825  542950  543074  543199 

531990  532117 
533263  533391 
534534534661 
535800  535927 
537063  537189 
538322538448 
539578  539703 
540830  540955 
542078  542203 
543323543447 

532245  53237i 
533518  53364E 
534787:534914 
536053o3617S 
537315537441 
538574  538699 
539829539954 
541080541205 
542327542452 
543571  543696 

53250U 
533772 
535041 
536306 
537567 
538825 
540079 
541330 
542576 
543820 

53262r 
53389£ 
53516" 
536432 
537693 
538951 
540204 
541454 
542701 
543944 

1-.8 
127 
127 
126 
126 
126 
125 
125 
125 
124 

350 
351 
352 
353 
354 
355 
356 
357 
358 
359 

544068544192 
545307  545431 
546543546666 
547775,547898 
549003549126 
550228550351 
551450551572 
552668552790 
553883,554004 
555094555215 

544316  544440  544564  544688 
545554  545678  545802  545925 
546789  546913  547036  547159 
548021  548144  548266  548389 
549249  549371  549494  549616 
550473  550595  550717  550840 
551694  551816  551938  552059 
552911  553033  553154  553276 
554126  554247  554368:554489 
555330  555457|555578  555699 

544812  544936 
546049'546172 
547282  547405 
548512548635 
549739J549861 
550962551084 
552181J552303 
553398,553519 
554610,554731 
555820,555940 

545060 
546296 
547529 
548758 
549984 
551206 
552425 
553640 
554852 
556061 

545183 
546419 
547652 
548881 
550106 
551328 
552546 
553762 
554973 
556182 

124 
124 
123 
123 
123 
122 
122 
121 
121 
121 

360 
361 
362 
363 
364 
365 
366 
367 
•  368 
369 

556302556423 
557507:557627 
558709558829 
559907560026 
561101561221 
562293562412 
563481  563600 
564666564784 
565848565966 
567026  567144 

556544  556664:556785  556905 
557748  557868,557988  558108 
558948  559068  559188:559308 
560146  560265  560385  560504 
561340  561456  561578  561698 
56253r562650  562769  562887 
563718  563837  563955  564074 
564903  565021  565139  565257 
566084  566202  566320  566437 
567262  567379  567497  567614 

557026,557146  557267  557387 
558228,558348  558469  558589 
559428,559548559667  559787 
560624  560743  560863  560982 
561817i561936  562055  562174 
563008,563125  563244  563362 
564192  564311  564429  564548 
565378^65494  565612  565730 
566555,566673  566791  566909 
567732567849  567967,568084 

1-20 
120 
120 
119 
119 
119 
119 
118 
-  118 
118 

370 
371 
372 
373 
-   374 
375 
376 
377 
378 
379 

568202  568319  568436 
569374569491569608 
570543570660570776 
571709571825571942 

572872572988573104 

568554568671,568788 
569725  569842  5G9959 
570893571010571126 
572058572174572291 
573220573336573452 

568905,569023 
370076;570193 
571243571359 
572407:572523 
573568573684 
574726574841 
575880!575996 
577032:577147 
578181578295 
579326579441 

569140569257 
570309570426 
571476571592 
372639572755 
573800573915 
574957  575072 
576111  576226 
577262;577377 
578410  578525 
579555579669 

117 
117 
117 
116 
116 
116 
115 
115 
115 
114 

574031  574147  574263  574379  574494  574610 
575188  575303  575419  575534  575650  575765 
5763411576457  576572  576687  576802  576917 
577492  577607  577721  577836  577951!578066 
578639  578754  578868  578983  579097  579212 

380 
381 
382 
383 
384 
385 
386 
387 
388 
389 

579784 
580925 
582063 
583199 
584331 
585461 
586587 
587711 
588832 
589950 

579898:580012 
581039581153 
582177  582291 
583312  583426 
584444584557 
585574585686 
586700  586812 
587823587935 
588944589056 
590061  590173 

580126 
581267 
582404 
583539 
584670 
585799 
586925 
588047 
589167 
590284 

580240580355 
581381  581495 
582518582631 
583652583765 
584783  584896 
585912  586024 
587037  587149 
588160'588272 
589279589391 
590396  590507 

580469,580583 
581608581722 
582745582858 
583879,583992 
585009585122 
586137,586250 
587262587374 
588384588496 
589503'589615 
590619,590730 

580697  580811 
581836281950 
582972  583085 
584105584218 
585235585348 
586362586475 
587486587599 
588608588720 
589726589838 
590842  590953 

114 
114 
114 
113 
113 
113 
112 
112 
112 
112 

390 
391 
392 
393 
394 
395 
396 
397 
398 
399 

5'J1065;591176  591287  591399  591510  591621 
592177  592288  592399  592510  592621  592732 
593286  593397  593508  593618  593729  593840 
594393  594503  594613  594724  59^834  594945 
595496  595606  595717  595827  595837  596047 
596597  596707  596817  596927  597037  597146 
597695  597805  597914  598024  598134  598243 
598790  598900  599009  599119  599228  599337 
599883  599992,600101  600210  600319  600428 
600973  601082  601190  601299  601408  601517 

591732  591843J591955  592066 
592843  592954  593064  593175 
593950o94061  594171  594282 
595055  595165  595276  595386 
596157  596267  596377  596487 
597256  597366  597476  597585 
598353*598462  598572  598681 
599446,599556  599665  599774 
600537,600644  600755  600864 
601625J601734  601843  601951 

111 
111 
111 

110 
110 
110 
110 
109 
109 
109 

0 

1 

2 

3 

4 

5  |  6 

7 

8 

9 

TABLE  I. 

LOGARITHMS  OF  NUMBERS. 

133 

No.  4 

ono 

,1 

GOO 

Log.  602060  ( 

562758 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

4UO 
401 
402 
403 
404 
405 
406 
407 
408 
409 

u02UGO 
603144 
604226 
605305 
6063S1 
607455 
608526 
609594 
610660 
611723 

002109  oO-^77  002386 
603253  603361  603469 
604334604442604550 
605413  G0552r605628 
G06489  606596  606704 
607562607669607777 
60S633  608740  608847 
609701  609808  609914 
610767610873610979 
611829611936612042 

002494  oo^oua 
603577  603686 
604658  60476G 
605736605844 
606811  606919 
607884  G07991 
608954609061 
600021610128 
611086611192 
612148612254 

60^711 
603794 
604874 
G05951 
G0702G 
608098 
609167 
610234 
611298 
612360 

602819 
603902 
604982 
606059 
607133 
608205 
609274 
610341 
611405 
612466 

602928,003031 
604010604116 
305089  605191 
606166  606274 
607241  60734* 
608312!60S41£ 
609381  609488 
610447  610554 
611511611617 
612572,612676 

108 
108 
108 
108 
107 
107 
107 
107 
106 
106 

410 
411 
412 
413 
414 
415 
416 
417 
418 
419 

612784  6128UO  612996 
613842613947614053 
614897615003615108 
615950616055616160 
61700o'617105  617210 
618048,618153618257 
619093619198619302 
620136  G20240  620344 
621176621280621384 
622214622318622421 

613101  613207  013313  613419:613525 
614159  614264  614370  614475  614581 
615213  615319,615424  615529  615634 
616265  616370  616475  616580  616685 
617315  617420  617524  617629  617734 
618362  618466  618571  618675  618780 
619406  619511  6i9615  619719  619823 
620448  620552  620656  620760  620864 
621488  621592  621695  621799  621903 
622525  622628  622732  622835,622939 

613630,613736 
614686614792 
615740615845 
616790616895 
617839,617943 
618884618989 
619928620032 
620968621072 
622007622110 
623042,623146 

106 
106 
105 
105 
105 
105 
104 
104 
104 
104 

420 
--421 
422 
423 
424 
425 
426 
427 
428 
429 

623249623353 
624282624385 
625312625415 
626340626443 
627366627468 
628389628491 
629410629511 
630428  630530 
631444631545 
632457|63255S 

623456 
624488 
625518 
626546 
627571 
G28593 
629613 
G30631 
331647 
G326GO 

023559 
624591 
625621 
626648 
627673 
628695 
629715 
630733 
631748 
632761 

623663 
624694 
625724 
626751 
627775 
628797 
629817 
630834 
631849 
632862 

623766 
624798 
625827 
626853 
627878 
628909 
629919 
630936 
631951 
632963 

623869 
624901 
625929 
626956 
627980 
629002 
630021 
631038 
932052 
633064 

623972 
625004 
626032 
627058 
628082 
629104 
630123 
631139 
632153 
633165 

624076:024179 
625107  625209 
626135626238 
627161  627263 
628184628287 
629206629308 
630224  630326 
6312411631342 
G32255  632356 
833266  6333G7 

103 
103 
103 
103 
102 
102 
102 
102 
101 
101 

43U 
431 
432 
433 
434 
435 
436 
437 
438 
439 

033468633569 
634477634578 
635484635584 
636488636588 
637490637590 
638489638589 
639486639586 
640481  640581 
641474641573 
642464;642563 

633670  633771  633872  633973  634074  634175  634276 
634679  634779  634880  634981  635081  635182  635283 
335685  635785  635886  635986  636086  636187  636287 
636688  636789  636889  63G989  637089  637189  637289 
637690  637790  637890  637990  638090  638190  63828'J 
638689  638789  638888  638988  639088  639188  639287 
639686  639785  639885  639984  640084  640183  640283 
640680  640779  640879  640978  641077  641176  641276 
641672  641771  641870  641970  642069  642168  642267 
642662  642761  642860  642959  643058  643156  643255 

034376 
635383 
636388 
637390 
638389 
639387 
640382 
641375 
642366 
643354 

101 
101 
100 
100 
100 
100 
99 
99 
99 
99 

440 
441 
442 
443 
444 
445 
446 
447 
448 
449 

643453,643551  643650  643749 
644439  644537  644635  644734 
645422  645520  645619  645717 
(546404  646502  646600  646698 
647383  647481  647579  647676 
648360  648458  648555  648653 
649335649432  649530  649627 
650307  650405  650502  650599 
651278  651375  651472  651569 
652246  652343  652440  652536 

643847  643946 
644832644931 
645815645913 
646796  64G894 
647774647872 
648750648848 
649724  649821 
650696  650793 
651666651762 
652633652730 

644044 
645029 
646011 
646991 
647969 
648945 
649919 
650890 
651859 
652826 

044143644242 
645127645226 
646109646208 
647089647187 
648067  648165 
649043649140 
650016650113 
650987  651084 
651956652053 
G52923  653019 

644340 
645324 
646306 
647285 
648262 
649237 
650210 
651181 
652150 
653116 

98 
98 
98 
98 
98 
97 
97 
97 
97 
97- 

450 
451 
452 
453 
454 
455 
456 
457 
458 
459 

653213  653309  653405,653502  653598  653695  653791  653888,653984  054080 
654176  654273  654369,654465  654562  654658  654754  654850  654940  655042 
655138  655234  655331  655427  G55523  655619  655714  655810  655906  656002 
656098656194  656290  656386  656481  656577  656673  656769  656864  656960 
657056  657151  657247  657343  657438  657534  657629  657725  657820  657916 
658011  658107  658202  658298  658393  C58488  658584  658679  658774  658870 
658965  659060  659155  659250  659346  659441  65953G  659631  659726  659821 
659916660011  66010G  660201  660296660391  660486660581  660676660771 
660865  660960  661055  661150  651245  661399  661434  661529  661G23  661718 
661813  661907  662002  662096  652191  662285  662380  662474  662569  662663 

96 
96 
96 
96 
96 
95 
95 
95 
95 
95 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

134                  TABLE  I. 

LOGARITHMS  OF  NUMBERS. 

No.  4 

fiftO       ^ 

200         Lo#.  662758  716003 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

4GU 
401 
462 
463 
464 
463 
4G6 
467 
468 
469 

36^758 
6G3701 
664642 
665581 
G66518 
667453 
668386 
669317 
670246 
371173 

66285* 
663795 
664736 
665675 
666612 
667546 
G68479 
669410 
670339 
671265 

66^947 
663889 
664830 
665769 
666705 
667640 
668572 
669503 
670431 
671358 

603041 
663983 
664924 
665862 
666799 
667733 
668665 
669596 
670524 
671451 

6631c5 
664078 
665018 
665956 
666892 
667826 
668758 
669689 
G70617 
671543 

663230 
664173 
665112 
666050 
666986 
667920 
668852 
669782 
670710 
671636 

6033^4 
664''.6G 
665206 
66614S 
667079 
668013 
668945 
669875 
670802 
671728 

1663416 
G64360 
665299 
666237 
667173 
66R106 
669038 
669967 
670895 
671821 

60351k 
664454 
365392 
666331 
66726C 
66819S 
669131 
67006C 
670988 
671913 

00300" 
66454fc 
66548" 
666424 
66735S 
668293 
669224 
670153 
67108C 
67200J 

l>'4 
94 
94 
94 
94 
93 
93 
93 
93 
93 

470 
471 
472 
473 

474 
475 
476 
477 
478 
479 

67*098 
673021 
673942 
(374861 
G75778 
G76694 
G77607 
378518 
G79428 
080335 

G72190 
673113 
G74034 
374953 
375870 
376785 
077698 
678609 
079519 
380426 

672283 
673205 
674126 
G75045 
G75962 
676876 
G777S9 
378700 
679610 
680517 

672375 

673297 
674218 
675136 
376053 
676968 
677881 
678791 
679700 
680607 

672467 
67339( 
674310 

675228 
676145 
677059 
677972 
678882 
679791 
680G98 

6725bO 
673482 
674402 
675320 
676236 
677151 
678063 
678973 
679882 
680789 

67^652 
673574 
674494 
675412 
676328 
677242 
678154 
679064 
679973 
680879 

67^744 
67366G 
674586 
67550C 
676419 
677333 
678245 
679155 
680063 
680970 

07283L 
673758 
674677 
675595 
676511 
677424 
678336 
679246 
680154 
681060 

6729*1] 
673850 
674769 
67568" 
67660^ 
677516 
67842' 
67933r 
680245 
681151 

92 
92 
92 
92 
92 
91 
91 
91 
91 
91 

480 
481 
482 
483 
484 
4»5 
486 
487 
488 
489 

681i:41 
G82145 
(383047 
683947 
G84845 
685742 
686636 
G87529 
688420 
G89309 

681332 
G82235 
G83137 
684037 
684935 
685831 
G8G726 
687618 
588509 
G89398 

08142* 
682323 
683227 
684127 
68502L 
685921 
686815 
687707 
688598 
689486 

681513 

682416 
683317 
684217 
685114 
686010 
68C904 
687796 
688687 
689575 

G816U3 
682506 
683407 
684307 
685204 
686100 
686994 
687886 
688776 
689664 

681693 
682596 
683497 
G84396 
685294 
686189 
687083 
687975 
688865 
689753 

681784 
682686 
683587 
684486 
685383 
686279 
687172 
688064 
688953 
689841 

681874 
682777 
683677 
684576 
685473 
686368 
687261 
688153 
689042 
689930 

681934 
6S2867 
683767 
684666 
685563 
686457 
687351 
688242 
689131 
690019 

68205;. 
682957 
683857 
684756 
6g5652 
686547 
68744C 
688331 
68922C 
690107 

90 
90 
90 
90 
90 
89 
89 
89 
89 
89 

490 
491 
492 
493 
494 
495 
496 
497 
493 
499 

G9019G 
691081 
691965 
692847 
G93727 
G94605 
395482 
396356 
387229 
698100 

660285 
691170 
G92053 
392935 
393815 
694693 
695569 
696444 
697317 
698188 

6903/3 
G91258 
692142 
693023 
693903 
694781 
695657 
696531 
697404 
698275 

690461 
691347 
692230 
693111 
693991 
694868 
695744 
696618 
697491 
69S362 

690550 
691435 
692318 
693199 
694078 
694956 
695832 
69G70G 
G97578 
698448 

690639 
691524 
692406 
693287 
694166 
695044 
695919 
696793 
697665 
698535 

690727 
691612 
692494 
693375 
694254 
695131 
696007 
696880 
697752 
698622 

690810 
691700 
692583 
693463 
694342 
695219 
696094 
696968 
697839 
698709 

G90905 
691789 
692671 
693551 
694430 
695307 
696182 
697055 
69792G 
69.S796 

69U993 
691877 
692759 
693639 
694517 
G95394 
696269 
697142 
69801S 
G9888S 

8J 
88 
88 
88 
88 
88 
87 
87 
87 
87 

5UJ 
501 
502 
503 
504 
505 
506 
507 
508 
509 

J989/0 
696838 
700704 
701568 
702430 
703291 
704150 
705008 
705864 
706718 

6U9057 
699924 
700790 
701654 
702517 
703377 
704236 
705094 
705949 
706803 

G99144 
700011 
700877 
701741 
702603 
703463 
704322 
705179 
706035 
706888 

699236 
700098 
700963 
701827 
702689 
703549 
704408 
705265 
706120 
706974 

699317 
700184 
701050 
701913 
702775 
703635 
704494 
705350 
706206 
707059 

699404 
700271 
701136 
701999 
702861 
703721 
704579 
705436 
706291 
707144 

698491 
700358 
701222 
702086 
702947 
703807 
704665 
705522 
706376 
707229 

G99578 
700444 
701309 
702172 
703033 
703893 
704751 
705607 
706462 
707315 

699604 
700531 
701395 
702258 
703119 
703979 
704837 
705693 
706547 
707400 

690751 
700617 
701482 
702344 
703205 
704065 
704922 
705778 
706632 
707485 

67 
87 
86 
86 
86 
86 
86 
86 
85 
85 

510 
511 
512 
513 
514 
515 
516 
517 
518 
519 

707570 
708421 
709270 
710117 
710963 
711807 
712650 
713490 
714330 
715167 

707655 
708506 
709355 
710202 
711048 
711892 
712734 
713574 
714414 
715251 

707740 
708591 
709440 
710287 
711132 
711976 
712818 
713658 
714497 
715335 

707826 
708676 
709524 
710371 
711216 
712060 
712902 
713742 
714581 
715418 

707911 
708761 
709609 
710456 
711301 
712144 
712986 
713826 
714665 
715502 

707996 
708846 
709694 
710540 
711385 
712229 
713070 
713910 
714749 
715586 

703081 
708931 
709779 
710625 
711470 
712313 
713154 
713994 
714832 
715669 

708106 
709015 
709863 
710710 
711554 
712397 
713238 
714078 
714916 
715753 

708251 
709100 
709948 
710794 
711638 
712481 
713322 
714162 
715000 
715836 

708rfb6 
709185 
710033 
710879 
711723 
712566 
71340G 
714246 
715084 
715920 

85 
85 
85 
85 
84 
84 
84 
84 
84 
84 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

TABLE  I. 

LOGARITHMS  OF  NUMBERS. 

135 

No.  5 

^00       *V 

$00 

Log.  71( 

5003 

63428 

No. 

0 

1 

2 

3 

4 

5 

G 

7 

8 

9   Diff. 

MO 
521 
522 
523 
524 
525 
526 
527 
528 
529 

710003 
716838 
717671 
718502 
719331 
720159 
720986 
721811 
722634 
723456 

71G087 
71G921 
717754 
718585 
719414 
720242 
721068 
721893 
72271G 
723538 

716170 
717004 
717837 
7186G8 
719497 
720325 
721151 
721975 
722798 
723620 

71G254 
717088 
717920 
718751 
719580 
720407 
721233 
722058 
722881 
723702 

716337 
717171 

718003 
718834 
719663 
720490 
721316 
722140 
7229G3 
723784 

716421 
717254 
718086 
718917 
719745 
720573 
721398 
722222 
723045 
723866 

716504 
717338 
718169 
719000 
719828 
720655 
721481 
722305 
723127 
723948 

716588  71GG7J 
717421  717504 
718253718336 
719083719165 
719911J719994 
720738720821 
721563i721646 
722387)722469 
723209  723291 
724030724112 

716754 
717587 
718419 
719248 
720077 
720903 
721728 
722552 
723374 
724194 

83 
83 
83 
83 
83 
83 
82 
82 
82 
82 

550 
531 
532 
533 
534 
535 
53G 
537 
533 
539 

72427(5 
725095 
725912 
726727 
727541 
828354 
729165 
729974 
730782 
731589 

724358 
725176 
725993 
726809 
727623 
728435 
729246 
730055 
730863 
731G69 

7^4440 
725258 
726075 
726890 
727704 
728516 
729327 
730136 
730944 
731750 

72452* 
725340 
72615G 
726972 
727785 
728597 
729408 
730217 
731024 
731830 

724603  724685 
725422725503 
726238  726320 
727053727134 
727866727948 
728678  728759 
729489729570 
730298730378 
7311051731186 
731911J731991 

724767 
725585 
726401 
727216 
728029 
728841 
729651 
730459 
731266 
732072 

724849 
725667 
726483 
727297 
728110 
728922 
729732 
730540 
731347 
732152 

724931 
725748 
726564 
727379 
728191 
729003 
729813 
730621 
731428 
732233 

725013 
72583(i 
726646 
727460 
728273 
729084 
729893 
730702 
731508 
732313 

82 
82 
82 
81 
81 
81 
81 
81 
81 
81 

54J 
541 
542 
543 
544 
545 
546 
5-17 
548 
549 

732394 
733197 
733999 
7348UO 
735599 
736396 
737193 
737987 
738781 
739572 

732474732555 
733278733358 
734079734159 
734880734960 
735679735759 
736476736556 
737272737352 
738067738146 
738860,738939 
739651J739730 

732635 
733438 
734240 
735040 
735838 
736635 
737431 
738225 
739018 
739810 

732715 
73351W 
734320 
735120 
735918 
736715 
437511 
738305 
739097 
739889 

732796 
733598 
734400 
735200 
735998 
73G795 
737590 
738384 
739177 
7399G8 

732876 
733679 
734480 
735279 
736078 
736874 
737670 
738463 
739256 
740047 

73295G 
733759 
734560 
735359 
736157 
736954 
737749 
738543 
739335 
740126 

733037 
733839 
734640 
735439 
736237 
737034 
737829 
738622 
739414 
740205 

733117 
733919 
734720 
735519 
736317 
737113 
737908 
G38701 
739493 
740284 

80 
80 
80 
80 
80 
80 
79 
79 
79 
79 

5130 
551 
552 
553 
554 
555 
556 
557 
558 
559 

740363 
741152 
741939 
742725 
743510 
744293 
745075 
G45855 
746G34 
747412 

740442 
741230 
742018 
742804 
743588 
744371 
745153 
745933 
746712 
747489 

740521 
741309 
742096 
742882 
743667 
774449 
745231 
746011 
746790 
747567 

740599 
741388 
742175 
742961 
743745 
744528 
745309 
746089 
746868 
747645 

740678 
741467 
742254 
743039 
743823 
744606 
745387 
746167 
746945 
747722 

740767 
741546 
742332 
743118 
743902 
744684 
745465 
746245 
747023 
747800 

740836 
741624 
742411 
74319G 
743980 
744740 
745543 
746323 
747101 

740915 
741703 
742489 
743275 
744058 
744819 
745621 
746401 
747179 

740994 
741782 
742568 
743353 
744136 
744917 
745699 
746479 
747256 

741073 
741860 
742G47 
743431 
744215 
744997 
745777 
746556 
747334 
748110 

79 
79 
79 

78 
78 
78 
78 
78 
78 
78 

747878  '7479«r>5|748033 

5GU 
5G1 
5G2 
563 
5G4 
565 
566 
507 
568 
5G9 

748188 
748963 
74973G 
750508 
751279 
752046 
75281C 
753583 
754348 
755112 

,  748206  748343 
749040,749118 
749814749891 
750586  7506G3 
751356751433 
752125752202 
752893  75297C 
753660  75373C 
75442575450] 
755189  75526E 

,748421 
749190 
749968 
75074C 
|75151C 
752273 
,753047 
75381S 
754578 
75534] 

i74849b 
749272 
750045 
750817 
751587 
752350 
,753123 
753889 
754654 
755417 

74857G  748653 
749350749427 
750123750200 
750894750971 
751664751741 
752433  752509 
753200753277 
753966  754042 
754730754807 
755494  75557C 

748731 
|749504 
750277 
751048 
751818 
752586 
753353 
754119 
754883 
755G46 

748808  748885 
749582749659 
750354]750431 
751125751202 
751895751972 
752663  752740 
753430  753506 
754195  754272 
754960755036 
755722  755799 

77 
77 
77 
77 
77 
77 
77 
77 
76 
76 

570 
571 
572 
573 
574 
575 
576 
577 
578 
579 

755875  75595] 
75G63G  75671', 
757396  75747i 
758155  75823( 
758912  75898* 
759668759741 
760422  76049* 
7G117G  76125] 
76192876200; 
762679  76275^ 

750027,750103  756180  75G256  75G332|75G408  756484  756560 
756788  756864)756940  75701675709217571681757244  757320 
757548,757624  757700  757775  757851  757927)758003  758079 
758306  758382  758458  758533  758609  758685  758761  758830 
(  759063  759139  759214  759290  759366  759441  759517  759592 
1  759819  759894  759970  760045  760121  760196  760272  760347 
i  7G0573  760649  760724  760799  760875  760950  761025  761101 
761326  761402i761477  761552  761627  761702  761778  761853 
}  762078  762153  762228  7G2303  762378  7G2453  762529  762604 
[  762829  762904  762978  763053J7G3128  763203  703278  763353 

76 
76 
76 
76 
76 
75 
75 
75 
75 
75 

0 

1 

2 

jxf  4 

5 

G 

7 

8 

9 

136                 TABLE  I. 

LOGARITHMS  OF  NUMBERS. 

No.  5 

300        CM 

100         Log.  76 

jjoq 

306180 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

58U 
581 
582 
533 
584 
585 
586 
587 
588 
589 

763428 
764176 
764923 
765669 
766413 
767156 
767898 
768638 
769377 
770115 

763oOa 
764251 
764998 
765743 
766487 
767230 
767972 
768712 
769451 
770189 

703578 
764326 
765072 
765818 
766562 
767304 
768046 
768786 
769525 
770263 

763653 
764400 
765147 
765892 
766636 
767379 
768120 
768860 
769599 
770336 

763727 
764475 
765221 
765966 
766710 
767453 
768194 
768934 
769673 
770410 

763802 
764550 
765296 
766041 
766785 
767527 
768268 
769008 
769746 
770484 

763877 
764624 
765370 
766115 
766859 
767601 
768342 
769082 
769820 
770557 

703952 
76469t 
765445 
766190 
766933 
76767,' 
768416 
769156 
769894 
770631 

7040^7 
764774 
765520 
766264 
767007 
767749 
768490 
769230 
769968 
770705 

7641U1 

764848 
765594 
766338 
767082 
767823 
768564 
769303 
77004-2 
770778 

75 
75 

75 
74 
74 
74 
74 
74 
74 
74 

59J 
591 
592 
593 
594 
595 
59G 
597 
598 
599 

770852 
771587 
772322 
773055 
773786 
774517 
775246 
775974 
776701 
777427 

770926 
771661 
772395 
773128 
773860 
774590 
775319 
776047 
776774 
777499 

770999 
771734 
772468 
773201 
773933 
774663 
775392 
776120 
776846 
777572 

771073 
771808 
772542 
773274 
774006 
774736 
775465 
776193 
776919 
777644 

771146 

771881 
772615 
773348 
774079 
774809 
775538 
776265 
776992 
777717 

771220 
771955 

772688 
773421 
774152 

774882 
775610 
776338 
777064 
777789 

771293 
772028 
772762 
773494 
774215 
774955 
775683 
776411 
777137 
777862 

771367 
772102 

772835 
773567 
774298 
775028 
775756 
776483 
777209 
777934 

771440 

772175 
772908 
773640 
774371 
775100 
775829 
776556 
777282 
778006 

171514 
772248 
772981 
773713 
774444 
475173 
775902 
776629 
777354 
778079 

74 
73 
73 
73 
73 
73 
73 
73 
73 
73 

GOO 
601 
602 
603 
60  i 
605 
606 
607 
608 
609 

778151 

778874 
779596 
780317 
781037 
781755 
782473 
783189 
783904 
784617 

7782*4 
778947 
779669 
780389 
781109 
781827 
782544 
783260 
783975 
784689 

778296 
779019 
779741 
780461 
781181 
781899 
782616 
783332 
784046 
784760 

778368 
779091 
779813 
780533 
781253 
781971 
782688 
783403 
784118 
784831 

778441 
779163 
779885 
780605 
781324 
782042 
782759 
783475 
784189 
784902 

778513 
779236 
779957 
780677 
781396 
782114 
782831 
783546 
784261 
784974 

778585 
779308 
780029 
780749 
781468 
782166 
782902 
783618 
784332 
785045 

778658 
779380 
780101 
780821 
781540 
782258 
782974 
783689 
784403 
785116 

778738 
779452 
780173 
780893 
781612 
782329 
783046 
783761 
784475 
785187 

7788U2 
779524 
780245 
780965 
781684 
782401 
783117 
783832 
784546 
785259 

72 
72 
72 
72 
72 
72 
72 
71 
71 
71 

610 
611 
612 
613 
614 
615 
616 
617 
618 
619 

785330 
786041 
786751 
787460 
788168 
788875 
789581 
790285 
790988 
791691 

785401 
786112 
786822 
787531 
788239 
788946 
789651 
790356 
791059 
791761 

785472 
786183 
786893 
787602 
788310 
789016 
789722 
790426 
791129 
791831 

785543 
786254 
786964 
787673 
788381 
789087 
789792 
790496 
791199 
791901 

785615 
786325 
787035 
787744 
788451 
789157 
789863 
790567 
791269 
791971 

785686 
786396 
787106 
787815 
788522 
789228 
789933 
790637 
791340 
792041 

785757 
786467 
787177 
787885 
788593 
789299 
790004 
790707 
791410 
792111 

785828 
786538 
787248 
787956 
788663 
789369 
790074 
790778 
791480 
792181 

785899 
786609 
787319 
788027 
788734 
789440 
790144 
790848 
791557 
792252 

785970 
786680 
787390 
788008 
788804 
789510 
790215 
790918 
791620 
792322 

71 
71 
71 
71 
71 
71 
70 
70 
70 
70 

620 
621 
622 
623 
624 
625 
626 
627 
628 
629 

792392 
793092 
793790 
794488 
795185 
795880 
796574 
797268 
797960 
798651 

792462 
793162 
793860 
794558 
795254 
795949 
796644 
797337 
798029 
798720 

792532 
793231 
793930 
794627 
795324 
796019 
796713 
797406 
798098 
798789 

792602 
793301 
794000 
794697 
795393 
796088 
796782 
797475 
798167 
798858 

792672 
793371 
774070 
794767 
795463 
796158 
796852 
797545 
798236 
798927 

792742 
793441 
794139 
794836 
795532 
796227 
796921 
797614 
798305 
798996 

792812 
793511 
794209 
794906 
795602 
796297 
796990 
797683 
798374 
799065 

792882 
793581 
794279 
774976 
795671 
796636 
797060 
797752 
798443 
799134 

792952 
793651 
794349 
795045 
795741 
796436 
797129 
797821 
798512 
799203 

793022 
793721 
794418 
795115 
795811 
796505 
797198 
797890 
798582 
799272 

70 
70 
70 
70 
69 
69 
69 
69 
69 
69 

630 
631 
632 
633 
634 
635 
636 
637 
638 
639 

7993411799409 
800029800098 
800717  800786 
801404801472 
802089802158 
802774802842 
803457803525 
804139  804208 
804821  804889 
805501  805569 

799478 
8001G7 
800854 
801541 
802226 
802910 
803594 
804276 
804957 
805637 

799547 
800236 
800923 
801609 
802295 
802979 
803662 
804344 
805025 
805705 

799616 
800305 
800992 
801678 
802363 
803047 
803730 
804412 
805093 
805773 

799685, 
800373 
801060 
801747 
802432 
803116 
803798 
804480 
805161 
805841 

799754 
800442 
801129 
801815 
802500 
803184 
803867 
804548 
805229 
805908 

799823 
800511 
801198 
801884 
802568 
803252 
803935 
804616 
805297 
805976 

799892 
800580 
801266 
801952 
S02637 
803321 
804003 
S04685 
305365 
B06044 

799961 
800648 
801335 
802021 
802705 
S03389 
304071 
304753 
805433 
300112 

69 
69 
69 
69 
68 
68 
68 
68 
68 
68 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLE  I.                 137 

LOGARITHMS  OP  NUMBERS. 

No.  6 

/inn      i 

000 

Log.  80 

^1  40       ! 

345098 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

640 
641 
642 
643 
644 
645 
646 
647 
648 
649 

800180 
806858 
807535 
808211 
808886 
809560 
810233 
810904 
811575 
812245 

806248  806310 
806926'806994 
807603807670 
808279808346 
808953809021 
809627  809694 
810300810367 
310971811038 
811642811709 
812312812378 

806384 
807061 
807738 
808414 
809088 
809762 
810434 
811106 
811776 
812445 

806451 
807129 
807806 
808481 
809156 
809829 
810501 
811173 
811843 
812512 

806519  806587 
807197  807264 
807873807941 
808549808616 
809223809290 
8G9896  8099G4 
810569810636 
811240811307 
811910811977 
812579812646 

80ob'55 
807332 
808008 
808684 
809358 
810031 
810703 
811374 
312044 
812713 

306723 
807400 
808076 
808751 
809425 
310098 
810770 
811441 
312111 
812780 

806790 
£07467 
308143 
803818 
809492 
810165 
810837 
811508 
812178 
812847 

08 
68 
68 
68 
67 
67 
67 
67 
67 
67 

650 
651 
652 
653 
654 
655 
656 
657 
658 
659 

81*913 
813581 
814248 
814913 
815578 
816241 
316904 
817565 
818226 
818885 

812980 
813648 
814314 
8149SO 
815644 
816308 
816970 
317631 
818292 
818951 

813047 
813714 
814381 
815046 
815711 
816374 
817036 
817698 
818358 
819017 

813114 
813781 
814447 
815113 
815777 
816440 
817102 
817764 
818424 
819083 

813181 
813848 
814514 
815179 
815843 
316506 
817169 
817830 
818490 
819149 

81324V 
813914 
814581 

815246 
815910 
816573 
817235 
81789G 
818556 
819215 

1813314 
813981 
814647 
815312 
815976 
816639 
817301 
817962 
81S622 
819281 

813381 
814048 
814714 
815378 
81C042 
816705 
817367 
818028 
818688 
819346 

8134481815614 
814114814181 
814780814847 
815445815511 
816109816175 
816771816838 
817433817499 
818094  818160 
818754818819 
819412819478 

67 
67 
<^67 
66 
66 
66 
66 
66 
66 
66 

(500 
661 
662 
663 
664 
665 
666 
6G7 
668 
669 

819J44 
820201 
820858 
821514 
822168 
S22822 
823474 
824126 
824776 
825426 

819610 
820267 
820924 
821579 
822233 
822887 
823539 
824191 
824841 
825491 

819675 
820333 
820989 
321644 
822299 
322952 
823605 
324256 
824906 
82555G 

819741 
820399 
821055 
821710 
822364 
823018 
823670 
824321 
824971 
825621 

819807 
820464 
821120 
821775 
822430 
823083 
823735 
824386 
825036 
825686 

819873 
820530 
821186 
821841 
822495 
823148 
823800 
824451 
825101 
825751 

819939 
820595 
821251 
821906 
822560 
823213 
823865 
824516 
825166 
825815 

820004  820070 
820661  820727 
821317821382 
821972  822037 
822626822691 
823279823344 
823930823996 
824581  824646 
825231  825296 
825880825945 

82013* 
820792 
821448 
822103 
822756 
823409 
8240G1 
824711 
825361 
826010 

66 
66 
66 
65 
65 
65 
65 
65 
65 
65 

670 
671 
672 
673 
674 
675 
676 
677 
678 
679 

820076 
826723 
327369 
S28015 
S28GGO 
829304 
829947 
830589 
831230 
831870 

826140 
826787 
827434 
828080 
828724 
829368 
830011 
830653 
831294 
831934 

826204 
326852 
827498 
828144 
828789 
829432 
830075 
830717 
831358 
831998 

826269 
826917 
827563 
828209 
828853 
829497 
830139 
830781 
831422 
832062 

826334 
826981 
827628 
828273 
828918 
829561 
830204 
830845 
831486 
832126 

826399 
827046 
827692 
828338 
828982 
829625 
830268 
830909 
831550 
832189 

826464 
827111 
827757 
828402 
829046 
829690 
830332 
830973 
831614 
832253 

826528 
827175 
827821 
828467 
829111 
829754 
830396 
831037 
831678 
832317 

826593 
827240 
827886 
828531 
829175 
829818 
830460 
831102 
831742 
832381 

826658 
827305 
827951 
828595 
829239 
829882 
830525 
831166 
831806 
832445 

65 
65 
65 
64 
64 
64 
64 
64 
64 
64 

6bO 
681 
682 
683 
684 
685 
686 
687 
688 
689 

832509 
833147 
833784 
834421 
835056 
835691 
836324 
836957 
837588 
838219 

832573 
833211 
833848 
834484 
835120 
835754 
836387 
837020 
837652 
838282 

832637 
833275 
833912 
834548 
835183 
835817 
836451 
837083 
837715 
838345 

832700 
833338 
833975 
834611 
835247 
835881 
836514 
837146 
837778 
838408 

832764 
833402 
834039 
834675 
835310 
835944 
836577 
837210 
837841 
838471 

832828 
833466 
834103 
834739 
835373 
836007 
836641 
837273 
837904 
838534 

832892 
833530 
834166 
834802 
835437 
836071 
836704 
837336 
837967 
838597 

832956 
833593 
83423C 
834866 
835500 
836134 
836767 
837399 
838030 
838660 

833020 
833657 
834293 
834929 
835564 
836197 
836830 
837462 
838093 
838723 

833083 
833721 
834357 
834993 
835627 
836261 
836894 
837525 
838156 
838786 

64 
64 
64 
64 
63 
63 
63 
63 
63 
63 

690 
691 
692 
693 
694 
695 
696 
697 
698 
699 

838849  838912  838975 
839478839541839604 
84010G  840169  840232 
840733840796840859 
841359  841422  841485 
841985842047842110 
842609842672842734 
343233843295843357 
843855843918843980 
844477)844539844601 

839038839101 
339667  839729 
840294!840357 
840921  840984 
841547841610 
842172842235 
842796842859 
843420843482 
844042844104 
844664844726 

839164 
839792 
840420 
841046 
841672 
842297 
842921 
843544 
844166 
844788 

839227 
839855 
840482 
841109 
841735 
842360 
842983 
843606 
844229 
844850 

839289 
839918 
840545 
841172 
841797 
842422 
843046 
843669 
344291 
844912 

839352 
839981 
840608 
841234 
841860 
342484 
343108 
343731 
344353 
343974 

839415 
840043 
840671 
841297 
841922 
842547 
843170 
343793 
344415 
345031', 

63 
63 
63 
63 
63 
62 
62 
62 
62 
62 

0 

1 

2 

3 

4 

5 

G 

7 

8 

9 

138                 TABLE  I. 

LOGARITHMS  OF  NUMBERS. 

No.  7 

000      7 

000 

Log.  84 

^OQS       ! 

480814 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

100 
701 
702 
703 
704 
705 
708 
707 
708 
709 

34509s 
845718 
84G337 
846955 
847573 
848189 
848805 
849419 
850033 
850646 

845100  84522* 
845780  845842 
846399846461 
847017  84707£ 
847634847696 
848251848312 
848866848928 
849481  849542 
850095850156 
850707850769 

845284 
845904 
84652J 
847141 
847758 
848374 
848983 
849604 
850217 
850830 

845346 
845966 
846584 
847202 
847819 
848435 
849051 
849665 
850279 
850891 

84540* 
846028 
846646 
847264 
847881 
848497 
849112 
849726 
850340 
850952 

845471 
84609C 
846708 
84732C 
84794c 
848551 
849174 
849788 
850401 
851014 

I84553i 
84615J 
846771 
84738J 
848004 
85862C 
84923S 
84984£ 
850462 
85107S 

i  84559^, 
846211 

346835 
847441 
84806( 
84868'. 
84929C 
849911 
850524 
851136 

1  84565( 
(84627; 
'84689^ 
847511 
84812* 
84874; 
849358 
849972 
85058E 
851191 

62 
62 
62 
62 
62 
02 
61 
61 
61 
61 

7iO 
711 
712 
713 
714 
715 
71G 
717 
718 
710 

851258 
851870 
352480 
353090 
853698 
854306 
354913 
355519 
356124 
856729 

851320 
851931 
852541 
853150 
853759 
854367 
854974 
855580 
856185 
856789 

851381 
851992 
852602 
853211 
853820 
854427 
855034 
855640 
856245 
856850 

851442851503 
852053852114 

852663  852724 
853272  853333 
853881  853941 
854488854549 
855095855156 
«55701  855761 
856306856366 
856910856970 

851564 
852175 
852785 
853394 
854002 
854610 
855216 
855822 
856427 
857031 

851625 
852236 
852846 
853455 
854063 
854670 
855277 
855882 
856487 
857091 

851686 
852297 
852907 
853516 
854124 
854731 
855337 
855943 
856548 
857151 

851747 
852358 
852968 
853576 
854185 
854792 
855398 
856003 
856608 
857212 

851808 
852419 
853029 
853637 
854245 
854852 
855459 
856064 
856668 
857272 

81 

61 
61 
61 
61 
61 
61 
61 
60 
60 

720 
721 
722 
723 
724 
725 
72G 
727 
728 
729 

857332 
857935 
858537 
359138 
359739 
360338 
860937 
861534 
862131 
8G2728 

857393 
857995 
858597 
859198 
859799 
860398 
860996 
861594 
862191 
862787 

857453 
858056 
858657 
859258 
859858 
860458 
861056 
861654 
862251 
862847 

857513 
858116 
358718 
859318 
859918 
860518 
861116 
861714 
862310 
862906 

857574 
858176 
858778 
859378 
859978 
860578 
861176 
861773 
862370 
862966 

857634 
858236 
858838 
859438 
360038 
860637 
861236 
861833 
862430 
863025 

857G94 
858297 
858898 
859499 
860098 
860697 
861295 
861893 
862489 
863085 

857754 
858357 
858958 
859559 
860158 
860757 
861355 
761952 
862549 
863144 

857815 
958417 
859018 
859619 
860218 
860817 
861415 
862012 
862608 
873204 

857875 
858477 
859078 
859679 
860278 
860877 
861475 
862072 
862668 
863263 

60 
60 
60 
60 
60 
60 
60 
60 
60 
60 

730 
731 
732 
733 
734 
735 
736 
737 
738 
739 

863323 
863917 
S64511 
865104 
865G96 
866287 
866878, 
867467J 
868056 
868644 

S63382 
863977 
864570 
865163 
865755 
866346 
866937 
867526 
868U5 
868703 

863442 
864036 
864630 
865222 
865814 
866405 
866996 
867585 
868174 
868762 

863501  863561  863620 
3G4096  864155  864214 
864689864748864808 
865282865341865400 
865874865933865992 
866465866524866583 
867055867114867173 
867644867703867762 
868233868292868350 
868821868879868938 

863680 
864274 
864867 
865459 
866051 
866642 
867232 
867821 
868409 
868997 

863739 
864333 
864926 
865518 
866110 
866701 
867291 
867880 
868468 
869056 

863798 
864392 
864985 
865578 
866169 
866760 
867350 
867939 
868527 
869114 

863858 
864452 
865045 
865637 
866228 
866819 
867409 
867998 
868586 
869173 

59 
59 
59 
59 
59 
59 
59 
59 
59 
59 

740 
741 
742 
743 
744 
745 
746 
747 
748 
749 

869232 

869818 
870404 
870989 
871573 
872156 
872739, 
8733211 
873902 
874482 

869290 
369877 
370462 
371047 
371631 
372215 
372797 
373379 
373960 
374540 

869349 
869935 
870521 
871106 
871690 
872273 
872855 
873437 
874018 
874598 

869408 
869994 
370579 
871164 
871748 
872331 
872913 
873495 
874076 
874656 

869466  869525 
870053870111 
870638870696 
871223871281 
871806:871865 
872389872448 
872972873030 
873553873611 
874134874192 
874714874772 

869584 
870170 
870755 
871339 
871923 
872506 
373088 
373669 
374250 
374830 

869642 
870228 
870813 
871398 
871981 
872564 
373146 
373727 
374308 
374887 

869701 
870287 
870872 
871456 
872040 
872622 
873204 
873785 
874366 
S74945 

8697(50 
870345 
870930 
871515 
872098 
872681 
873262 
873844 
374424 
375003 

59 
59 
58  . 
58 
58 
58 
58 
58 
58 
58 

1M 
751 
752 
753 
754 
755 
75G 
757 
758 
759 

875061875119,875177 
875640875698875756 
376218-876276876333 
376795876853876910 
377371877429877486 
377947878004878062 
B78522  878579  878G37 
379096879153879211 
379669879726879784 
380242880299880356 

875235  875293875351  875409 
875813875871  875929875987 
876391!876449  876507  876564 
376968  877026  877083  877141  ! 
377544  877602  877659  877717  f 
B78  1  19  878  177  878234  878292  J 
378694!878751  878809  878866  ! 
379268:879325  879383  879440  ! 
379841  879898  879956  880013  ! 
380413,880471  880528  880585  ! 

375466 
376045 
376622 
377198 
377774 
3783491 
378924! 
379497  1 
380070! 
380642! 

375524 
376102 
376680 
377256! 
377832! 
378407! 
378981  ! 
379555! 
380127! 
380699! 

375582 
376160 
376737 
377314 
377889 
378464 
379038 
379612 
380185 
380756 

58 
58 
58 
58 
58 
57 
57 
57 
57 
57 

0 

1 

2 

3 

4 

5    G 

7 

8 

9 

TABLE  I.                  139 

LOGARITHMS  OF  NUMBERS. 

No.  7 

(!()  II      ft 

200         Log.  88 

)81  1 

313814 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

760 
761 
762 
763 
764 
765 
766 
767 
7G8 
7G9 

880814 
881385 
881955 
882524 
883093 
883661 
884229 
884795 
885361 
885926 

88U871 
881442 
882012 
882581 
883150 
883718 
884285 
884852 
885418 
885983 

8809^8 
881499 
882069 
882638 
883207 
883775 
884342 
884909 
885474 
886039 

88u985 
881556 
882126 

882695 
883264 
883832 
884399 
884965 
885531 
886096 

881042 
881613 
882183 
88275- 
883321 
883888 
884455 
885022 
885587 
886152 

881099881156 
881670881727 
882240882997 
882809  88286G 
883377883434 
883945884002 
884512884560 
885078885135 
885644^85700 
886209886265 

881213 
881784 
882354 
882923 
88349  J 
884059 
884625 
885192 
885757 
886321 

881271, 
881841 
882411 
882980 
883548 
884115 
884682 
885248 
885811 
886378 

881328 
881898 
882468 
883037 
883605 
894172 
884739 
885305 
885870 
886431 

57 
57 
57 
57 
57 
57 
57 
57 
57 
56 

770 
771 
772 
773 
774 
775 
776 
777 
778 
779 

886491 
88705-J 
887617 
888178 
888741 
389302 
8S9862 
S90421 
890980 
$91537 

886547 
887111 
887674 
888236 
888797 
889358 
889918 
890477 
891035 
39169S 

886604 
887167 
887730 
888292 
888853 
889414 
889974 
890533 
891091 
891649 

886MU 
887223 
887786 
888348 
688909 
889470 
890030 
890589 
891147 
891705 

886716 
887280 
88784-2 
888404 
888965 
889526 
890086 
890644 
891203 
891760 

886773 
887336 
887898 
888460 
889021 
889582 
890141 
890700 
891259 
891816 

8808*9 
887392 
887955 
888516 
889077 
889638 
890197 
890756 
891314 
891872 

886885 
887440 
888011 
888573 
889134 
889694 
890253 
890812 
891370 
891928 

886942 
887505 
888067 
888629 
889190 
889750 
890309 
890868 
891426 
891983 

880998 
887561 
888123 
888685 
889246 
889806 
890365 
890924 
891482 
892039 

56 
56 
56 
56 
56 
56 
56 
56 
56  » 
56 

780 
781 
782 
783 
784 
785 
786 
787 
7b8 
789 

3K2U9,, 
392651 
593207 
893762 
394316 
J94870 
394423 
895975 
S9652G 
397077 

S9215U 
892707 
893262 
893817 
394371 
^94925 
895478 
896030 
896581 
897132 

j9220ti 
392762 
893318 
893873 
394427 
894980 
395533 
396085 
396636 
897187 

892262 
892818 
893373 
893928 
874482 
895036 
895588 
896140 
896692 
897242 

892317 
892873 
893429 
893984 
394538 
895091 
895643 
896195 
896747 
897297 

892373 
892929 
893484 
894039 
894593 
895146 
895699 
896251 
896802 
897352 

S92429 
892985 
693540 
894094 
894648 
895201 
895754 
896306 
896857 
897407 

892484 
893040 
893595 
894150 
894704 
895257 
895809 
896361 
896912 
897462 

892540 
893096 
893651 
894250 
894759 
895312 
895864 
896416 
896967 
897517 

o92595 
393151 
893706 
894261 
894814 
895367 
895920 
896471 
897022 
897572 

56 
56 
56 
55 
55 
55 
55 
55 
55 
55 

Tad 

791 
792 
793 
794 
795 
793 
797 
798 
799 

S97627 
898176 
598725 
399273 
899820 
900367 
900913 
901458 
902003 
902547 

397682 
898231 
898780 
899328 
899875 
900422 
900968 
901513 
902057 
902601 

897757 
898286 
898835 
899383 
899930 
900476 
901022 
901567 
902112 
902655 

897792 
898341 
898890 
899437 
899985 
900531 
901077 
901622 
902166 
902710 

897847 
898396 
898944 
S99492 
900039 
900586 
901131 
901676 
902221 
902764 

897902 
898451 
898999 
899547 
900094 
900640 
901186 
901731 
902275 
902818 

897957 
898506 
899054 
899602 
900149 
900695 
901240 
901785 
902329 
902873 

898012 
898561 
899109 
899o56 
900203 
900749 
901295 
901840 
902384 
902927 

8980G7 
898615 
899164 
899711 
900258 
900804 
901349 
901894 
902438 
902981 

S98122 
898670 
899218 
899766 
900312 
900858 
901404 
901948 
902491 
903036 

55 
55 
55 
55 
55 
55 
55 
54 
54 
54 

8UO 
801 
802 
803 
804 
805 
806 
807 
808 
809 

J03090 
903632 
904174 
904715 
905256 
905796 
90G335 
906873 
907411 
907948 

903144 
903687 
904228 
904770 
905310 
905850 
906389 
906927 
907465 
908002 

903198 
903741 
904283 
904824 
905364 
905904 
906443 
906981 
907519 
908056 

J05253 
903795 
904337 
904878 
905418 
905958 
906497 
907035 
907573 
908109 

903307 
903849 
904391 
904932 
905472 
906012 
906550 
907089 
907626 
908163 

903361 
903903 
904445 
904986 
905526 
90C065 
906604 
907142 
907680 
908217 

903416 
903958 
904499 
905040 
905580 
906119 
906658 
907196 
907734 
908270 

903470 
904012 
904553 
905094 
905634 
906173 
906712 
907250 
907787 
908324 

903524 
904066 
904607 
905148 
905688 
906227 
906766 
907304 
907841 
908378 

903o78 
904120 
904661 
905202 
905742 
906281 
906820 
907358 
907895 
908431 

54 
54 
54 
54 
54 
54 
54 
54 
54 
54 

810 
811 
812 
813 
814 
815 
816 
817 
818 
819 

908485 
909021 
909556 
910090 
910624 
911158 
911690 
912222 
912753 
913284 

908539 
909074 
909609 
910144 
910678 
911211 
911743 
912275 
912806 
913337 

908592 
909128 
909663 
910197 
910731 
911264 
911797 
912328 
912859 
913390 

908646 
909181 
909716 
910251 
910784 
911317 
911850 
912381 
912913 
913143 

908699 
909235 
909770 
910304 
910838 
911371 
911903 
912435 
912966 
913496 

908753 
909288 
909823 
910358 
910891 
911424 
911956 
912488 
913019 
913549 

908807 
909342 
909877 
910411 
910944 
911477 
912009 
912541 
913072 
913G02 

9(.,'«S60 
909395 
909930 
910464 
910998 
91153( 
91206S 
912494 
913125 
913655 

908914 
909449 
909984 
910518 
911051 
911584 
912116 
912647 
913178 
913708 

908967 
909502 
910037 
910571 
911104 
911637 
912169 
912700 
913231 
913761 

54 
54 
53 
53 
53 
53 
53 
53 
53 
53 

0 

1 

2 

3 

4 

5 

G 

7 

8 

9 

140                 TABLE  I. 

LOGARITHMS  OF  NUMBERS. 

No.  8200—  —8800         Log.  91 

^81  \      ' 

)44483 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

820 
821 
822 
823 
824 
825 
826 
827 
828 
829 

913814 
914343 
914872 
915400 
915927 
916454 
916980 
917505 
918030 
918555 

913SG7 
91  4396 
914925 
915453 
915980 
916507 
917033 
917558 
918083 
918607 

91392U 
914449 
914977 
915505 
916033 
916559 
917085 
917610 
918135 
918659 

913973 
914502 
915030 
915558 
916085 
916612 
917138 
917663 
918188 
918712 

914U2G  914079 
914555914608 
915083915136 
915611915664 
916138916191 
916664916717 
917190917243 
917715917768 
918240918292 
918764918816 

914131914184 
914660914713 
915189915241 
915716915769 
916243916296 
916770916822 
917295917348 
917820917873 
918345918397 
918869918921 

914237 
914766 
915294 
915822 
91634P 
916875 
917400 
917925 
918450 
918973 

914^90 
914819 
915347 
9  J  5874 
916401 
916927 
917453 
917978 
918502 
919026 

53 
53 
53 
53 
53 
53 
53 
52 
52 
52 

830 
831 
832 
833 
834 
835 
830 
837 
838 
839 

91907t> 
919601 
920123 
920645 
921166 
921686 
922206 
922725 
923244 
9237654 

919130 
919653 
920175 
920697 
921218 
921738 
922258 
922777 
923296 
923814 

919183 
919705 
920228 
920749 
921270 
921790 
922310 
922829 
923348 
923865 

919235 
919758 
920280 
920801 
921322 
921842 
922362 
922881 
923399 
923917 

919287 
919810 
920332 
920853 
921374 
921894 
922414 
922933 
923451 
923969 

91934UI919392  919444  91949t> 
919862  919914  919967  920019 
920384  920436  920489  920541 
920906  920958  921010  921062 
921426  921478  921530  921582 
921946  921998  922050  922102 
922466  922518  922570  922622 
922985  923037  923088  923140 
923503  923555  923607  923658 
924021|924072  924124  924176 

919549 
920071 
920593 
921114 
921634 
922154 
922674 
923192 
923710 
924228 

52 
52 
52 
52 
52 
52 
52 
52 
52 
52 

840 
841 
842 
843 
844 
845 
846 
847 
848 
849 

924279 
924796 
925312 
925828 
926342 
926857 
927370 
927883 
928396 
928908 

924331 
924848 
925364 
925879 
926394 
926908 
927422 
927935 
928447 
928959 

924383 
924899 
925415 
925931 
926445 
926959 
92747S 
927986 
928498 
929010 

924434 
924951 
925467 
925982 
926497 
927011 
927524 
928037 
928549 
929061 

924486 
925002 
925518 
926034 
926548 
927062 
927576 
928088 
928601 
929112 

924538 
925054 
925570 
926085 
926600 
927114 
927627 
928140 
928652 
929163 

924589  924041  1924093 
925106  925157,925209 
925621925673925724 
926137926188926239 
926651926702926754 
927165  927216  927268 
927678927730927781 
928191928242928293 
928703  928754  928805 
929214J929266  929317 

924744 
925260 
925776 
926291 
926805 
927319 
927832 
928345 
928856 
929368 

52 
52 
52 
51 
51 
51 
51 
51 
51 
51 

850 
851 
852 
853 
854 
855 
856 
857 
858 
859 

929419 
929930 
930440 
930949 
931458 
931966 
932474 
932981 
933487 
933993 

929470 
929981 
930491 
931000 
931509 
932017 
932524 
933031 
933538 
934044 

929521 
930032 
930541 
931051 
93156G 
932068 
932575 
933082 
933588 
934094 

929572 
930083 
930592 
931102 
931610 
932118 
932626 
933133 
933639 
934145 

929023 
930134 
930643 
931153 
931661 
932169 
932677 
933183 
933690 
934195 

929674 
930185 
930694 
931203 
931712 
932220 
932727 
933234 
933740 
934246 

929725 
930236 
930745 
931254 
931763 
932271 
932778 
933285 
933791 
934296 

929770 
930287 
930796 
931305 
931814 
932321 
932829 
933335 
933841 
934347 

929827 
930338 
930847 
931356 
931864 
932372 
932879 
933386 
933892 
934397 

929878 
930389 
930898 
931407 
931915 
932423 
932930 
933437 
933943 
934448 

51 
51 
51 
51 
51 
51 
51 
51 
51 
51 

860 
861 
862 
863 
864 
865 
866 
867 
868 
8G9 

934496 
935003 
935507 
936011 
936514 
937016 
937518 
938019 
938520 
939020 

934549 
935054 
935558 
936061 
936564 
937066 
937568 
938069 
938570 
939070 

9345U9 
935104 
935608 
936111 
936614 
937116 
937618 
938119 
938620 
939120 

934050 
935154 
935658 
936162 
936664 
937167 
937668 
938169 
938670 
939170 

934700 
935205 
935709 
9L6212 
936715 
937217 
937718 
938219 
938720 
939220 

934751 
935255 
935759 
936262 
936765 
937267 
937769 
938269 
938770 
939270 

934801 
935306 
935809 
936313 
936815 
937317 
937819 
938319 
938820 
939319 

934852 
935356 
935860 
936363 
936865 
937367 
937869 
938370 
938870 
939369 

934902 
935406 
935910 
936413 
936916 
937418 
937919 
938420 
938920 
939419 

U34953 
935457 
935960 
936463 
936966 
937468 
937969 
938470 
938970 
939469 

50 
50 
50 
50 
50 
50 
50 
50 
50 
50 

870 
871 
872 
873 
874 
875 
876 
877 
878 
879 

939519 
940018 
940516 
941014 
941511 
942008 
942504 
943000 
943494 
943989 

939509 
940068 
940566 
941064 
941561 
942058 
942554 
943049 
943544 
944038 

939019 
940118 
940616 
941114 
941611 
942107 
942603 
943099 
943593 
944088 

939669 
940168 
940666 
941163 
941660 
942157 
942653 
943148 
943643 
944137 

939719 
940218 
940716 
941213 
941710 
942206 
942702 
943198 
943692 
944186 

939769 
940267 
940765 
941263 
941760 
942256 
942752 
943247 
943742 
944236 

939819 
940317 
940815 
941313 
941809 
942306 
942801 
943297 
943791 
944285 

939808 
940367 
940865 
941362 
941859 
942355 
942851 
943346 
943841 
944335 

93991893996s 
940417940467 
940915940964 
941412941462 
941909941958 
942405942454 
942900942950 
943396943445 
943890943939 
944384944433 

50 
50 
50 
50 
50 
50 
50 
49 
49 
49 

0 

1 

2    3 

4 

5 

6 

7 

8 

9 

TABLE  I. 

LOGARITHMS  OP  NUMBERS. 

141 

No.  8 

ROO      ') 

100         Log.  944483  973128 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

880 
881 
882 
883 
884 
885 
886 
887 
888 
889 

944483 
944976 
945469 
945961 
946452 
946943 
947434 
947924 
948413 
948902 

.J4463* 
345025 
945518 
946010 
946501 
946992 
947483 
947973 
948462 
948951 

944681 
945074 
945567 
946059 
946550 
947041 
947532 
948021 
948511 
948999 

944631 
945124 
945616 
946108 
946600 
947090 
947581 
948070 
948560 
949048 

94468u 
945173 
945665 
946157 
946649 
947139 
947630 
948119 
948608 
949097 

9447*9 
945222 
945715 
946207 
946698 
947189 
947679 
948168 
948657 
949146 

944771; 
945272 
J45764 
946256 
946747 
947238 
947728 
948217 
948706 
949195 

944828 
945321 
945813 
946305 
946796 
947287 
947777 
948266 
948755 
949244 

;944s77 
1945370 
.945862 
946354 
946845 
947336 
947826 
948315 
948804 
949292 

944927 
94541C 
945911 
946403 
946894 
947385 
947875 
948364 
948853 
949341 

49 
49 
49 
49 
49 
49 
49 
49 
49 
49 

890 
891 
892 
893 
894 
895 
896 
897 
898 
899 

94939U 
949878 
950365 
950851 
951337 
951823 
952308 
952792 
953276 
953760 

949459 
949926 
950413 
950900 
951386 
951872 
952356 
952841 
953325 
953808 

94948ft 
J49975 
950462 
950949 
951435 
951920 
952405 
952889 
953373 
953856 

949536 
950024 
950511 
950997 
951483 
951969 
952453 
952938 
953421 
953905 

949585 
950073 
950560 
951046 
951532 
952017 
952502 
952986 
953470 
953953 

949634 
950121 
950608 
951095 
951580 
i  952066 
952550 
953034 
953518 
954001 

954484 
954966 
955447 
955928 
956409 
956888 
957368 

949683 
950170 
950657 
951143 
951629 
952114 
952599 
953083 
953566 
954049 

949731 
950219 
950705 
951192 
951677 
952163 
952647 
953131 
953615 
954098 

949780 
950267 
950754 
951240 
951726 
952211 
952696 
953180 
953663 
954146 

9498*9 
950316 
950803 
951289 
951774 
952259 
952744 
953228 
953711 
954194 

49 
49 
49 
49 
49 
48 
48  , 
48 
48 
48 

900 
901 
902 
903 
904 
905 
906 
907 
908 
909 

96424*  954291 
954725954773 
955206955255 
953688  955736 
956168956216 
956649  956697 
957128957176 

9o4339  954387 
954821  954869 
955303  955351 
955784  955832 
956264  956312 
956745  956792 
957224957272 

954435 
954918 
955399 
955880 
956361 
956840 
957320 

964532 
955014 
955495 
955976 
956457 
956936 
957416 

954580 
955062 
955543 
956024 
956505 
956984 
957464 
957942 
958420 
958898 

9546*8  y  5467  7 
955110955158 
955592955640 
956072  956120 
956553956601 
957032957C80 
957511957559 
957990  958038 
958468  958516 
958946958994 

48 
48 
48 
48 
48 
48 
48 
48 
48 
48 

957607  957655 
958086958134 
958564J958612 

957703 
958181 
958659 

95/751 
958229 
958707 

957799  957847 
958277  958325 
958755  958803 

957894 
958373 
958850 

910 
911 
912 
913 
914 
915 
9)6 
917 
918 
919 

959041  959089  959137 
959516  959566  959614 
959995960042960090 
960471  960518  960566 
960946960994  961041 
961421  961469  961516 
961895.961943961990 
962369,962417  962464 
962843  962890  962937 
963315963363963410 

959184 
959661 
960138 
960613 
961089 
961563 
962038 
962511 
962985 
963457 

969232 
959709 
960185 
960661 
961136 
961611 
962085 
962559 
963032 
963504 

959*80;95y32b 
959757  959804 
960233960281 
960709960756 
961184961231 
961658961706 
962132962180 
962606962653 
963079963126 
9635521963599 

95'y375j95945*3 

959852959900 
960328;960376 
960804,960851 
961279961326 
961753961801 
962227  1962275 
962701962748 
963174963221 
963646963693 

J59471 
959947 
960423 
960899 
961374 
961848 
962322 
962795 
963268 
963741 

48 
48 
48 
48 
48 
47 
47 
47 
47 
47 

920 
921 
922 
923 
924 
925 
926 
927 
928 
929 

963788963835 
964260964307 
964731  964776 
965202  965249 
965672965719 
966142966189 
966611  966658 
967080967127 
967548967595 
968016968062 

96388* 
964354 
964825 
965296 
965766 
966236 
966705 
967173 
967642 
968109 

963929 
964401 
964872 
965343 
965813 
966283 
966752 
967220 
967688 
968156 

963977 
964448 
964919 
965390 
965860 
966329 
966798 
967267 
967735 
968203 

964024 
964495 
964966 
965437 
965907 
966376 
966845 
967314 
967782 
968249 

964071 
964542 
965013 
965484 
965954 
966423 
966892 
967361 
967829 
968296 

964118 
964590 
965060 
965531 
966001 
966470 
966939 
967408 
967875 
968343 

964165964*1* 
964637  964684 
965108965155 
965578965625 
966048966095 
966517  966564 
966986967033 
967454967501 
967922967969 
968389968436 

47 
47 
47 
47 
47 
47 
47 
47 
47 
47 

930 
931 
932 
933 
934 
935 
936 
937 
938 
939 

968483  968530  968576  968623 
968950  968996  969043  969090 
969416  969462  969509  969556 
969882  969928  969975  970021 
970347  970393  970440  970486 
970812  970858  970904  970951 
971276  971322  971369  971415 
971740  971786  971832  971879 
972203  972249  972295*972342 
972666  972712  972758  972804 

968670 
969136 
969602 
970068 
970533 
970997 
971461 
971925 
972388 
972851 

968716i96870b 
969183969229 
969649969695 
970114970161 
970579970626 
971044971090 
971508971554 
971971972018 
972434972480 
972897972943 

908810 
969276 
969742 
970207 
970672 
971137 
971600 
972064 
972527 
972989 

968856  968903 
969323969369 
969788969835 
970254  970300 
970719970765 
971183971229 
971647971693 
972110972156 
972573972619 
973035973082 

47 
47 
47 
47 
47 
46 
46 
46 
46 
46 

0 

1 

2 

« 

4 

5 

0 

7  |  b 

y 

142                  TABLE  I. 

LOGARITHMS  OF  NUMBERS. 

No.  9 

100      14 

3000        Lop.  973128  000000 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

940 
941 
942 
943 
944 
945 
946 
947 
948 
949 

973128 
973590 
974051 
974512 
97497-2 
975432 
975891 
976350 
97680S 
977-266 

973174^73220 
973636:973682 
974097  974143 
974558  974604 
975018975064 
975478  075524 
975937  975983 
976396  976442 
976854  976900 
977312977358 

973266 
973728 
974189 
974650 
975110 
975570 
97C029 
976487 
976946 
977403 

973313 

973774 
974235 
974696 
975156 
975616 
976075 
976533 
976991 
977449 

973359 
973820 
974281 
974742 
975202 
975661 
976121 
976579 
977037 
977495 

973405,9734511973497 
973866973913973959 
974327:974373974420 
974788974834974880 
975248  975294  975340 
975707  975753  975799 
976166976212976258 
976625976671976717 
977083  977129  977175 
977541977586977632 

973543 
974005 
974466 
974926 
975386 
975845 
976304 
976762 
97722C 
977678 

40 
46 
46 
46 
46 
46 
46 
46 
46 
46 

950 
951 
952 
953 
954 
955 
956 
957 
958 
959 

97/724 
978180 
978637 
979093 
97954* 
980003 
9S0458 
930912 
931365 
931819 

07//69 
978226 
978683 
979138 
979594 
980049 
980503 
980957 
981411 
981864 

97/815 
978272 
978728 
979184 
979639 
980094 
980549 
981003 
98145G 
981909 

977861 
978317 
978774 
979230 
979685 
980140 
980594 
981048 
981501 
981954 

977906 
978363 
978819 
979275 
979730 
980185 
980640 
981093 
981547 
982000 

97795^ 
978409 
978865 
979321 
979776 
980231 
980685 
981139 
981592 
982045 

977998,978043 
978454  978500 
978911978956 
979366979412 
979821979867 
980276980322 
980730980776 
981184981229 
081637981683 
982090,982135 

978089 
978546 
979002 
979457 
979912 
980367 
980821 
981275 
981728 
982181 

078135 
978591 
979047 
979503 
979958 
980412 
980867 
981320 
981773 
982226 

46 
46 
46 
46 
46 
45 
45 
45 
45 
45 

960 
961 
962 
963 
964 
935 
966 
967 
968 
969 

9822Y1 
982723 
933175 
983626 
984077 
984527 
984977 
985426 
985875 
986324 

982310 
982769 
983220 
983671 
984122 
9S4572 
985022 
985471 
985920 
936369 

982362 
982814 
983265 
983716 
984167 
984617 
985067 
985516 
985965 
986413 

982407 
982859 
983310 
983762 
984212 
984662 
985112 
985561 
986010 
986458 

98*152 
982904 
983356 
983807 
984257 
984707 
985157 
985606 
986055 
986503 

982497 
982949 
983401 
983852 
984302 
984752 
985202 
985651 
986100 
986548 

982543  082588 
982994  983040 
983446  983491 
983897  983942 
984347  984392 
984797  984842 
985247  985292 
985696  985741 
986144  986189 
986593986637 

98-2633 
983085 
983536 
983987 
984437 
984887 
985337 
985786 
986234 
986682 

982678 
983130 
983581 
984032 
984482 
984932 
985382 
985830 
986279 
986727 

46 
45 
45 
45 
45 
45 
45 
45 
45 
45 

970 
971 
972 
973 
974 
975 
97(5 
-•  977 
978 
979 

9807  Y  2 
98721C 
98766C 
988113 
988559 
989005 
989450 
989895 
990339 
990783 

9(30810 
987264 
987711 
988157 
93S603 
989049 
989494 
989939 
990383 
990827 

986861  ^86906 
987309987353 
987756987800 
988202  988247 
988648988693 
989094989138 
989539  989583 
989983  99002& 
990428  990472 
990871  990916 

986951 
987398 
987845 
988291 
988737 
989183 
989628 
990072 
990516 
990960 

986995 
987443 
987890 
988336 
988782 
989227 
989672 
990117 
990561 
991004 

987040 
987487 
987934 
988381 
988826 
989272 
989717 
990161 
990605 
991049 

987085 
987532 
987979 
988425 
988871 
989316 
989761 
990206 
990650 
991093 

987130 
987577 
988024 
988470 
988915 
989361 
989806 
990250 
990694 
991137 

987174 
987622 
988068 
988514 
988960 
989405 
989850 
990294 
990738 
991182 

45 
45 
45 
45 
45 
45 
44 
44 
44 
44 

980 
981 
982 
983 
984 
985 
986 
987 
988 
989 

90122U 
991669 
992111 
992553 
992995 
993436 
993877 
994317 
994757 
995196 

991270 
991713 
992156 
992598 
993039 
993480 
993921 
994361 
994801 
995240 

991315991359 
991757  991802 
992200992244 
992642  992686 
993083993127 
993524993568 
993965994009 
994405994449 
994845  994889 
995284  99532S 

991403 
991846 
992288 
992730 
993172 
993613 
994053 
994493 
994933 
985372 

991448 
991890 
9,2333 
992774 
993216 
993657 
994097 
994537 
994977 
995416 

991492  991536 
991934  991979 
992377  992421 
992818992863 
993260993304 
993701  993745 
994141  994185 
994581  994625 
995021  995064 
995460995504 

991580 
992023 
992465 
992907 
993348 
993789 
994229 
994669 
995108 
995547 

991625 
992067 
992509 
992951 
993392 
993833 
994273 
994713 
995152 
995591 

44 
44 
44 
44 
44 
44 
44 
44 
44 
44 

990 
991 
992 
993 
994 
995 
996 
997 
998 
99D 

J'J5(53o 
996074 
996512 
996949 
997386 
997823 
998259 
998695 
999130 
999565 

995079 
996117 
996555 
99G993 
997430 
997867 
998303 
998739 
999174 
999609 

995723995767 
996161  996205 
996599996643 
997037  997080 
997474  997517 
997910  997954 
998346  99839C 
998782  998826 
999218  999261 
999652999696 

995811 
996249 
996687 
997124 
997561 
997998 
99843  1 
998869 
999305 
999739 

995854 
996293 
996730 
997168 
997605 
998041 
998477 
998913 
999348 
999783 

995898  995942  995986 
996336996380996424 
996774996818996862 
997212997255997299 
997648997692997736 
998085998128998172 
998521998564998608 
998956999000999043 
999392999435999478 
999826999870999913 

996030 
996468 
996905 
997343 
997779 
998216 
998652 
999087 
999522 
999957 

44 
44 
44 
44 
44 
44 
44 
44 
44 
43 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLE  II.                 143 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

0  Decree. 

if. 

Sine. 

Co-sine.  (Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

u 

u.oououo 

10.000000 

O.UUUOOO 

lutiuue. 

10.0UOUOO 

lull  Bite. 

GO 

l 

6.463726 

10.000000 

6.463726 

13.531274 

10.00.000 

13.53(>274 

59 

2 

6.764756 

10.000000 

6.764756 

13  2J5244 

10.000000 

13  235244 

58 

3 

6  94')847 

10.000000 

6.940847 

13.059153 

10.  00  '000 

13.059153 

57 

4 

7.065786 

10.000000 

7.065786 

12.934214 

10.000000 

12  934214 

56 

5 

7.162696 

10.000000 

7.162696 

12.837304 

10.  000!  100 

12.837304 

55 

6 

7.241877 

9.999999 

7.241878 

12.758122 

10.000001 

12.758123 

54 

7 

7.308824 

9  999999 

7.30S825 

12.091175 

10.000001 

12.691176 

53 

8 

7.366816 

9.999999 

7.366817 

12.633183 

10.00«)U01 

12  633184 

52 

9 

7.417968 

9.999999 

7.417970 

12.582030 

10.000001 

12  58-032 

51 

10 

7  463726 

9.993938 

7.463727 

12  536273 

10  (100002 

12.536274 

50 

11 

7.5U5118 

9.V9999tf 

7.5uolzU 

12.494(580 

1U.OUUUU2 

1-^.494862 

49 

12 

7  542906 

9.909997 

7  54-1909 

12  457091 

10  000003 

12.457094 

48 

13 

7.5776(58 

9  999097 

7.577(572 

12  422328 

10.000003 

12  422332 

47 

14 

7.609853 

9.999996 

7  609857 

12.390143 

10.000004 

12  390147 

46 

15 

7.639816 

9.999996 

7.639820 

12  360180 

10.000004 

12.330184 

45 

16 

7  667845 

9.999995 

7.667849 

12.332151 

10  000005 

12.332155 

44 

17 

7.694173 

9.999995 

7.694179 

12.305821 

10.000005 

1-2.305827 

43 

18 

7.718997 

9.99:)!'94 

7.719003 

12.280997 

10.000006 

12.281003 

42 

19 

7.742478 

9.999993 

7  742484 

12  257516 

10.000007 

12.257522 

41 

20 

7.764754 

9.999993 

7.764761 

12.235239 

10.000007 

12.235246 

40 

VJl 

V.78o'J43 

y.yyyyy-2 

7  7So951 

12.214U49 

10.000008 

12.214057 

39 

22 

7.806146 

9.999991 

7.803155 

12.193815 

10.000009 

12.1938r)4 

£8 

23 

7.825451 

9.999990 

7.825460 

12.174540 

10.000010 

12.174549 

37 

24 

7  843934 

9.999989 

7.843944 

12.156056 

10.000011 

12.156066 

36 

25 

7.861662 

9.999989 

7.861674 

12.138326 

10.00C011 

12.138338 

35 

26 

7,878695 

9.999988 

7.878708 

12.121292 

10.000012 

12.121305 

34 

27 

7.895085 

9.999987 

7.895099 

12.104901 

10.000013 

12.104915 

33 

28 

7.910879 

9.999986 

7.910894 

12.089106 

10.000014 

12.089121 

32 

29 

7.926119 

9.999985 

7.926134 

12.073866 

10.000015 

12.073881 

31 

30 

7.910842 

9.999983 

7  910858 

12.059142 

10.000017 

12.059158 

30 

31 

7.  955032 

y.9y9982 

Y.'Joo  100 

12  044'JUO 

10.000018 

12.044918 

•29 

32 

7.968870 

9.999981 

7.968889 

12.031111 

10.000019 

12.031130 

28 

33 

7.982233 

9.999980 

7  082253 

12.017747 

10.000020 

12.017767 

27 

3i 

7.995198 

9.  999979 

7.995219 

12.004781 

10.000021 

12.004802 

2(5 

35 

8  007787 

3.999977 

8.007809 

11.992191 

40.000023 

11.992213 

25 

36 

8.020021 

9.999976 

8.020045 

11.979955 

10.000024 

11.979979 

24 

37 

8.031919 

y  999975 

8.031945 

11.968055 

10.000025 

11.968081 

23 

33 

8  043501 

9.999973 

8.043527 

11.956473 

10.000027 

11.956499 

22 

39 

8.054781 

9.999972 

8.054809 

11.945191 

10.000028 

11.945219 

21 

40 

8.065776 

9.999971 

8.065806 

11.934191 

10.000029 

11.934224 

20  | 

41 

8.  076500 

9.  999969 

8  076531 

11.923469 

10.000031 

11.923500 

19 

42 

8.086965 

9.999968 

8.086997 

11.913003 

10.000032 

11.913035 

18 

43 

8.097183 

9.999966 

8.097217 

11.902783 

10.000034 

11  902817 

17 

44 

8.107167 

9.999964 

8.107202 

11.892798 

10.000036 

11.892833 

1C 

45 

8.11C926 

9.999963 

8.116963 

11.883037 

10.000037 

11.883074 

15 

46 

8.126471 

9.999961 

8.126510 

11.873490 

10.000039 

11.873529 

14 

47 

8.135810 

9  999959 

8.135851 

11.864149 

10.000041 

11.864190 

13 

48 

8.144953 

9.999958 

8.144996 

11.855004 

10.000042 

11.855047 

12 

49 

8.153907 

9.999956 

8.153952 

11.846018 

10.000044 

11.84(i093 

11 

50 

8-162681 

9.999954 

8.162727 

11.837273 

10.000046 

11.837319 

10 

51 

8.171280 

y.yyyy52 

8.1713*8 

11.828672 

1U.  000048 

11.828720 

y 

52 

8.179713 

9.999950 

8.179763 

11.820237 

10.000050 

11  820287 

8 

53 

8.187985 

9.999948 

8.188036 

11.811964 

10.000052 

11.812015 

7 

54 

8.193102 

9  999946 

8.196156 

11.803844 

10.000054 

11.80381)8 

6 

55 

8.204070 

9  999944 

8.204126 

11.795874 

10.000056 

11.795930 

5 

56 

8.211895 

9  909942 

8.211953 

11.788047 

10.000058 

11.788105 

4 

57 

8.219581 

9.999940 

8.219641 

11.780359 

10.000060 

11.780419 

3 

58 

8.227134 

9.999938 

8.227195 

11.772805 

10.000062 

11.772866 

2 

59 

8.234557 

9.999936 

8.234621 

11.765379 

10.000064 

11.765443 

1 

CO 

8.241855 

9.999934 

8.241922 

11.758078 

10.000066 

11.758145 

0 

M. 

Co-sine. 

Sine.   |Co-tang. 

Tangent. 

Co-sec. 

Secant.  |  M. 

SO  Degrees. 

144                 TABLE  II. 

LOOAEITHM1C  SIXES,  TANGENTS,  AND  SECANTS. 

1  Degree. 

M. 

Sine. 

Co-sine.  |Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

u 

8.24185s 

9.yyyy34 

8.241921 

11.75SU79 

10.0UUOG6 

11.758145 

GO 

1 

8.249033 

9.999932 

8.249102 

11.750898 

10.000068 

11.750967 

59 

2 

8.256094 

9.999929 

8.256165 

11.743835 

10.000071 

11.743906 

58 

3 

8.263042 

9.999927 

8.263115 

11.736885 

10.000073 

11.736958 

57 

4 

8  269881 

9.999925 

8.269956 

11.730044 

10.000075 

11.730119 

56 

5 

8.276614 

9.999922 

8.276691 

11.723309 

10.000078 

11.723386 

55 

6 

8.283243 

9.999920 

8.283323 

11.716677 

10.000080 

11.716757 

54 

7 

8.289773 

9.999918 

8.289856 

11.710144 

10.000082 

11.710227 

53 

8 

8.29G2u7 

9.999915 

8.296292 

11.703708 

10.000085 

11.703793 

52 

9 

8.302546 

9.999913 

8.302634 

11.697366 

10.000087 

11.697454 

51 

10 

8  308794 

9.999910 

8.308884 

11.C91116 

10.000090 

11.691206 

50 

11 

8.314954 

9  999907 

8.315046 

11.684954 

1U.OOOU93 

11.685046 

49 

12 

8.321027 

9.999905 

8  321122 

11.678878 

10.000095 

11.678973 

48 

18 

8  327016 

9.999902 

8.327114 

11.672886 

10.000098 

11.672984 

47 

14 

8.332924 

9.999899 

8.333025 

11.666975 

10.000101 

11.667076 

46 

15 

8.338753 

9.999897 

8.338856 

11.661144 

10.000103 

11.661247 

45 

16 

8.344504 

9.999b94 

8.344610 

11.655390 

10.000106 

11.655496 

44 

17 

8.350181 

9.999891 

8.350289 

11.649711 

10.000109 

11.649819 

43 

18 

8.355783 

9.999888 

8.355895 

11.644105 

10.000112 

11.644217 

42 

19 

8.361315 

9.999885 

8.361430 

11.638570 

10.000115 

11.638685 

41 

20 

8.366777 

9.999882 

8  366895 

11.633105 

10.000118 

11.633223 

40 

21 

8.37:4171 

9.99987'j 

8.372292 

11.027708 

lo.ouul2l 

ll.b2Y629 

39 

22 

8.377499 

9.99J876 

8  377622 

11.622378 

10.000124 

11.622501 

38 

23 

8.332702 

9.999373 

8.382889 

11.617111 

10.000127 

11.617238 

37 

24 

8.3879G2 

9.999670 

8.388092 

11.611908 

10.000130 

11.612038 

36 

25 

8.393101 

9.999867 

8.393234 

11.606766 

10.000133 

11.606899 

35 

26 

8.398179 

9.999864 

8.398315 

11.601685 

10.000136 

11.601821 

34 

27 

8.403199 

9.999S61 

8.403338 

11.596662 

10.000139 

11.596801 

33 

28 

8.408161 

9.993858 

8.408304 

11.591696 

10.000142 

11.591839 

32 

29 

8.413068 

9.999854 

8.413213 

11.586787 

10.000146 

11.586932 

31 

30 

8.417919 

9.999851 

8.418068 

11.581932 

10.000149 

11.582081 

30 

31 

8.422717 

9.99J848 

8.4*2869 

11.577131 

10.000162 

11.577283 

29 

32 

8.427462 

9.999844 

8.427618 

11.572382 

10.000156 

11.572538 

28 

33 

8  432156 

9.999841 

8.432315 

11.567685 

10.000159 

11.567844 

27 

34 

8.436800 

9  999838 

8.436962 

11.563038 

10.000162 

11.563200 

26 

35 

8.441394 

9.999834 

8.441560 

11.558440 

10.000166 

11.558606 

25 

36 

8.445941 

9.999S31 

8.446110 

11.553890 

10.000169 

11.554059 

24 

37 

8.450440 

9.999827 

8.450613 

11.549387 

10.000173 

11.549560 

23 

38 

8.454893 

9.999824 

8.455070 

11.544930 

10.000176 

11.545107 

22 

39 

8.459301 

9.993820 

8.459481 

11.540519 

10.000180 

11.540699 

21 

40 

8.463665 

9.999816 

8.463849 

11.536151 

10.000184 

11.536335 

20 

41 

8.467985 

9.9U9813 

8.4(36172 

11.531828 

1U.L00187 

11.532015 

19 

42 

8.472263 

9.999809 

8.472454 

11.527546 

10.000191 

11.527737 

18 

43 

8.47649S 

9.999S05 

8.476693 

11.523307 

10.000195 

11.523502 

17 

44 

8.480693 

9.999801 

8.480892 

11.519108 

10.000199 

11.519307 

16 

45 

8.484848 

9.999797 

8.485050 

11.514950 

10.000203 

11.515152 

15 

46 

8.488963 

9.999794 

8.489170 

11.510830 

10.000206 

11.511037 

14 

47 

8.493040 

9.999790 

8.493250 

11.506750 

10.000210 

11.506960 

13 

48 

8.497078 

9.999786 

8.497293 

11.502707 

10.000214 

11.502922 

12 

49 

8.501080 

9.999782 

8.501298 

11.498702 

10.000218 

11.498920 

11 

50 

8.505045 

9.999778 

8.505267 

11.494733 

10  000222 

11.494955 

10 

51 

8.508974 

9.999774 

8.509200 

11.490»UO 

10.0U0220 

11.491026 

9 

52 

8.512867 

9.999769 

8.513098 

11.486902 

10.000231 

11.487133 

8 

53 

8.516726 

9.999765 

8.516961 

11.483039 

10.000235 

11.483274 

7. 

54 

8.520551 

9.999761 

8.520790 

11.479210 

10.000*>39 

11.479449 

6 

55 

8.524343 

9.999757 

8.524586 

11.475414 

10.000243 

11.475657 

5 

56 

8.528102 

9.999753 

8.528349 

11.471651 

10.000247 

11.471698 

4 

57 

8.531828 

9.999748 

8.532080 

11.467920 

10.000252 

11.468172 

3 

58 

8.535523 

9.999744 

8.525779 

11.464221 

10.000256 

11.464477 

2 

59 

8.539186 

9.999740 

8.539447 

11.460553 

10.000260 

11.460814 

1 

60 

8.542819 

9.999735 

8.543084 

11.456916 

10.000265 

11.457181 

0 

M. 

Co-sine. 

Sine.   |Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

88  l>«»grees. 

TABLE  II.                 145 

LOGARITHMIC  SIGNS,  TANGENTS  AND  SECANTS. 

2  Degrees. 

M.   Sine. 

Co-sine.  (Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

u 

8.542819 

y.  999/35 

8.543U84 

11.450916 

1U.OU0205 

11.46/151 

00 

1 

8.546422 

9  999731 

8.546691 

11.453309 

10.000269 

11.453578 

£9 

2 

8.549995 

9.999726 

8.550268 

11.449732 

10.000274 

11.450005 

58 

3 

8.553539 

9  999722 

8.553817 

11.440183 

10.000278 

11.4464G1 

57 

4 

8.557054 

9.999717 

8.557336 

11.442664 

10.000283 

11.44-2946 

56 

5 

8.5G0540 

9.999713 

8.560828 

11.439172 

10.000287 

11.439460 

55 

G 

8.56^999 

9'999708 

8.564291 

11.435709 

10.000292 

11.436001 

54 

7 

8.5G7431 

9.999704 

8.567727 

11.432273 

10.000296 

11.432569 

53 

8 

8.570836 

9  999G99 

8.571137 

11.428863 

10.000301 

11.429164 

52 

9 

8.574214 

9.999694 

8  574520 

11.425480 

10.000306 

11.425786 

51 

10 

8  577566 

9.999689 

8.577877 

11.422123 

lO.OOf  311 

11.422434 

50 

11 

8  .  550o92 

9  999085 

8.5«1208 

11.418792 

10.000315 

11.419108 

49 

12 

0.584193 

9.999G80 

8  584514 

11.415486 

10.000320 

11.415807 

48 

13 

8.587469 

9  999675 

8.587795 

11.412205 

10.000325 

11.412531 

47 

14 

8.590721 

9  999670 

8.591051 

11.408949 

10.000330 

11.409279 

46 

15 

8.593948 

9  999665 

8.594283 

11.405717 

10.000335 

11.406052 

45 

1C 

8.597152 

9.999660 

8.597492 

11.402508 

10.000340 

11.402848 

44 

17 

8.600332 

9.999655 

8.600677 

11.399323 

10.000345 

11.399668 

43 

18 

8.603489 

9.999650 

8.603839 

11.396161 

10.000350 

11.396511 

42 

19 

8.606623 

9.999645 

8  606978 

11.393022 

10.000355 

11.393377 

41 

20 

8  609734 

9.999640 

8.610094 

11.389906 

10.000360 

11.390266 

40 

21 

8.0128*3 

9.999635 

8.613ifc9 

11.380811 

10.000305 

11.387177 

39 

22 

8.615891 

9  999G29 

8.616262 

11.383738 

10.000371 

11.3841C9 

38 

23 

8.618937 

9.999624 

8.619313 

11.380687 

10.000376 

11.3810G3 

37 

24 

8.621962 

9.999619 

8.622343 

11-377657 

10.000381 

11.378038 

36 

25 

8.624965 

9.999614 

8.625352 

11.374648 

10.000386 

11.375035 

35 

2G 

8.627948 

9.999608 

8.628340 

11.371660 

10.000392 

11.372052 

34 

27 

8  630911 

9.999603 

8.631308 

11.368692 

10.000397 

11.369089 

33 

28 

8.633854 

9.999597 

8.634256 

11.365744 

10.000403 

11.366146 

32 

29 

8.636776 

9.999592 

8.637184 

11.362816 

10.000408 

11.363224 

31 

30 

8.639380 

9.999586 

8.640093 

11.359907 

10.000414 

11.360320 

30 

31 

8.042503 

9.999581 

8.642982 

11.357018 

10.000419 

11.357437 

29 

32 

8.645428 

9.999575 

8.645853 

11.354147 

10.000425 

11.354572 

28 

33 

8.648274 

9  999570 

8.648704 

11.351296 

10.000430 

11.351726 

27 

34 

8.651102 

9.999564 

8.651537 

11.348463 

10.000436 

11.348898 

26 

35 

8.653911 

9.999558 

8.654352 

11.345648 

10.000442 

11.346089 

25 

3G 

8.656702 

9.999553 

8.657149 

11.342851 

10.000447 

11.343298 

24 

37 

8.659475 

9.999547 

8.659928 

11.340072 

10.000453 

11.340525 

23 

38 

8.6G2230 

9.999541 

8.662689 

11.337311 

10.000459 

11.337770 

22 

39 

8.664968 

9  999535 

8.665433 

11.334567 

10.000465 

11.335032 

21 

40 

8.667689 

9.999529 

8.G68160 

11.331840 

10.000471 

11.332311 

20 

41 

8.070393 

9.999524 

8.670870 

11.329130 

10.000470 

'  11.329607 

19 

42 

8.673080 

9.999518 

8.673563 

11.326437 

10.C00482 

11.326920 

18 

43 

8  G7o751 

9.999512 

8.676239 

11.323761 

10.000488 

11.324249 

17 

44 

8.678405 

9.999506 

8.678900 

11.321100 

10.000494 

11.321595 

16 

45 

8.G81043 

9.999500 

8.681544 

11.318456  . 

10.000500 

11.318957 

15 

4G 

8.683665 

9.999493 

8.684172 

11.315828 

10.000507 

11.316335 

14 

47 

8.68G272 

9.999487 

8.686784 

11.313216 

10.000513 

11.31S728 

13 

48 

8.688863 

9.999481 

8.689381 

11.310619 

10.000519 

11.311137 

12 

49 

8.691438 

9.999475 

8.691963 

11.308037 

10.000525 

11.308562 

11 

50 

8.693998 

9.999469 

8.G94529 

11.305471 

10.000531 

11.306002 

10 

51 

S  .  690543 

9.999403 

8.097081 

11.302919 

10.000537 

11.303457 

9 

52 

8.699073 

9.999456 

8.G99617 

11.300383 

10.000544 

11.300927 

8 

53 

8.701589 

9.999450 

8.702139 

11.297861 

10.000550 

11.298411 

7 

51 

8.704090 

9.999443 

8.704646 

11.295354 

10.000557 

11.295910 

6 

55 

8.705577 

9.999437 

8.707140 

11.292860 

10.000563 

11.293423 

5 

56 

8.709049 

9.999431 

8.709618 

11.290382 

10.0005G9 

11.290951 

4 

57 

8.711507 

9.999424 

8.712083 

11.287917 

10.000576 

11.288493 

3 

58 

8.713952 

9.999418 

8.714534 

11.285466 

10.000582 

11.286048 

2 

59 

8.716383 

9.999111 

8.716972 

11.283028 

10.000589 

11.283617 

1 

GO 

8.718800 

9.999404 

8.719390 

11.280CO! 

10.000596 

11.C81200 

0 

M.  Co-sine. 

Sine.   |Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

HI  Oesrces. 

146                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

8  Degrees. 

M. 

•Sine. 

Co-sine. 

Tangent 

.  Co-tang. 

Secant. 

Co-sec.   M. 

U 

8.718800 

y  .  'J99i04 

8.719J9U 

11  *8UOUi 

10.000596 

11.28121X) 

GO 

1 

8.  '72  1-204 

9.999398 

8.721806 

11.278194 

10.000602 

11.278796 

59 

2 

8.723595 

9.999391 

8.724-04 

11.275796 

10.000609 

11.276405 

58 

3 

8.725972 

9.999384 

8.726588 

11.273412 

10.000616 

11.274028 

57 

4 

8  728337 

9.999378 

8.728959 

11.271041 

10.000622 

11.271663 

56 

5 

8.730688 

9.999371 

8.731317 

11.268683 

10.000629 

11.269312 

55 

6 

8.733027 

9.999364 

8.733663 

11.266337 

10.000636 

11.266973 

54 

7 

8.735354 

9.999357 

8.735996 

11.264004 

10.000643 

11.264646 

53 

8 

8.737667 

9.999350 

8.738817 

11.261683 

10.000650 

11.262333 

52 

9 

8.739969 

9.999343 

8.740626 

11.259374 

10.000657 

11.260031 

51 

10 

8.742259 

9.999336 

8.742922 

11.257078 

10.0C0664 

11.257741 

50 

11 

8.744036 

9  999329 

8.745207 

11.254793 

10.000671 

11.255464 

49 

12 

8  746802 

9.999322 

8.747479 

11.252521 

10.000678 

11.253108 

48 

13 

8.749055 

9.999315 

8.749740 

11.250260 

10.000685 

11.250945 

47 

14 

8.751207 

9  999308 

8.751989 

11.248011 

10.000692 

11.248703 

46 

15 

8  753528 

9.999301 

8.754227 

11.245773 

10.000699 

11.246472 

45 

16 

8.755747 

9.999294 

8.756453 

11.243547 

10.000706 

11.244253 

44 

17 

8.757955 

9  999287 

8.758668 

11.241332 

10.000713 

11.242045 

43 

18 

8.760151 

9.999279 

8.760872 

11.239128 

10.000721 

11.239849 

42 

19 

8.762337 

9  999272 

8  763065 

11.236935 

10.000728 

11.237663 

41 

20 

8.764511 

9.999265 

8.765246 

11.234754 

10.000735 

11.235489 

40 

•21 

8.766t)75 

9.999257 

8.7U7417 

11.232683 

10.000743 

ll.'2333i.5 

3D 

22 

8.768828 

9.999250 

8.769578 

11.230422 

10.000750 

11.231172 

38 

23 

8.770970 

9.999242 

8,771727 

11.228273 

10.000758 

11.229030 

37 

24 

8  773101 

9.999235 

8.773866 

11.226134 

10.000765 

11.226899 

36 

25 

8.775223 

9  999227 

8.775995 

11.224005 

10.000773 

11.224777 

35 

26 

8.777333 

9  999220 

8  778114 

11.221886 

10.000780 

11.222667 

34 

•27 

8.779434 

9  999212 

8.780222 

11.219778 

10.000788 

11.220566 

33 

28 

8.781524 

9.999205 

8.782320 

11.217680 

10.000795 

11.218476 

32 

29 

8.783605 

9.999197 

8  784408 

11.215592 

10.000803 

11.216395 

31 

30 

8.785675 

9.999189 

8.786486 

11.213514 

10.000811 

11.214325 

30 

31 

8.787736 

9.999181 

8.788554 

11.211446 

10.000819 

11.212-204 

5i9 

32 

8  789787 

9  999174 

8  790613 

11.209387 

10.000826 

11.210213 

28 

33 

8.791828 

9.999166 

8.792662 

11.207338 

10.000834 

11.208172 

27 

34 

8.793859 

9.999158 

8.794701 

11.205299 

10.000842 

11.206141 

26 

35 

8.795881 

9.999150 

8.796731 

11.203269 

10.000850 

11.204119 

25 

36 

8  797894 

9.999142 

8.798752 

11.201248 

10.000858 

11.202106 

24 

37 

8.799897 

9  999134 

8.800763 

11.199237 

10.000866 

11.200103 

23 

38 

8.801892 

9.999126 

8.802765 

11.197235 

10.000874 

11.198108 

22 

39 

8.803876 

9.999118 

8.804758 

11.195242 

10.000882 

11.196124 

21 

40 

8.805852 

9.999110 

8.806742 

11.193-258 

10.000890 

11.194148 

20 

41 

8.807819 

9.999102 

6.808717 

11.191283 

10.000898 

11.192181 

19 

42 

8.809777 

9.999094 

8.810683 

11.189317 

10.000906 

11.190223 

18 

43 

8.811726 

9.999086 

8.812641 

11.187359 

10.000914 

11.188274 

17 

44 

8.813667 

9.999077 

8.814589 

11.185411 

10.000923 

11.186333 

10 

45 

8.815599 

9.999069 

8.816529 

11.183471 

10.000931 

11.184401 

15 

46 

8.817522 

9.999061 

8.818461 

11.181539 

10.000939 

11.182478 

14 

47 

8  819436 

9.999053 

8.820384 

11.179616 

10.000947 

11.180564 

13 

48 

8.821343 

9.999044 

8.822298 

11.177702 

10.000956 

11.178657 

12 

49 

8.823240 

9.999036 

8.824205 

11.175795 

10.000964 

11.170760 

11 

50 

8.825130 

9.999027 

8.826103 

11.173897 

10.000973 

11.174870 

10 

1  51 

8.8-27011 

9.999019 

8.8^v  992 

11.172008 

10.000981 

Il.17k.9o9 

9 

52 

8.828884 

9.999.ilO 

8.829874 

11.170126 

10.000990 

11.171116 

8 

53 

8.830749 

9.999002 

8.831748 

11.168252 

10.000998 

11.169251 

7 

54 

8.832607 

9.998993 

8.833613 

11.166387 

10.001007 

11.167393 

6 

55 

8  831456 

9.998984 

8  835471 

11.164529 

10.001016 

11.165544 

5 

56 

8.836297 

9.998976 

8.837321 

11.162679 

10.001024 

11.163703 

4 

57 

8.838130 

9  998967 

8.839163 

11.160837 

10.001033 

11.161870 

3 

58 

8.839956 

9.998958 

8.840998 

11.159002 

10.001042 

11.160044 

2 

59 

8.841774 

9.99S950 

8.842825 

11.157175 

10.001050 

11.158226 

1 

GO 

8.843585 

9.998941 

8.844644 

11.155356 

10.001059 

11.156415 

0 

H. 

Co-sine. 

Sine. 

3  o  -tang. 

Tangent. 

Co-sec. 

Secant. 

1C. 

8(>  iX'.srrees. 

TABLE  II.                 147 

LOGARITHMIC  SINES,  TANGENTS.  AND  SECANTS. 

4  Decrees. 

M.   Sine. 

Co-sine.  Tangent.  Co-tang. 

Secant.   Co-sec. 

M. 

u 

8.843585 

9.998941 

»  .  844U44 

11.155356 

10.001059 

ll.lo(J4lo 

CO 

1 

8.845387 

9.998932 

8.846455 

11.153545 

10.001068 

11.154613 

59 

2 

8.847183 

9.99S923 

8.848260 

11.151740 

10.001077 

11.152817 

58 

3 

8.848971 

9.998914 

8.850057 

11.149943 

10.001086 

11.151029 

57 

4 

8  850751 

9.998905 

8.851846 

11.148154 

10.001095 

11.149249 

56 

5 

8.852525 

9.998896 

8.853628 

11.146372 

10.001104 

11.147475 

£5 

6 

8.854291 

9.998887 

8.855403 

11.144597 

10.001113 

11.145709 

54 

7 

8  856049 

9.998878 

8.857171 

11.142829 

10.001122 

11.143951 

53 

8 

8.857801 

9.998869 

8.858932 

11.141068 

10.001131 

11.142199 

52 

9 

8.859516 

9.998860 

8.  861  "686 

11.139314 

10.001140 

11.140454 

51 

10 

8.861283 

9.998851 

8.862433 

11.137567 

10.001149 

11.138717 

50 

11 

8.  865014 

9  998841 

8.864173 

11.135827 

10.001159 

11.136986 

49 

12 

8.864738 

9.998832 

8.865906 

11.134094 

10.001168 

11.135262 

48 

13 

8.866455 

9.998823 

8.867632 

11.132368 

10.001177 

11.133545 

47 

U 

8.868165 

9.998813 

8  869351 

11.130649 

10.001187 

11.131835 

46 

15 

8.869868 

9.993804 

8.871064 

11.128936 

10.001196 

11.130132 

45 

)6 

8.871565 

9.998795 

8.872770 

11.127230 

10.001205 

11.128435 

44 

17 

8.873255 

9.998785 

8.874469 

11.125531 

10.001215 

11.126745 

43 

18 

8.874938 

9.998776 

8.876162 

11.123838 

10.001224 

11.125062 

42 

19 

8.876615 

9.998766 

8.877849 

11.122151 

10.001234 

11.123385 

41 

20 

8.878285 

9  993757 

8.879529 

11.120471 

10.001243 

11.121715 

40 

21 

8.679949 

9.998Y47 

8  881202 

11.118798 

10.001253 

1  1.120051 

*:*J 

22 

8.881607 

9.998738 

8.882869 

11.117131 

10.001262 

11.118393 

38 

23 

8.883258 

9  998728 

8.884530 

11.115470 

10.001272 

11.116742 

37 

24 

8.884903 

9.998718 

8.886185 

11.113815 

10.001282 

11.115097 

3G 

25 

8.886542 

9.998708 

8  887833 

11.112167 

10.001292 

11.113458 

35 

26 

8  888174 

9.998699 

8.889476 

11.110524 

10.001301 

11.111826 

3i 

27 

8  889801 

9.998689 

8  891112 

11.108888 

10.001311 

11.110199 

33 

28 

8.891421 

9.998679 

8.892742 

11.107258 

10.001321 

11.108579 

32 

29 

8.893035 

9.998669 

8.894366 

11.105634 

10.001331 

11.106965 

31 

30 

8  894643 

9.998659 

8.895984 

11.104016 

10.001341 

11.105357 

30 

31 

8.896246 

9  .  998649 

8.897596 

11.102404 

10.001351 

11.1037o4 

29 

32 

8.897842 

9.998639 

8.899.03 

11.100797 

10.001361 

11.102158 

28 

33 

8.899432 

9.998629 

8.900803 

11.099197 

10.001371 

11.100568 

27 

34 

8.901017 

9.998619 

8.902398 

11.097602 

10.001381 

11.098983 

26 

35 

8.902596 

9.998609 

8.903987 

11.098013 

10.001391 

11.097404 

25 

3G 

8.904169 

9.998599 

8.965570 

11.094430 

10.001401 

11.095831 

24 

37 

8  905736 

9.998589 

8.907147 

11.092853 

10.001411 

11.094264 

23 

38 

8.907297 

9.998578 

8.908719 

11.091281 

10.001422 

11.092703 

22 

30 

8.908853 

9.998568 

8.910285 

11.089715 

10.001432 

11.091147 

21 

40 

8  9HI404 

9.998558 

8.911846 

11.088154 

10.001442 

11.089596 

20 

41 

8.911949 

9.998548 

8.913401 

11.086599 

10.001452 

11.088051 

19 

42 

8.913488 

9.998537 

8.914951 

11.085049 

10.001463 

11.086512  , 

18 

43 

8.915022 

9.998527 

8.916495 

11.083505 

10.001473 

11.084978 

17 

44 

8.916550 

9.998516 

8.918034 

11.081966 

10.001484 

11.083450 

16 

45 

8.918073 

9.998506 

8.919568 

11.080432 

10.001494 

11.081927 

15 

4G 

8.919591 

9.998495 

8.921096 

11.078904 

10.001505 

11.080409 

14 

47 

8.921103 

9.998485 

8.922619 

11.077381 

10.001515 

11.078897 

13 

48 

8.922610 

9.998474 

8.924136 

11.075864 

10.001526 

11.077390 

12 

49 

8.924112 

9.998464 

8.925649 

11.074351 

10.001536 

11.075888 

11 

50 

8.925609 

9.998453 

8.927156 

11.072844 

10.001547 

11.074391 

10 

51 

8.927100 

9.998442 

8.928658 

11.071342 

10.001558 

11.072900 

9 

52 

8.928587 

9.998431 

8.930155 

11.069845 

10.001569 

11.071413 

8 

53 

8.930068 

9.998421 

8.931647 

11.068353 

10.001579 

11.069932 

7 

54 

8.931544 

9.998410 

8.933134 

11.066866 

10.001590 

11.068456 

6 

55 

8.933015 

9.998399 

8.934616 

11.065384 

10.001601 

11.066985 

5 

56 

8.934481 

9.998388 

8.936093 

11.063907 

10.001612 

11.065519 

4 

57 

8.935942 

9.998377 

8.937565 

11.062435 

10.001623 

11.C64058 

3 

58 

8.937398 

9.998366 

8.939032 

11.060968 

10.001634 

11.062602 

2 

59 

8.938850 

9.998355 

8.  94049  i 

11.059506 

10.001645 

11.061150 

1 

no 

8.940296 

9.  998:^1  1 

8.9<19r,2 

11.058048 

10.001656 

11.059704 

0 

M.  Co-sine.   Sine.   Co-tan;?.  Tangent. 

Co-sec.   Secant. 

M. 

K5  Decree*. 

148                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

5  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec.  |  M. 

U 

8.940^1/6 

9  .  998344 

8.941952 

11.058048 

10.00i6o6 

11.059704 

60 

1 

8  941738 

9.998333 

8.943401 

11.056596 

10.001667 

11.058262 

59 

2 

8  943174 

9.99S322 

8.944852 

11.055148 

10.001678 

11.056826 

58 

3 

8  944G06 

9.998311 

8.946295 

11.053705 

10.001689 

11.055391 

57 

4 

8  946034 

9  9983CO 

8.947734 

11.052266 

10.001700 

11.053966 

56 

5 

8.947456 

9.998289 

8  949168 

11.050832 

10  001711 

11.052544 

55 

6 

8.948874 

9.998277 

8  950597 

11.049403 

10.001723 

11.051126 

54 

7 

8.  950187 

9.998266 

8.952021 

11.047979 

10.001734 

11.049713 

53 

8 

8.951G93 

9.998255 

8.953441 

11.046559 

10.001745 

11.048304 

52 

9 

8.953100 

9.998243 

8.954856 

11.045144 

10.001757 

11.046900 

51 

10 

8  954-199 

9.998232 

8  956267 

11.043733 

10.001768 

11.045501 

50 

11 

8.955894 

9.998220 

8.9576/4 

11.042326 

10.001780 

11.044106 

49 

12 

8.957284 

9.998209 

8.959075 

11.040925 

10.001791 

11.042716 

48 

13 

8.958670 

9.998197 

8.960473 

11.039527 

10.001803 

11.041330 

47 

14 

8.960052 

9.998186 

8  961866 

11.038134 

10.001814 

11.039948 

46 

15 

8.961429 

9.998174 

8.963255 

11.033745 

10.001826 

11.038571 

45 

16 

8.962801 

9.998163 

8  964639 

11.035361 

10.001837 

11.037199 

44 

17 

8.964170 

9.998151 

8.966019 

11.033981 

10.C01849 

11.035830 

43 

18 

8  965534 

9.998139 

8  967394 

11.032606 

10.001861 

11.034466 

42 

19 

8.966893 

9.998128 

8.968766 

11.031234 

10.001872 

11  033107 

41 

20 

8.988249 

9.998116 

8  970133 

11.029867 

10.001884 

11.031751 

4!) 

iil 

8.  969(30  J 

9.998104 

8.971496 

11.028504 

10.001896 

11.030400 

by 

22 

8.970947 

9.998092 

8.972855 

11.027145 

10.001908 

11.029053 

38 

23 

8.972-289 

9.998080 

8.974209 

11.025791 

10.001920 

11.027711 

S7 

24 

8.973628 

9  998068 

8.975560 

11.024440 

10.001932 

11.026372 

36 

25 

8.974962 

9.993056 

8.976906 

11.023094 

10  001944 

11.025038 

35 

26 

8.976293 

9.998044 

8.978248 

11.021752 

10.001956 

11.023707 

34 

27 

8  977619 

9.998032 

8.979586 

11.020414 

10.001968 

11.022381 

33 

28 

8.978941 

9.998020 

8  980921 

11.019079 

10.001980 

11.021059 

32 

20 

8.980259 

9.998008 

8.982251 

11.017749 

10.001992 

11.019741 

31 

SO 

8.981573 

9.997993 

8.983577 

11.016423 

10.002004 

11.018427 

30 

31 

8.98:i883 

9.997984 

8.984899 

11.015101 

10.002016 

11.017117 

*9 

32 

8  981189 

9  997972 

8.986217 

11.013783 

10.002028 

11.015811 

28 

33 

8.985491 

9.997959 

8.987532 

11.012468 

10.002041 

11.014509 

27 

34 

8  98G78D 

9.997947 

8.988842 

11.011158 

10.002053 

11.013211 

26 

35 

8.938083 

9.997935 

8.990149 

11.009351 

10.002065 

11.011917 

25 

36 

8.9S9G74 

9.997922 

8.991451 

11.008549 

10.002078 

11.010626 

24 

37 

8.9903:0 

9  997910 

8.992750 

11.007250 

10.002090 

11.009340 

23 

38 

8.991943 

9.997897 

8.994045 

11.005955 

10.002103 

11.008057 

22 

39 

8.993222 

9.997885 

8.995337 

11.004663 

10.002115 

11.006778 

21 

4Q 

8  991407 

9.997872 

8  996624 

11.003376 

10.002128 

11.005503 

1:0 

41 

8.  99676  J 

9  99/8(30 

8  997908 

11.002092 

10.002140 

11.00423^ 

1'J 

42 

8.997036 

9  997847 

8.999188 

11.000812 

10.002153 

11.  00296  i 

18 

43 

8.993299 

9.997835 

9.000465 

10.999535 

10.002165 

11.001701 

17 

44 

8.9095GO 

9  997822 

9.001733 

10.998262 

10.002178 

11.000440 

16 

45 

9.000316 

9.997809 

9.003007 

10  996993 

10.002191 

10.999184 

15 

46 

9.002069 

9  997797 

9  004272 

10.995728 

10.002203 

10.997931 

14 

47 

9.003318 

9.997784 

9.005534 

10.994466 

10002216 

10.996682 

13 

48 

9  004563 

9.997771 

9.006792 

10.993208 

10.002229 

10.995437 

12 

49 

9.005805 

9  997758 

9.008047 

10.991953 

10.002242 

10.994195 

11 

50 

9  007044 

9.997745 

9  009298 

10.990702 

10  002255 

10.992956 

10 

51 

9.00^78 

9.997732 

9.010546 

10.989454 

10.002268 

10.991722 

9 

52 

9.009510 

9  997719 

9  011790 

10.988210 

10.002281 

10.990490 

8 

53 

9.010737 

9.997706 

9.013031 

10.986969 

10.002294 

10.989263 

7 

54 

9.011962 

9.997693 

9.0142G8 

10.985732 

10.002307 

10.988038 

6 

55 

9.013182 

9.997680 

9.015502 

10.984498 

10.002320 

10.986818 

5 

56 

9.014400 

9.997667 

9.016732 

10.983268 

10.002333 

10.985600 

4 

57 

9.015613 

9.997654 

9  017959 

10.982041 

10.002316 

10.984387 

3 

58 

9.016824 

9.997641 

9.019183 

10.980817 

10.002359 

10.983176 

2 

59 

9.018031 

9.997628 

9.020403 

10.979597 

10.002372 

10.981969 

1 

CO 

9.019235 

9.997614 

9.021620 

10.978S80 

10.002386 

10.9807C5 

0 

M.  |  (Jo-siiie. 

Sine.   |Co-tang. 

Tangent.   Co-sec. 

Secant.  |  TI. 

«4  U^jjrccs. 

TABLE  II.                 149 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

G  Degrees. 

M.   Sine.  |  Co-sine.  (Tangent 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

9.019.^0 

y.t»jVG14 

U.  0-^10^0 

I0.9783fc0 

10.0Ui:38G 

10.980(05 

CD 

l 

9.020435 

9.997601 

9.022834 

10.977166 

10.002399 

10.979565 

59 

2 

9.021632 

9.997588 

9.024044 

10.975956 

10.002412 

10.978368 

58 

3 

9  022825 

9  997574 

9.025251 

10.974749 

10.002426 

10  977175 

57 

4 

9.02401G 

9.997561 

9  026455 

10.973545 

10.002439 

10.975984 

C6 

5 

9.025203 

9.997547 

9.027655 

10.972345 

10.002153 

10.974797 

55 

G 

9.026386 

9.997534 

9.028852 

10.971148 

10.002466 

10.973614 

54 

7 

9.027G67 

9.997520 

9.030046 

10.969954 

10.002480 

10.072433 

53 

8 

9.028744 

9  997507 

9.031237 

10.968763 

10.002493 

10.971256 

52 

9 

9.029918 

9.997493 

9.032425 

10.967575 

10.002507 

10.970082 

51 

10 

9.031089 

9.997480 

9.033G09 

10.966391 

10  002520 

10.968911 

50 

Jl 

9.032257 

9.99/406 

9.034791 

10.9652U9 

10.002534 

10  907743 

49 

12 

9.033421 

9.997452 

9.035969 

10.964031 

10.002548 

10.966579 

48 

13 

9.034582 

9.997439 

9.037144 

10.962856 

10.002561 

10.965418 

47 

14 

9  035741 

9.997425 

9.038316 

10.961684 

10.C02575 

10.934259 

46 

15 

9.03G89G 

9.907411 

9.039485 

10.960515 

10.002589 

10.963104 

45 

1C 

9.038048 

9.997397 

9.040651 

10.959349 

10.002603 

10  961952 

44 

17 

9.039197 

9.997383 

9.041813 

10.958187 

10.002617 

10.9C0803 

43 

18 

9  010342 

9.997369 

9.042973 

10.957027 

10.002631 

10.959658 

42 

19 

9.041485 

9  997355 

9  044130 

10.955870 

10.002645 

10.958515 

41 

20 

9  042625 

9.997341 

9.045284 

10.954716 

10.002659 

10.957375 

40 

•tl 

9.043702 

9.997dn7 

9.046434 

10.953506 

10.002073 

10.950-38 

o9 

22 

9.044895 

9.997313 

9.047582 

10.952418 

10.002687 

10.955105 

38 

23 

9.046026 

9.997299 

9.048727 

10.951273 

10.002701 

10.953974 

37 

24 

9  047154 

9.997285 

9  049b69 

10.950131 

10.002715 

10.952846 

36 

25 

9.048279 

9.997271 

9  051008 

10.948992 

10.002729 

10.951721 

35 

20 

9.049100 

9.997257 

9.052144 

10.947856 

10.002743 

10.950600 

3i 

27 

9.050519 

9.997242 

9  053277 

10.946723 

10.002758 

10.949481 

33 

£8 

9  051635 

9  997228 

9.054407 

10.945593 

10.002772 

10.948365 

32 

29 

9.052749 

9.997214 

9.055535 

10.944465 

10.002786 

10.947251 

31 

30 

9  053859 

9.997199 

9.056659 

10.943341 

10.002801 

10.940141 

30  • 

31 

9  064906 

9.997185 

9.057781 

10.942219 

10.002815 

lU.94503i 

it) 

32 

9.05G071 

9.997170 

9.058900 

10.941100 

10.002830 

10.913929 

28 

33 

9.057172 

9.997156 

9.0G0016 

10.939984 

10.002844 

10.942828 

27 

31 

9  058271 

9.997141 

9.061130 

10.938870 

10.002859 

10.941729 

26 

35 

9.0593G7 

9.997127 

9.062240 

10.937760 

10  002873 

10.940633 

25 

33 

9.060460 

9.997112 

9.063348 

10.936652 

10.002888 

10.939540 

24 

37 

9  061551 

9  997098 

9.064453 

10.935547 

10.002902 

10.938449 

23 

38 

9.062639 

9  997083 

9.065556 

10  934444 

10.002917 

10.937361 

22 

39 

9.063724 

9  997068 

9.066655 

10.933345 

10.002932 

10.936276 

21 

40 

9.06480G 

9  997053 

9.067752 

10.932248 

10.002917 

10.935194 

£0 

41 

9  005885 

9  9970b9 

9  063846 

10.931154 

10.002961 

10.934115 

J9 

42 

9.066962 

9.997024 

9.069938 

10.930062 

10.C0.976 

10.933038 

18 

43 

9  068036 

9  997009 

9.071027 

10.928973 

10.002991 

10.931964 

17 

44 

9.069107 

9.996994 

9.072113 

10  927887 

10.003006 

10.930893 

16 

45 

9.070176 

9.996979 

9.073197 

10.926803 

10.003021 

10.929824 

15 

4G 

9.071242 

9.9969G4 

9.074278 

10.9ii5722 

10.003036 

10.928758 

14 

47 

9.072306 

9.996949 

9.075356 

10.924644 

10.003051 

10.927694 

13 

48 

9.073366 

9.996934 

9.076432 

10.923568 

10.003066 

10.926634 

12 

49 

9.074124 

9.99G919 

9.077505 

10.922495 

10.003081 

10.925576 

11 

no 

9.075480 

9.936904 

9.078576 

10.921424 

10.003096 

10.924520 

10 

51 

9.0765jJ 

9.9Ju«89 

9.079044 

10  920356 

10.003J11 

10.923467 

9 

52 

9.077583 

9.996874 

9.080710 

10.919290 

10.003126 

10.922417 

8 

53 

9.078631 

9.996858 

9.081773 

10.918227 

10.003142 

10.921369 

7 

54 

9.079676 

9.996843 

9.082833 

10.917167 

10.003157 

10.920324 

G 

55 

9.080719 

9.996828 

9.083891 

10.916109 

10.003172 

10.919281 

5 

5G 

9.081759 

9.99G812 

9.084947 

10.915053 

10.003188 

10.918241 

4 

57 

9.082797 

9.996797 

9.086000 

10.914000 

10.003203 

10.917203 

3 

58 

9.083832 

9.996782 

9.087050 

10.912950 

10  003218 

10.916168 

2 

59 

9.084864 

9.996766 

9.088098 

10.911902 

10.003234 

10.915136 

1 

CO 

9.085894 

9.99G7.r)l 

9  089144 

10  910856 

10.003249 

J0.91410G 

0 

M.  (Co-nine. 

Sine.   |  Co-tang. 

Tangent. 

Co-sec.   Secant. 

M. 

83  Degree**. 

150                 TABLE  II. 

LOGAKITHMIO  SINES,  TANGENTS,  AND  SECANTS. 

7  Degrees. 

M. 

Sine. 

Co-sine.  Tangent. 

Co-tang1.   Secant. 

Co-sec. 

M. 

0 

9  08-J6U4 

9.9jo7ol 

9.U89144 

10.910tt^6 

lU.COoL-19 

10.9141U5 

to 

1 

9.086922 

9.996735 

9.090-87 

10.909813 

10.003265 

10.913C78 

C9 

2 

9.C87947 

9.996720 

9  091228 

10.908772 

10.003280 

10.912053 

58 

3 

9.088970 

9.996704 

9.092266 

10.907734 

10.003296 

10.911030 

57 

4 

9.089990 

9.996688 

9  093302 

10.906698 

10.003312 

10.910010 

56 

5 

9.091008 

9.996673 

9.094336 

10.905664 

10.003327 

10.908S92 

55 

6 

9.092024 

9.996657 

9.095367 

10.904633 

10.003343 

10.907976 

54 

7 

9  093037 

9  996641 

9.096395 

10.903605 

10.003359 

10.906903 

53 

8 

9.091047 

9.996625 

9.097422 

10.902578 

10.003375 

10.905953 

52 

9 

9.095056 

9.996610 

9.098446 

10.901554 

10.003390 

10.904944 

51 

10 

9.096062 

9.996594 

9.099468 

10.900532 

10.003406 

10.903938 

50 

11 

9.097UG5 

9.996578 

9.100487 

10.899513 

10.003422 

10.902935 

49 

12 

9.098066 

9.996562 

9.101504 

10.898496 

10.003438 

10.90  1C454 

48 

13 

9.099065 

9.996546 

9.102519 

10.897481 

10.003454 

10.9C0935 

47 

14 

9.100062 

9.996530 

9.103532 

10.896468 

10.003470 

10.899938 

46 

15 

9.101056 

9  996514 

9.104542 

10.895458 

10.003486 

10.898944 

45 

16 

9.102048 

9.996498 

9.105550 

10.894450 

10.003502 

10.897952 

44 

17 

9.103037 

9.996482 

9.106556 

10.893444 

10  003518 

10.896963 

43 

18 

9.104025 

9.996465 

9.107559 

10.892441 

10.003535 

10.895975 

42 

19 

9.105010 

9.996449 

9.108560 

10.891440 

10.003551 

10.894990 

41 

20 

9.105992 

9.996433 

9  109559 

10.890441 

10.C035G7 

10.894008 

40 

21 

9.106973 

9.996417 

9.110556 

10.889444 

10.003583 

10.8930*7 

39 

22 

9.107951 

9.996400 

9.111551 

10.888449 

10.003600 

10.892049 

38 

23 

9.108927 

9  996384 

9.112543 

10.887457 

10003616 

10.891073 

37 

21 

9  .  109901 

9.996368 

9.113533 

10.886467 

10.003632 

10.890099 

36 

25 

9.119873 

9  996351 

9.114521 

10.885479 

10.003649 

10.889127 

35 

26 

9.111842 

9.996335 

9.115507 

10.884493 

10.003665 

10.888158 

34 

27 

9.112809 

9.996318 

9  116491 

10.883509 

10.003682 

10.887191 

33 

28 

9  113774 

9  996302 

9.117472 

10.882528 

10.003698 

10.886226 

32 

29 

9.114737 

9.996285 

9.118452 

10.881548 

10.003715 

10.885263 

31 

3;) 

9.115698 

9.996269 

9.119429 

10.880571 

10.003731 

10.884302 

30 

31 

9.111565(5 

9.996252 

9.120404 

10.8V  9596 

10.003748 

10.883344 

*9 

32 

9.117613 

9.996235 

9.121377 

10.878623 

10.003765 

10.882387 

28 

33 

9.118567 

9.936219 

9.122348 

10.877652 

10.003781 

10.881433 

27 

34 

9.119519 

9.996202 

9.123317 

10.876683 

10.003798 

10.880481 

26 

35 

9.120469 

9.996185 

9.124284 

10.875716 

10.003815 

10.879531 

•25 

36 

9.121417 

9.996168 

9  125249 

10.874751 

10.003832 

10.878583 

24 

37 

9.122362 

9.996151 

9  126211 

10.873789 

10.003849 

10.877638 

23 

33 

9.123306 

9.996134 

9.127172 

10.872828 

10.003866 

10.876694 

22 

39 

9.124248 

9.996117 

9.128130 

10.871870 

10.003883 

10.875752 

21 

40 

9.125187 

9.996100 

9  .  129087 

10.870913 

10.003900 

10.874813 

20 

41 

9.126125 

9.996083 

9  130041 

10.869959 

10.003917 

10.873875 

19 

4'2 

9.127060 

9  996066 

9.130994 

10.869006 

10.003934 

10.872940 

18 

43 

9.127993 

9.996049 

9  131944 

10.868056 

10.003951 

10.872007 

17 

44 

9.128925 

9.996032 

9  132893 

10.867107 

10.003968 

10.871075 

16 

45 

9  129854 

9.996015 

9.133839 

10.866161 

10.003985 

10.870146 

15 

4G 

9  .  130781 

9.995998 

9.134784 

10.865216 

10.004002 

10.869219 

14 

47 

9.131706 

9.995980 

9.135726 

10.864274 

10.004020 

10.868294 

13 

43 

9.132630 

9.995963 

9.136667 

10.863333 

10.004037 

10.867370 

12 

49 

9.133551 

9.995946 

9.137605 

10.862395 

10.004054 

10.866449 

11 

CO 

9.131470 

9.995928 

9.138542 

10.861458 

10.004072 

19.865530 

10 

51 

9  .  135387 

9.995911 

9  .  139476 

10.860524 

10.004089 

10.864613 

9 

52 

9.136303 

9.995894 

9.140409 

10.859591 

10.004106 

10.863697 

8 

53 

9.137216 

9.995876 

9.141340 

10.858660 

10.004124 

10.862784 

7 

54 

9.138128 

9.995859 

9.142269 

10.857731 

10.004141 

10.861872 

6 

55 

9.139037 

9.995841 

9.143196 

10.856804 

10.004159 

10.860963 

5 

56 

9.139944 

9.995823 

9.144121 

10.855879 

10.004177 

10.860056 

4 

57 

9.140850 

9.995806 

9.145044 

10.854956 

10.004194 

10.859150 

3 

53 

9.141754 

9.995788 

9.145966 

10.854034 

10.004212 

10.858246 

2 

59 

9.142655 

9.995771 

9.146885 

10.853115 

10.004229 

10.857345 

1 

60 

9.113:5") 

9.993753 

9.147803 

10.852197 

10.004247 

10.856445 

0 

M. 

Co-sine.   Sine. 

Co-tang. 

Tangent. 

Co-sec.   Secant.   M. 

M  :  i  .«"j;i'««'s. 

TABLE  II.                 151 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

8  Degrees. 

M. 

Sine. 

Co-sine.  (Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

u 

9  .  143555 

9.995753 

9.147803 

10.852197 

10004247 

10.856445 

00 

1 

9.144453 

9.995735 

9.148718 

10.851282 

10.004265 

10.855547 

59 

2 

9  .  145349 

9.995717 

9.149632 

10.850368 

10.004283 

10.854651 

58 

3 

9.146243 

9.995699 

9.150544 

10.849456 

10.004301 

10.853757 

57 

4 

9.147136 

9.995681 

9.151454 

10.848546 

10.004319 

10.852864 

56 

5 

9.148026 

9.995664 

9.152363 

10.847637 

10.004336 

10.851974 

55 

6 

9.148915 

9.995646 

9.153269 

10.846731 

10  004354 

10.851085 

54 

7 

9.149802 

9.995628 

9.154174 

10.845826 

10.004372 

10.850198 

53 

8 

9.150686 

9.995610 

9.155077 

10.844923 

10.004390 

10.849314 

52 

9 

9.151569 

9.995591 

9.155978 

10.844022 

10.C04409 

10.848431 

51 

10 

9.152451 

9.995573 

9.156877 

10.843123 

10.004427 

10.847549 

50 

11 

9.153330 

9.995555 

9.157775 

10.842225 

10.004445 

10.846670 

49 

12 

9  .  154208 

9.995537 

9.158671 

10.841329 

10.004463 

10.845792 

48 

13 

9.155083 

9.995519 

9.159565 

10.840435 

10.004481 

10.844917 

47 

14 

9.155957 

9.995501 

9.160457 

10.839543 

10.004499 

10.844043 

46 

15 

9.156830 

9.995482 

9.161347 

10.838653 

10.004518 

16  843170 

45 

16 

9.157700 

9.995464 

9.162236 

10.837764 

10.004536 

10.842300 

44 

17 

9.158569 

9.995446 

9.163123 

10.836877 

10.004554 

10.841431 

43 

18 

9.159435 

9.995427 

9.164008 

10.835992 

10.004573 

10.840565 

42 

19 

9.160301 

9.995409 

9.164892 

10.835108 

10.004591 

10.839699 

41 

20 

9.161164 

9.995390 

9.165774 

10.834226 

10.004610 

10.838836 

4(1 

21 

9  .  162025 

9.995372 

9.166654 

10.833346 

10.004628 

10.837975 

39 

22 

9.162885 

9.995353 

9.167532 

10.832468 

10.004647 

10.837115 

38 

23 

9.163743 

9.995334 

9.168409 

10.831591 

10.004666 

10.836257 

37 

24 

9  .  164600 

9.995316 

9.169284 

10.830716 

10.004684 

10.835400 

36 

25 

9.165454 

9.995297 

9.170157 

10.829843 

10.004703 

10.834546 

35 

26 

9.166307 

9.995278 

9.171029 

10.828971 

10.004722 

10.833693 

34 

27 

9.167159 

9.995260 

9.171899 

10.828101 

10.004740 

10.832841 

33 

28 

9.168008' 

9  995241 

9.172767 

10.827233 

10.004759 

10.831992 

32 

29 

9.168856 

9.995222 

9.173634 

10.826366 

10.004778 

10.831144 

31 

30 

9  169702 

9.995203 

9.174499 

10.825501 

10.004797 

10.830298 

30 

31 

9.170547 

9.995184 

9.175362 

10.824638 

10.004816 

10.829453 

K9 

32 

9.171389 

9.995165 

9.176224 

10.823776 

10.004835 

10.828611 

28 

33 

9.172230 

9  995146 

9.177084 

10.822916 

10.004854 

10.827770 

27 

34 

9.173070 

9.995127 

9.177942 

10.822058 

10.004873 

10.826930  ' 

26 

35 

9.173908 

9.995108 

9.178799 

10.821201 

10.004892 

10.826092 

25 

36 

9.174744 

9.995089 

9.179655 

10.820345 

10.004911 

10.825256 

24 

37 

9.175578 

9.995070 

9.180508 

10.819492 

10.004930 

10.824422 

23 

38 

9.176411 

9.995051 

9.181360 

10.818640 

10.004949 

10.823589 

22 

39 

9.177242 

9.995032 

9.182211 

10.817789 

10.004968 

10.822758 

21 

40 

9.178072 

9.995013 

9.183059 

10.816941 

10.004987 

10.821928 

i:0 

41 

9.178900 

9.994993 

9.183907 

10.816093 

10.005007 

10.821100 

19 

42 

9.179726 

9.994974 

9.184752 

10.815248 

10.005026 

10.820274 

18 

43 

9.180551 

9.994955 

9.185597 

10.814403 

10.005045 

10.819449 

17 

44 

9.181374 

9.994935 

9.186439 

10.813561 

10.005065 

10.818626 

16 

45 

9.182196 

9.994916 

9.187280 

10.812720 

10.005084 

10.817804 

15 

46 

9.183016 

9.994896 

9.188120 

10.811880 

10.005104 

10.816984 

14 

47 

9.183834 

9.994877 

9.188958 

10.811042 

10.005123 

10.816166 

13 

48 

9.184651 

9.994857 

9.189794 

10.810206 

10.005143 

10.815349 

12 

49 

9.185466 

9.994838 

9.190629 

10.809371 

10.005162 

10.814534 

11 

50 

9.186280 

9.994818 

9.191462 

10.808538 

10.005182 

10.813720 

10 

51 

9.187092 

9.994798 

9.192294 

10.807706 

10.005202 

10.812908 

9 

52 

9.187903 

9.994779 

9.193125 

10.806876 

10.005221 

10.812097 

8 

53 

9.188712 

9.994759 

9.193953 

10.806047 

10.005241 

10.811288 

7 

54 

9.189519 

9.994739 

9.194780 

10.805220 

10.005261 

10.810481 

6 

55 

9.190325 

9.994720 

9.195606 

10.804394 

10.005281 

10.809675 

5 

56 

9.191130 

9.994700 

9.196430 

10.803570 

10.005300 

10.808870 

4 

57 

9.191933 

9.994680 

9.197253 

10.802747 

10.005320 

10.808067 

3 

58 

9.192734 

9.994660 

9.198074 

10.801926 

10.005340 

10.807266 

2 

59 

9.193534 

9.994640 

9.198894 

10.801106 

10.005360 

10.806466 

1 

60 

9.194H32 

9.994620 

9.199713 

10.800287 

10.005380 

10.805668 

0 

M. 

Co-sine. 

Sine.   |  Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

SI  IM--T  ••<•,. 

152                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

9  Degrees. 

M. 

Sine. 

Co-sine.  Tangent.  Co-tang1. 

Secant. 

Co-sec. 

M. 

V 

9.194332 

9.9946-/0 

9.199U3 

10.800287 

10.005380 

10.«05<it)S 

ui 

1 

9.195129 

9.994600 

9.200529 

10.799471 

10.005400 

10.804871 

£9 

2 

9.195925 

9.994580 

9.201345 

10.798655 

10.005420 

10.804075 

58 

3 

9.196719 

9.994560 

9.202159 

10.797841 

10.005440 

10.803281 

57 

4 

9.197511 

9.994540 

9.202971 

10.797029 

10.005460 

10.802489 

56 

5 

9.198302 

9.994519 

9.203782 

10.796218 

10.005481 

10.801698 

55 

6 

9.199091 

9.994499 

9.204592 

10.795408 

10.005501 

10.800909 

54 

7 

9.199879 

9.994479 

9.205400 

10.794600 

10.005521 

10.800121 

53 

8 

9.200666 

9.994459 

9.206207 

10.793793 

10.005541 

10.799334 

52 

9 

9.201451 

9.994438 

9.207013 

10.792987 

10.005562 

10.798549 

51 

10 

9.202234 

9.994418 

9.207817 

10.792183 

10.005582 

10.797766 

50 

11 

9.203017 

9.994398 

9.208619 

10.791381 

10.00560-2 

10.796983 

49 

12 

9.203797 

9.994377 

9.209420 

10.790580 

10.005623 

10.796203 

48 

13 

9.204577 

9.994357 

9.210220 

10.789780 

10.005643 

10.795423 

47 

14 

9.205354 

9.994336 

9.211018 

10.788982 

10.005664 

10.791646 

46 

15 

9.206131 

9.994316 

9.211815 

10.788185 

10.005684 

10.793869 

45 

16 

9.206906 

9.994295 

9.212611 

10.787389 

10.005705 

10.793094 

44 

17 

9.207679 

9.994274 

9.213405 

10.786595 

10.005726 

10.792321 

43 

18 

9.208452 

9.994254 

9.214198 

10.785802 

10.005746 

10.791548 

42 

19 

9.209222 

9.994233 

9.214989 

10.785011 

10.005767 

10.790778 

41 

20 

9.209992 

9.994212 

9.215780 

10.784220 

10.005788 

10.790008 

40 

21 

9.  210700 

9.994191 

9.  '2  16568 

10.783432 

10.005809 

10.789240 

39 

22 

9.211526 

9.994171 

9.217356 

10.782644 

10.005829 

10.788474 

38 

23 

9.212291 

9.994150 

9.218142 

10.781858 

10.005850 

10.787709 

37 

24 

9.213055 

9.994129 

9.218926 

10.781074 

10.005871 

10.786945 

36 

25 

9.213818 

9.994108 

9.219710 

10.780290 

10.005892 

10.786182 

35 

23 

9.214579 

9.994087 

9.220492 

10.779508 

10.005913 

10.785421 

34 

27 

9.215338 

9.994066 

9.221272 

10.778728 

10.005934 

10.784662 

33 

28 

9.216097 

9.994045 

9.222052 

10.777948 

10.005955 

10.783903 

32 

29 

9.216854 

9.994024 

9.222830 

10.777170 

10.005976 

10.783146 

31 

30 

9.217609 

9.994003 

9.223607 

10.776393 

10.005997 

10.782391 

30 

31 

9.218363 

9.993982 

9.2-2438-2 

10.775618 

10.006018 

10.7S163/ 

*y 

32 

9.219116 

9.993960 

9.225156 

10.774844 

10.006040 

10.780884 

23 

33 

9.219868 

9.993939 

9.225929 

10.774071 

10.006061 

10.780132 

27 

31 

9.220618 

9.993918 

9.226700 

10.773300 

10.006082 

10.779382 

26 

35 

9.221367 

9.993897 

9.227471 

10.772529 

10.006103 

10.778633 

25 

30 

9.222115 

9.993875 

9.228239 

10.771761 

10.006125 

10.777885 

24 

37 

9.222861 

9.993854 

9.229007 

10.770993 

10.006146 

10.777139 

23 

38 

9.22360G 

9.993832 

9.229773 

10-770227 

10.006168 

10.776394 

22 

39 

9.224349 

9.993811 

9.230539 

10.769461 

10.006189 

10.775651 

21 

40 

9.225092 

9.993789 

9.231302 

10.768698 

10.006211 

19.774908  - 

,20 

41 

9.2-25833 

9.993768 

9.232065 

10.767935 

10.00623-2 

10.774167 

ia 

42 

9.226573 

9.993746 

9  232826 

10.767174 

10.006254 

10.773427 

18 

43 

9.227311 

9.993725 

9.233586 

10.766414 

10.006275 

10.772689 

17 

44 

9.228048 

9.993703 

9.234345 

10.765655 

10.006297 

10.771952 

16 

45 

9.228784 

9  993681 

9.235103 

10.764897 

10.006319 

10.771216 

15 

46 

9.229518 

9.993660 

9.235859 

10.764141 

10.006340 

10.770482 

14 

47 

9.230252 

9.993638 

9.236614 

10.763386 

10.006362 

10.769748 

13 

48 

9.230984 

9.993616 

9.237368 

10.762632 

10.006384 

10.769016 

12 

49 

9.231715 

9.993594 

9.238120 

10.761880 

10.006406 

10.768285 

11 

50 

9.232444 

9.993572 

9.238872 

10.761128 

10.006428 

10.767556 

10 

51 

9.233172 

9.993550 

9.239622 

10.760378 

10.006450 

10.766828 

9 

52 

9.233899 

9.993528 

9.240371 

10.759629 

10.006472 

10.766101 

8 

53 

9.234625 

9.993506 

9.241118 

10.758882 

10.006494 

10.765375 

7 

54 

9.235349 

9.993484 

9.241865 

10.758135 

10.006516 

10.764651 

(5 

55 

9.236073 

9.993462 

9.242610 

10.757390 

10.006538 

10.763927 

5 

56 

9.236795 

9.993440 

9.243353 

10.756646 

10.006560 

10.763205 

4 

57 

9.237515 

9.993418 

9.244097 

10.755903 

10.006582 

10.762485 

3 

58 

9.238235 

9.993396 

9.244839 

10.755161 

10.006604 

10.761765 

2 

59 

9.238953 

9.993374 

9.245579 

10.754421 

10.006626 

10.761047 

1 

60 

9.239670 

9.993351 

9.246319 

10.753681 

10.006649 

10.760330 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

8O  Degrees. 

TABLE  II.                 153 

LOGARITHMIC  SIGNS,  TANGENTS  AND  SECANTS. 

10  Degrees. 

M.   Sine.   Co-sine.  Tangent. 

Co-tang.   Secant.    Co-sec.   M. 

0 

9  .  -^39670 

9.993351 

9.2i0319 

10.7o366l 

10.00o049 

10.VOUo30 

00 

1 

9.  2-10380 

9  993329 

9.247057 

10.752943 

10.000671 

10.759814 

59 

2 

9.241101 

9.993307 

9.247794 

10.752206 

10.006693 

10.758899 

58 

3 

9.241814 

9.993285 

9.248530 

10.751470 

10.006715 

10.758186 

57 

4 

9  242526 

9.993262 

9.249264 

10.750736 

10.006738 

10.757474 

56 

5 

9.243-237 

9.993240 

9.249998 

10.750002 

10.006760 

10.756763 

55 

6 

9.243947 

9.993217 

9.250730 

10.749/70 

10.000783 

10.756053 

54 

7 

9.244656 

9.993195 

9.251461 

10.748539 

10.000805 

10.755344 

53 

8 

9.245363 

9.993172 

9.252191 

10.747809 

10.006828 

10.754637 

52 

9 

9.24(5069 

9.  99  3  149 

9.252920 

10.747080 

10.006851 

10753931 

51 

10 

9  246775 

9.993127 

9.253648 

10.746352 

10.006873 

10.753225 

50 

11 

9.247478 

9.993104 

9.254374 

10.745020 

10.000896 

10.75^5^ 

49 

12 

9.248181 

9.993081 

9.255100 

10.744900 

10.006919 

10.751819 

48 

13 

9.248883 

9.993059 

9.255824 

10.744176 

10.006941 

10.751117 

47 

14 

9.249583 

9.993036 

9.256547 

10.743453 

10.006964 

10.750417 

46- 

15 

9.250282 

9.993013 

9.257269 

10.742731 

10.006987 

10.749718 

45 

16 

9.25U980 

9.992990 

9.257990 

10.742010 

10.007010 

10.749020 

44 

17 

9.251677 

9  992967 

9.258710 

10.741290 

10.007033 

10.748323 

43 

18 

9.252373 

9.992944 

9.259429 

10.740571 

10.007056 

10.747027 

42 

19 

9.253067 

9.992921 

9.260146 

10.739854 

10.007079 

10.746933 

41 

20 

9.253761 

9  992898 

9.260803 

10.739137 

10.007102 

10.740239 

40 

21 

9  .  254453 

9.9928Y5 

9.201578 

10.738422 

10.007125 

10.74o547 

o9 

22 

9  255144 

9.992852 

9.262292 

10.737708 

10.007148 

10.744856 

38 

23 

9  255834 

9  992829 

9.263005 

10.736995 

10.007171 

10.744106 

37 

24 

9.256523 

9.992806 

9.263717 

10.736283 

10.007194 

10.743477 

36 

25 

9.257211 

9.992783 

9.264428 

10.735572 

10.007217 

10.742789 

35 

26 

9  257898 

9.992759 

9.265138 

10.734862 

10.007241 

10.742102 

34 

27 

9  258583 

9.992736 

9.265847 

10.734153 

10.007264 

10.741417 

33 

28 

9  259268 

9.992713 

9.266555 

10.733445 

10.007287 

10.740732 

32 

29 

9.259951 

9.992690 

9.267261 

10.732739 

10.007311 

10.740049 

31 

30 

9  260633 

9.992666 

9.267967 

10.732033 

10.007334 

10.739367 

3J 

31 

9.201314 

9.992043 

9.208071 

10.731329 

10.007357 

10.738006 

29 

32 

9.261994 

9.992619 

9.269375 

10.730625 

10.007381 

10.738006 

28 

33 

9.262673 

9.992596 

9.270077 

10.729923 

10.007404 

10.737327 

27 

34 

9.263351 

9.992572 

9.270779 

10.729221 

10.007428 

10.736649 

26 

35 

9.264027 

9.992549 

9.271479 

10.728521 

10.007451 

10.735973 

25 

36 

9.264703 

9.992525 

9.272178 

10.727822 

10.007475 

10.735297 

24 

37 

9.265377 

9.992501 

9.272878 

10.727124 

10.007499 

10.734623 

23 

38 

9.266051 

9.992478 

9.273573 

10.726427 

10.007522 

10.733949 

22 

39 

9.266723 

9.992454 

9.274269 

10.725731 

10.007546 

10.733277 

21 

40- 

9.267395 

9.992430 

9.274964 

10.725036 

10.007570 

10.732005 

20 

41 

9.208005 

9.99<J406 

9.275058 

10.724342 

10.007594 

10.731935 

19 

42 

9.268734 

9.992382 

9.276351 

10.723649 

10.007618 

10.731266 

18 

43 

9.269402 

9.992358 

9.277043 

10.722957 

10.007642 

10.730598 

17 

44 

9.270069 

9.992335 

9.277734 

10.722266 

10.007665 

10.729931 

16 

45 

9.270735 

9.992311 

9.278424 

10.721576 

10.007689 

10.729265 

15 

46 

9.271400 

9.992287 

9.279113 

10.720887 

10.007713 

10.728600 

14 

47 

9.272064 

9.992263 

9.279801 

10.720199 

10.007737 

10.727936 

13 

48 

9.272726 

9.992239 

9.280488 

10.719512 

10.007761 

10.727274 

12 

49 

9.273388 

9.992214 

9.281174 

10.718826 

10.007786 

10.726612 

11 

50 

9.274049 

9.992190 

9.281858 

10.718142 

10.007810 

10.725951 

10 

51 

9.274708 

9.992100 

9.282542 

10.717458 

10.007834 

10.725292  |  9 

52 

9.275367 

9.992142 

9.283225 

10.716775 

10.007858 

10.724633 

8 

53 

9.276025 

9.992118 

9.283907 

10.716093 

10.007882 

10.723975 

7 

54 

9.276681 

9.992093 

9.284588 

10.715412 

10.007907 

10.723319 

6 

55 

9.277337 

9.992069 

9.285268 

10.714732 

10.007931 

10.722663 

5 

56 

9.277991 

9.992044 

9.285947 

10.714053 

10.007956 

10.722009 

4 

57 

9.278645 

9.992020 

9.286624 

10.713376 

10.007980 

10.721355 

3 

58 

9.279297 

9.991996 

9.287301 

10.712699 

10.008004 

10.720703 

2 

59 

9.279948 

9.991971 

9.287977 

10.712023 

10.008029 

10.720052 

1 

60 

9.280599 

9.991947 

9.288652 

10.711348 

10.008053 

10.719401 

0 

M. 

Co  -sine.   Sine.   Co-tang. 

Tangent. 

Co-sec. 

Secant.  I  M. 

79  Degrees. 

154                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

11  Degrees. 

M. 

Sine. 

Co-sine.  Tangent.  Co-tang. 

Secant. 

Co-sec.   M. 

1  u 

y.280uyy 

y  .  99i9i7 

9.288602 

10  VI  1348 

10.008U53 

10.719101  j  (30  i 

1 

9.281248 

9.991922 

9.289326 

10.710674 

10.008078 

10.718752 

59 

2 

9.281897 

9.991897 

9.289999 

10.710001 

10.008103 

10.718103 

58 

3 

9.282544 

9.991873 

9.290671 

10.709329 

10.008127 

10.717456 

57 

4 

9  283190 

9.991848 

9.291342 

10.708658 

10.008152 

10.716810 

56 

5 

9.283836 

9.991823 

9.292013 

10.707987 

10.008177 

10.716164 

55 

6 

9.284480 

9.991799 

9.292682 

10.707318 

10.008201 

10.715520 

54 

7 

9.285124 

9.991774 

9.293350 

10.706650 

10.008226 

10.714876 

53 

8 

9.285766 

9.991749 

9.294017 

10.705983 

10.008251 

10.714234 

52 

9 

9.286408 

9.991724 

9.294684 

10.7053J6 

10.008276 

10.713592 

51 

10 

9  287048 

9.991699 

9  295349 

10.704651 

10.008301 

10.712952 

50 

11 

y.  287688 

9  991b74 

9  .  296013 

10.703987 

10.0U8326 

10.712312 

49 

12 

9  288326 

9.991649 

9.296677 

10.703323 

10.008351 

10.711674 

48 

13 

9.288964 

9.991624 

9.297339 

10.702661 

10.008376 

10.711036 

47 

14 

9.289600 

9  991599 

9.298001 

10.701999 

10.008401 

10.710400 

46 

15 

9  290236 

9.991574 

9.298662 

10.701338 

10.008426 

10.709764 

45 

16 

9.290870 

9.991549 

9.299322 

10.700678 

10.008451 

10.709130 

44 

17 

9.291504 

9  991524 

9.299980 

10.700020 

10.008476 

10.708496 

43 

18 

9.292137 

9.991498 

9.300638 

10.699362 

10.008502 

10.707863 

42 

19 

9.292768 

9  991473 

9  301295 

10.698705 

10.008527 

10.707232 

41 

20 

9.293399 

9.991448 

9.301951 

10.698049 

10.008552 

10.706601 

40 

21 

9.294019 

9.991422 

9.302607 

10.697393 

10.008578 

10.705971 

39 

22 

9.294658 

9.991397 

9.303261 

10.696739 

10.008603 

10.705342 

38 

23 

9.295286 

9.991372 

9.303914 

10.696086 

10.008628 

10.704714 

37 

24 

9  295913 

9.991346 

9.304567 

10.695433 

10.008654 

10.704087 

36 

25 

9.296539 

9  991321 

9.305218 

10.694782 

10.008679 

10.703461 

35 

26 

9.297164 

9.991295 

9.305869 

10.694131 

10.008705 

10.702836 

34 

•27 

9.297788 

9.991270 

9.306519 

10.693481 

10.008730 

10.702212 

33 

28 

9.298412 

9.991244 

9.307168 

10.692832 

10.008756 

10.701588 

32 

29 

9.299034 

9.991218 

9  307815 

10.692185 

10.008782 

10.700966 

31 

30 

9  299655 

9  991193 

9.308463 

10.691537 

10.008807 

10.7<0345 

30 

31 

9.  301)27  b 

9.991167 

9.309109 

10.690891 

10.008833 

10.699724 

gf 

32 

9  300895 

9.991141 

9  309754 

10.690246 

10.008859 

10.699105 

28 

33 

9.301514 

9.991115 

9.310398 

10.689602 

10.008885 

10.698486 

27 

34 

9.302132 

9.991090 

9.311042 

10.688958 

10.008910 

10.697868 

26 

35 

9  302748 

9.991064 

9.311685 

10.688315 

10.008936 

10.697252 

25 

3G 

9.303364 

9.991038 

9.312327 

10.687673 

10.008962 

10.696636 

24 

37 

9.303979 

9  991012 

9.312967 

10.687033 

10.008988 

10.696021 

23 

38 

9.304593 

9.990986 

9.313608 

10.686392 

10.009014 

10.695407 

22 

39 

9.305207 

9.990960 

9.314247 

10.685753 

10.009040 

10.694793 

21 

40 

9.305819 

9.  99;  '934 

9  314885 

10.685115 

10.009066 

10.694181 

£0 

41 

9.306430 

9.990908 

9.315523 

10.684477 

10.009092 

10.693570 

19 

42 

9.307041 

9.990882 

9.316159 

10.683841 

10.009118 

10.692959 

18 

43 

9.307650 

9.990855 

9.31C795 

10.683205 

10.009145 

10.692350 

17 

44 

9  308259 

9.990829 

9  317430 

10.682570 

10.009171 

10.691741 

16 

45 

9.308867 

9.990803 

9.318064 

10.681936 

10.009197 

10.691133 

15 

46 

9.309474 

9.990777 

9.318697 

10.681303 

10.009223 

10.690526 

14 

47 

9  310080 

9.990750 

9.319329 

10.680671 

10.009250 

10.689920 

13 

48 

9.310685 

9.990724 

9.319961 

10.680039 

10.009276 

10.689315 

12 

49 

9.311289 

9.990697 

9.320592 

10.679408 

10.009303 

10.088711 

11 

50 

9.311893 

9.990671 

9.321222 

10.678778 

10.009329 

10.688107 

10 

51 

9  .  312495 

9.990645 

9.321851 

10.078149 

10.U09365 

10.687605 

9 

52 

9  313097 

9.99(618 

9.322479 

10.677521 

10.009382 

10.686903 

8 

53 

9.313698 

9.990591 

9.323106 

10.676894 

10.009409 

10.686302 

7 

54 

9.314297 

9.990565 

9.323733 

10.676267 

10.009435 

10.685703 

6 

55 

9  314897 

9.990538 

9  324358 

10.675642 

10.009462 

10.685103 

5 

56 

9.315495 

9.990511 

9.324983 

10.675017 

10.009489 

10.684505 

4 

57 

9.316092 

9  990485 

9.325607 

10.674393 

10.009515 

10.683908 

3 

58 

9.316689 

9.990458 

9.326231 

10.673769 

10.009542 

10.683311 

2 

59 

9.317284 

9.990431 

9.326853 

10.673147 

10.009569 

10.682716 

1 

60 

9  317879 

9.990404 

9.327475 

10.67-25-25 

10.009596 

10.682121 

0 

M. 

Co-sine. 

Sine.   jCo-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

7H  Degrees.                               j 

TABLE  II.                 155 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

12  Decrees. 

M. 

Sine. 

Co-sine.  Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

u 

y.3i7879 

9.9904U4 

9.3^7474 

10.6V  *oi!6 

10.0U9596 

10.0821*1 

to 

l 

9.318473 

9.990378 

9.328095 

10.671905 

10.009622 

10.681527 

59 

2 

9.319066 

9.990351 

9.328715 

10.671285 

10.009649 

10.680934 

58 

3 

9.319658 

9.990324 

9.329334 

10.670666 

10.009676 

10.680342 

57 

4 

9.320249 

9.990297 

9.329953 

10.67^  047 

10.009703 

10.679751 

56 

5 

9.320840 

9.990270 

9.330570 

10.669430 

10.009730 

10.679160 

55 

6 

9.321430 

9.990243 

9  331187 

10.668813 

10.009757 

10.678570 

54 

7 

9.322019 

9.990215 

9.331803 

10.668197 

10.009785 

10.677981 

53 

8 

9.322607 

9  990188 

9.332418 

10.667582 

10.009812 

10.677393 

52 

9 

9.323194 

9.990161 

9.333033 

10.666967 

10.009839 

10.676806 

51 

10 

9  .  323780 

9.990134 

9.333646 

ld.666354 

10.009866 

10.676220 

50 

11 

y  .  324366 

9  990107 

9.334259 

10.665741 

10.U09893 

10.675634 

49 

12 

9.324950 

9.990079 

9.334871 

10.6651-29 

10.009921 

10.675050 

48 

13 

9.325534 

9.990052 

9.335482 

10.664518 

10.009948 

10.674466 

47 

14 

9.326117 

9.990025 

9.336093 

10.663907 

10.009975 

10.673883 

46 

15 

9.326700 

9.989997 

9.336702 

10.663298 

10.010003 

10.673300 

45 

16 

9.327281 

9.989970 

9.337311 

10.662689 

10.010030 

10.672719 

44 

17 

9.327862 

9.989942 

9.337919 

10.662081 

10.010058 

10.672138 

43 

18 

9.328442 

9.989915 

9.338527 

10.661473 

10.010085 

10.671558 

42 

19 

9.329021 

9.989887 

9.339133 

10.660867 

10.010113 

10.670979 

41 

20 

9.329599 

9.989860 

9.339739 

10.660261 

10.010140 

10.670401 

40 

21 

9.330176 

9.989832 

9.340344 

10.659656 

10.010168 

10.069824 

39 

22 

9.330753 

9.989804 

9.340948 

10.659052 

10.010196 

10.669247 

38 

23 

9.331329 

9.989777 

9.341552 

10.658448 

10.010223 

10.668671 

37 

24 

9.331903 

9.989749 

9.342155 

10.657845 

10.010251 

10.668097 

36 

25 

9.332478 

9  989721 

9.342757 

10.657243 

10.010279 

10.667522 

35 

26 

9.333051 

9.989693 

9.343358 

10.656642 

10.010307 

10.666949 

34 

27 

9.333624 

9.989665 

9.343958 

10.656042 

10.010335 

10.666376 

33 

28 

9  334195 

9.989637 

9.344558 

10.655442 

10.010363 

10.665805 

32 

29 

9.334767 

9.989610 

9.345157 

10.654843 

10.010390 

10.665233 

31 

30 

9.335337 

9.989582 

9.345755 

10.654245 

10.010418 

10.664663 

30 

31 

9.335906 

9.989553 

9.346353 

10.653647 

10.010447 

10.664094 

•M 

32 

9.336475 

9.989525 

9.346949 

10.653051 

10.010475 

10.663525 

28 

33 

9.337043 

9.989497 

9.347545 

10.652455 

10.010503 

10.662957 

27 

34 

9.337610 

9.989469 

9.348141 

10.651859 

10.010531 

10.662390 

26 

35 

9.338176 

9.989441 

9.348735 

10.651265 

10.010559 

10.661824 

25 

36 

9.338742 

9.989413 

9.349329 

10.650671 

10.010587 

10.661258 

24 

37 

9.339307 

9.989385 

9.349922 

10.650078 

10.010615 

10.660693 

23 

38 

9.339871 

9.989356 

9.350514 

10.649486 

10.010644 

10.660129 

22 

39 

9.340434 

9.989328 

9.351106 

10.648894 

10.010672 

10.659566 

21 

40 

9.34099G 

9.989300 

9.351697 

10.648303 

10.010700 

10.659004 

20 

41 

9.341558 

9.989271 

9.352287 

10.647713 

10.010729 

10.658442 

19 

4-2 

9.342119 

9.989243 

9.352876 

10.647124 

10.010757 

10.657881 

18 

43 

9.342679 

9.989214 

9.353465 

10.646535 

10.010786 

10.657321 

17 

44 

9.343239 

9.989186 

9  354053 

10.645947 

10.010814 

10.656761 

16 

45 

9.343797 

9.989157 

9.354640 

10.645360 

10.010843 

10.656203 

15 

46 

9.344355 

9.989128 

9.355227 

10.644773 

10.010872 

10.655645 

14 

47 

9.344912 

9.989100 

9.355813 

10.644187 

10.010900 

10.655088 

13 

48 

9.345469 

9.989071 

9.356398 

10.643602 

10.010929 

10.654531 

12 

49 

9.346024 

9.989042 

9.356982 

10.643018 

10.010958 

10.653976 

11 

50  i  9.316579 

9.989014 

9.357566 

10.642434 

10.010986 

19.653421 

10 

51 

9.347134 

9.988985 

9.358149 

10.641851 

10.011015 

10.652866 

9 

52 

9.347687 

9.988956 

9.358731 

10.641269 

10.011044 

10.652313 

8 

53 

9.348240 

9.988927 

9.359313 

10.640687 

10.011073 

10.651760 

7 

54 

9.348792 

9.988898 

9.359893 

10.640107 

10.011102 

10.651208 

6 

55 

9.349343 

9.988869 

9.360474 

10.639526 

10.011131 

10.650657 

5 

56 

9.349893 

9.988840 

9.361053 

10.638947 

10.011160 

10.650107 

4 

57 

9.350443 

9.988811 

9.361632 

10.638368 

10.011189 

10.649557 

3 

58 

9.350992 

9.988782 

9.362210 

10.637790 

10.011218 

10.649008 

2 

59 

9.351540 

9.988753 

9.362787 

10.637213 

10.011247 

10.648460 

1 

60 

9.352088 

9.988724 

9.363364 

10.636636 

10.011276 

10.647912 

0 

M.  Co-sine. 

Sine.   |  Co-tang. 

Tangent.   Co-sec.    Secant. 

M. 

77  Uejfrees. 

156                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

13  Degrees. 

M. 

Sine. 

Co-sine.  |Tangent. 

Co-tang. 

Secant. 

Co-sec.   M. 

U 

y.y«ji.0iid 

9  9o8<2i 

y  .  303<ju4 

lU.03u036 

10.011^7(5 

lU.  Oil  912 

00 

1 

9^352635 

9.988695 

9.363940 

10.6360CO 

10.011305 

10.647365 

59 

2 

9  353181 

9  988666 

9.864515 

10.635485 

10.011334 

10  616819 

58 

3 

9.353726 

9.988636 

9.365090 

10.634910 

10.011364 

10.646274 

57 

4 

9.354271 

9.988607 

9.365664 

10.634336 

10.011393 

10.645729 

C6 

5 

9.354815 

9.988578 

9.366237 

10.633763 

10.011422 

10.645185 

55 

6 

9.355358 

9.988548 

9.366810 

10.633190 

10.011452 

10.C44642 

54 

7 

9.355901 

9.988519 

9.367382 

10.632618 

10.011481 

10.644099 

53 

8 

9.356443 

9.083489 

9.367953 

10.632047 

10.011511 

10.643557 

52 

9 

9.356984 

9  988460 

9.368524 

10.631476 

10.011540 

10.643016 

51 

10 

9.357524 

9.938430 

9.369094 

10.630906 

10.011570 

10.642476 

50 

11 

9.35S064 

9.98J401 

9  .  309(503 

10  .631)337 

10.011599 

10.641936 

49 

12 

9.353603 

9.988371 

9.370232 

10.629768 

10.011629 

10.641397 

48 

13 

9.359141 

9.988342 

9.370799 

10.629201 

10.011658 

10.640859 

47 

14 

9.359678 

9.988312 

9.371367 

10.628633 

10.011688 

10.640322 

46 

15 

9.360215 

9.988282 

9.371933 

10.628067 

10.011718 

10.639785 

45 

16 

9.360752 

9.988252 

9.372499 

10.627501 

10.011748 

10.639248 

44 

17 

9.361287 

9.988223 

9.373064 

10.626936 

10.011777 

10.638713 

43 

18 

9  361822 

9.988193 

9.373629 

10.626371 

10.011R07 

10.638178 

42 

19 

9.362356 

9  988163 

9  374193 

10.625807 

10  011837 

10.637644 

41 

20 

9.362889 

9  988133 

9.374756 

10.625244 

10.011867 

10.6C7111 

40 

21 

9.363422 

9.9o8l03 

9.375319 

10.624681 

10.011697 

10.030578 

i>9 

22 

9.363954 

9.983073 

9.375881 

10.624119 

10.011927 

10.636046 

38 

23 

9.364485 

9.988043 

9.376442 

10.623558 

10.011957 

10.635515 

37 

24 

9  365016 

9.988013 

9  377003 

10.622997 

10.011987 

10.634984 

36 

25 

9.365546 

9.987983 

9  377563 

10.622437 

10.012017 

10.634454 

35 

26 

9.366075 

9.987953 

9.378122 

10.621878 

10.012047 

10.633925 

34 

27 

9.366604 

9.987922 

9  378681 

10.621319 

10.012078 

10.633396 

33 

28 

9  367131 

9.987892 

9.379239 

10.620761 

10.012108 

10.632869 

32 

29 

9.367659 

9.987862 

9.379797 

10.620203 

10.012138 

10.632341 

31 

30 

9  368185 

9.987832 

9.380354 

10.619G46 

10.012168 

10.631815 

30 

31 

9.U3b7ll 

9.987801 

9.380910 

10.619090 

10.012199 

10  031289 

k.9 

32 

9.369236 

9.987771 

9.381466 

10.618534 

10.012229 

10.630764 

28 

33 

9.369761 

9.987740 

9.382020 

10.617980 

10.012260 

10.630239 

.27 

34 

9.370285 

9.987710 

9.382575 

10.617425 

10.012290 

10.629715 

26 

35 

9.370C08 

9.987679 

9.383129 

10.616871 

10.012321 

10.629192 

25 

36 

9.371330 

9.987649 

9.383682 

10.616318 

10.012351 

10.628670 

24 

37 

9.371852 

9.987618 

9.384234 

10.615766 

10.012382 

10.628148 

23 

38 

9.372373 

9  987588 

9.384786 

10.615214 

10.012412 

10.627627 

22 

39 

9.372894 

9.987557 

9.385337. 

10.614663 

10.012443 

10.627106 

21 

40 

9.373414 

9.987526 

9.385888 

10.614112 

10.012474 

10.626586 

20 

41 

9  3739J3 

9.987496 

9.386438 

10.613562 

l'J.012504 

10.0ii6007 

19 

42 

9.374452 

9.987465 

9.386987 

10.613013 

10.012535 

10.625548 

18 

43 

9  374970 

9.987434 

9.387586 

10.612464 

10.012566 

10.625030 

17 

44 

9.375487 

9.987403 

9.388084 

10.611916 

10.012597 

10.624513 

16 

45 

9.376003 

9.987372 

9.388631 

10.611369 

10.012628 

10.623997 

15 

46 

9.376519 

9.987341 

9.389178 

10.610822 

10.012659 

10.623481 

14 

47 

9.377035 

9.987310 

9.389724 

10.610276 

10.012690 

10.622965 

13 

48 

9.377549 

9.987279 

9.390270 

10.609730 

10.012721 

10.622451 

12 

49 

9.378063 

9.987248 

9.390815 

10.609185 

10.012752 

10.621937 

11 

50 

9.378577 

9.987217 

9.391360 

10.608640 

10.012783 

10.621423 

10 

51 

9.  3  i  9089 

9.987186 

9.391903 

10.608097 

10.012814 

10.6^0911 

9 

52 

9.379601 

9.987155 

9.392447 

10.607553 

10.012845 

10.620399 

8 

53 

9.380113 

9.987124 

9.392989 

10.607011 

10.012876 

10.619887 

7 

54 

9.380624 

9.987092 

9.393531 

10.606469 

10.012908 

10.619376 

6 

55 

9.381134 

9.987061 

9.394073 

10.605927 

10.012939 

10.618866 

5 

56 

9.381643 

9.987030 

9.394614 

10.605386 

10.012970 

10.618357 

4 

57 

9.382152 

9.936998 

9.395154 

10.604846 

10.013002 

10.617848 

3 

58 

9.382661 

9.986967 

9.395694 

10.604306 

10.013033 

10.617339 

2 

59 

9.383168 

9.986936 

9.396233 

10.603767 

10.013064 

10.616832 

1 

CO 

9.38H675 

9.986904 

9  396771 

10.603229 

10.013096 

10.61G325 

0 

M.  |  Co-sine. 

Sine.   |  Co-tang. 

Tangent. 

Co-sec. 

Secant.   M. 

7O  Uogrees. 

TABLE  II.                 157 

LOGAKITH3VIIC  SINES,  TANGENTS,  AND  SECANTS. 

14  Degrees. 

M.  |  Sine. 

Co-sine.  Tangent. 

Co-tang-. 

Secant. 

Co-sec. 

M. 

u 

9.383675 

9.986904 

9.390771 

10.6032-^9 

10.013096 

lO.OiGozS 

00 

l 

9.384182 

9.986873 

9.397309 

10.602691 

10.013127 

10.615318 

f9 

2 

9.384687 

9.986841 

9.397846 

10.602154 

10.013159 

10.615313 

58 

3 

9.385192 

9.986809 

9.398383 

10.601617 

10.013191 

10.614808 

57 

4 

9.385697 

9.986778 

9.393919 

10.601081 

10.013222 

10.614303 

56 

5 

9.386201 

9.986746 

9.399455 

10.600545 

10.013254 

10.613799 

55 

6 

9.386704 

9.986714 

9.399990 

10.600010 

10.013286 

10.613296 

54 

7 

9.387207 

9.986683 

9.400524 

10.599476 

10.013317 

10.612793 

53 

8 

9.387709 

9.986651 

9.401058 

10.598942 

10.013349 

10.612291 

52 

9 

9.388210 

9.986619 

9.401591 

10.598409 

10.013381 

10.611790 

51 

10 

9.388711 

9.986587 

9.402124 

10.597876 

10.013413 

10.611289 

50 

11 

9.3892J1 

9.986555 

9.402656 

10.597344 

10.013445 

10.610*89 

49 

12 

9.389711 

9.986523 

9.403187 

10.596813 

10.013477 

10.610289 

48 

13 

9.390210 

9.986491 

9.403718 

10.596282 

10.013509 

10.609790 

47 

14 

9.390708 

9.986459 

9.404249 

10.595751 

10.013541 

10.609292 

46 

15 

9.391206 

9.986427 

9.404778 

10.595222 

10.013573 

10  608794 

45 

16 

9.391703 

9.986395 

9.405308 

10.594692 

10.013605 

10.608297 

44 

17 

9.392199 

9.986363 

9.405836 

10.594164 

10.013637 

10.607801 

43 

18 

9.392695 

9.986331 

9.406364 

10.593636 

10.013669 

10.607305 

42 

19 

9.393191 

9.986299 

9.406892 

10.593108 

10.013701 

10.606810 

41 

20 

9.393685 

9.986266 

9.407419 

10.592581 

10.013734 

10.606315 

40 

21 

9.394179 

9.986234 

9.407945 

10.592055 

10.013766 

10.605821 

ij'J 

22 

9.394673 

9.986202 

9.408471 

10.591529 

10.013798 

10.605327 

38 

23 

9.395166 

9.986169 

9.408997 

10.591003 

10.013831 

10.604834 

37 

24 

9.395658 

9.986137 

9.409521 

10.590479 

10.013863 

10.604342 

36 

25 

9.396150 

9.986104 

9.410045 

10.589955 

10.013896 

10.603850 

35 

26 

9.396641 

9.986072 

9.410569 

10.589431 

10.013928 

10.603359 

34 

27 

9.397132 

9.986039 

9.411092 

10.588908 

10.013961 

10.602868 

33 

28 

9.397621 

9  986007 

9.411615 

10  588385 

10.013993 

10.602379 

32 

29 

9.398111 

9.985974 

9.412137 

10.587863 

10.014026 

10.601889 

31 

30 

9.398600 

9.985942 

9.412658 

10.587342 

10.014058 

10.6014'JO 

30 

31 

9.399086 

9.985909 

9.413179 

10.586821 

10.014091 

10.600912 

i.9 

32 

9.399575 

9.985876 

9.413699 

10.586301 

10.014124 

10.600425 

28 

33 

9.400062 

9.985843 

9.414219 

10.585781 

10.014157 

10.599938 

27 

34 

9.400549 

9.935811 

9.414738 

10.585262 

10.014189 

10.599451 

26 

35 

9.401035 

9.985778 

9.415257 

10.584743 

10.014222 

10.598965 

25 

36 

9.401520 

9.985745 

9.415775 

10.584225 

10.014255 

10.598480 

24 

37 

9.402005 

9.985712 

9.416293 

10.583707 

10.014288 

10.597995 

23 

33 

9.402489 

9.985679 

9.416810 

10.583190 

10.014321 

10.597511 

22 

39 

9.402972 

9.985646 

9.417326 

10.582674 

10.014354 

10.597028 

21 

40 

9.403455 

9.985613 

9.417842 

10.582158 

10.014387 

10.593545 

'20 

41 

9.403938 

9.9«55(?0 

9.418358 

10.581642 

10.014420 

10.596062 

19 

42 

9.404420 

9.985547 

9  418873 

10.581127 

10.014453 

10.595580 

18 

43 

9.404901 

9.985514 

9.419387 

10.580613 

10.014486 

10.595099 

17 

44 

9.405382 

9.985480 

9  419901 

10.580099 

10.014520 

10.594618 

16 

45 

9.405862 

9  985447 

9.420415 

10.579585 

10.014553 

10.594138 

15 

46 

9.406341 

9.985414 

9  420927 

10.579073 

10.014586 

10.593659 

14 

47 

9.408820 

9.985381 

'9.421440 

10.578560 

10.014619 

10.593180 

13 

48 

9.407299 

9.985347 

9.421952 

10.578048 

10.014653 

10.592701 

12 

49 

9.407777 

9.985314 

9.422463 

10.577537 

10.014686 

10.592223 

11 

•SO 

9.408254 

9.985280 

9.422974 

10.577026 

10.014720 

10.591746 

10 

51 

9.408731 

9.985^47 

9.423484 

10.576516 

10.014753 

10.591269 

9 

52 

9.409207 

9.985213 

9.423993 

10.576007 

10.014787 

10.590793 

8 

53 

9.409682 

9.985180 

9.424503 

10.575497 

10.014820 

10.590318 

7 

54 

9.410157 

9.985146 

9.425011 

10.574989 

10.014854 

10.589843 

8 

55 

9.410632 

9.985113 

9.425519 

10.574481 

10.014887 

10.589368 

5 

56 

9.411106 

9.985079 

9.426027 

10.573973 

10.014921 

10.588894 

4 

57 

9.411579 

9.985045 

9.426534 

10.573466 

10.014955 

10.588421 

3 

58 

9.412052 

9.985011 

9.427041 

10.572959 

10.014989 

10.587948 

2 

59 

9.412524 

9.984978 

9.427547 

10.572453 

10.015022 

10.587476 

1 

60 

9.412993 

9  934944 

9.423052 

10.571948 

10.015056 

10.587004 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

75  l>eKree«. 

158                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

15  Degrees. 

M.   Sine. 

Co-sine. 

Tangent. 

Co-tang.   Secant. 

Co-sec,  j  M. 

u 

y.  41*99(5 

1).  984914 

y.4_8oo2 

J0.57i9i8 

10  OioOoU 

10.5bv004 

ou 

1 

9.413467 

9.984910 

9.428557 

10.571443 

10.015090 

10.586533 

59 

2 

9.41C938 

9.984876 

9.429062 

10.570938 

10.015124 

10.586062 

58 

3 

9.414403 

9.984842 

9.429566 

10.570434 

10.015158 

10.585592 

57 

4 

9.414878 

9.984808 

9.430G70 

10.569930 

10.015192 

10.585122 

56 

5 

9.415347 

9.984774 

9.430573 

10.569427 

10.015226 

10.5846:3 

55 

6 

9.415815 

9.984740 

9.431075 

10.568925 

10  015260 

10.584185 

54 

7 

9.416283 

9.984706 

9.431577 

10.568423 

10.015294 

10.583717 

53 

8 

9.416751 

9.984672 

9.432079 

10.567921 

10.015328 

10.583249 

52 

9 

9.417217 

9.984638 

9.432580 

10.567420 

10.015362 

10.582783 

51 

1C) 

9.417G84 

9.984C03 

9.433080 

10.566920 

10.015397 

10.582316 

50 

11 

9.418150 

9.984o69 

9.433580 

10.5664*0 

10.015431 

10.5818uU 

49 

12 

9.418615 

9.984535 

9.434080 

10.565920 

10.015465 

10.581385 

48 

13 

9.419079 

9.984500 

9.434579 

10.565421 

10.015500 

10.580921 

47 

14 

9.419544 

9.984466 

9.435078 

10.564922 

10.015534 

10.580456 

46 

15 

9.420007 

9.984432 

9.435576 

10.564424 

10.015568 

10  579993 

45 

16 

9.420470 

9.984397 

9.436073 

10.563927 

10.015603 

10.579530 

44 

17 

9.420933 

9.984363 

9.436570 

10.563430 

10.015637 

10.579067 

43 

18 

9.421395 

9.984328 

9.437067 

10.562933 

10.015672 

10.578605 

42 

19 

9.421857 

9.984294 

9.437563 

10.562437 

10.015706 

10.578143 

41 

20 

9.422318 

9.984259 

9.438059 

10.561941 

10.015741 

10.577682 

40 

21 

9.4*2776 

9  .  984224 

9.43c>554 

10.561446 

10.015776 

10.5772*2 

39 

22 

9.423238 

9.984190 

9.439048 

10.560952 

10.015810 

10.576762 

38 

23 

9.423697 

9.981155 

9.439543 

10.560457 

10.015845 

10.576303 

37 

24 

9.424156 

9.984120 

9.440036 

10.559964 

10.015880 

10.575844 

36 

25 

9.424615 

9.984085 

9.440529 

10.559471 

10.015915 

10.575385 

35 

26 

9.425073 

9.984050 

9.441022 

10.558978 

'10.015950 

10.574927 

34 

27 

9.425530 

9.984015 

9.441514 

10.558486 

10.015985 

10.574470 

33 

28 

9.425987 

9  983981 

9.442006 

10.557994 

10.016019 

10.574013 

32 

29 

9.426443 

9.983946 

9.442497 

10.557503 

10.016054 

10.573557 

31 

30 

9  426899 

9.983911 

9.442988 

10.557012 

10016089 

10.573101 

30 

31 

9.427354 

9.983875 

9.443479 

10.550521 

10.016125 

10.57*04(3 

19 

32 

9.427809 

9.983840 

9.443968 

10.556032 

10.016160 

10.572191 

28 

33 

9.428263 

9  983805 

9.444458 

10.555542 

10.016195 

10.571737 

27 

34 

9.428717 

9.933770 

9.444947 

10.555053 

10.016230 

10.571283 

26 

35 

9.429170 

9.983735 

9.445435 

10.554565 

10.016265 

10.570830 

25 

!  36 

9.429623 

9.983700 

9.445923 

10.554077 

10.016300 

10,570377 

24 

!  37 

9.430075 

9.983664 

9.446411 

10.553589 

10.016336 

10.569925 

k3 

38 

9.430527 

9.983629 

9.446898 

10.553102 

10.016371 

10.569473 

22 

39 

9.430978 

9.983594 

9.447384 

10.552616 

10.016406 

10.569022 

21 

40 

9.431429 

9.983558 

9.447870 

10.552130 

10.016442 

10.568571 

iO 

41 

9.431679 

9.983o23 

9.448356 

10.551644 

10.016477 

10.568121 

19 

!  42 

9.432329 

9.983487 

9.448841 

10.551159 

10.016513 

10.567671 

18 

!  43 

9  432778 

9.983452 

9.449326 

10.550674 

10.016548 

10.567222 

17 

j  44 

9.433226 

9.983416 

9.449810 

10.550190 

10.016584 

10.566774 

16 

!  45 

9.433675 

9.983381 

9.450294 

10.549706 

10.016619 

10.566325 

15 

i  46 

9.434122 

9.983345 

9.450777 

10.549223 

10.016655 

10.565878 

14 

47 

9.434569 

9.983309 

9.451260 

10.548740 

10.016691 

10.565431 

13 

48 

9.435016 

9.983273 

9.451743 

10.548257 

10.016727 

10.564984 

12 

49 

9.435462 

9.983238 

9.452225 

10.547775 

10.016762 

10.564538 

11 

50 

9.435908 

9.983202 

9.452706 

10.547294 

10.016798 

10.564092 

10 

51 

9.436353 

9.983166 

9.453187 

10.546813 

10.016834 

10.563647 

9 

52 

9.436798 

9.983130 

9.453668 

10.546332 

10.016870 

10.563202 

8 

53 

9.437242 

9.983094 

9.454148 

10.545852 

10.016906 

10.562758 

7 

54 

9.437686 

9.983058 

9.454628 

10.545372 

10.016942 

10.562314 

6 

55 

9.438129 

9.983022 

9.455107 

10.544893 

10.016978 

10.561871 

5 

56 

9.438572 

9.982986 

9.455586 

10.544414 

10.017014 

10.561428 

4 

57 

9.439014 

9.982950 

9.456064 

10.543936 

10.017050 

10.560986 

3 

58 

9.439456 

9.982914 

9.456542 

10.543458 

10.017086 

10.560544 

2 

59 

9.439897 

9.982878 

9.457019 

10.542981 

10.017122 

10.560103 

1 

60 

9.440338 

9.982842 

9.457496 

10.542504 

10.017158 

10  559662 

0 

M.  Co-sine. 

Sine. 

Co-tang-. 

Tangent. 

Co-sec. 

Secant. 

M. 

74  l>egrees. 

TABLE  II.                 159 

LOGAEITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

16  Degrees. 

1C. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec.   M. 

u 

y.  440338 

y.98_84i5 

9.4u74'jO 

1U.54_504 

1U.017158 

10.059602 

60 

1 

9  440778 

9.982805 

9.457973 

10.54-_027 

10.017195 

10.559222 

59 

2 

9  441218 

9.  982709 

9.458449 

10.541551 

10.017231 

10.558782 

58 

3 

9.441658 

9.98^733 

9.  458925 

10.541075 

10.017267 

10.558312 

57 

4 

9  442096 

9  982693 

9.459400 

10.540600 

10.017304 

10.557904 

56 

5 

9.442535 

9.982660 

9  459875 

10.549125 

10  017340 

10.557465 

55 

6 

9.44-2973 

9.982624 

9.460349 

10.530651 

10.017376 

10.557027 

54 

7 

9.443410 

9.982587 

9.460823 

10.539177 

10.017-il3 

10.55C590 

53 

8 

9.443847 

9.982551 

9.461297' 

10.538703 

10.017449 

10.556153 

52 

9 

9.444284 

9.982514 

9.461770 

10.538230 

10.017486 

10.555716 

51 

10 

9.444720 

9.982477 

9  462242 

10.537758 

10.017523 

10.555280 

50 

11 

9.445155 

9.t;82441 

9.4u_714 

10.5b/L8o 

iu.ui756y 

10.554845 

49 

12 

9.445590 

9.982404 

9.463186 

10.53G814 

10.017596 

10.554410 

48 

13 

9.446025 

9.982367 

9.463658 

10.536342 

10.017633 

10.553975 

47 

14 

9.446459 

9.982331 

9  464128 

10.535872 

10.017609 

10.553541 

46 

15 

9.446893 

9.982294 

9.464599 

10.535401 

10.017706 

10.553107 

45 

16 

9.447326 

9  982257 

9  465069 

10.534931 

10.017743 

10.552674 

44 

17 

9.447759 

9.982220 

9.465539 

10.634461 

10.017780 

10.552241 

43 

18 

9.448191 

9.982183 

9  4G6G08 

10.533992 

10.017817 

10.551809 

42 

19 

9.448623 

9.982146 

9.466476 

10533524 

10.017854 

10.551377 

41 

i  '20 

9.448054 

9.  982  109 

9  466945 

10.533055 

10.017891 

10.550946 

40 

SI 

9.  449480 

9  .  Ubzo72 

9.407413 

lO.bSzob? 

10.0179-^8 

10.5oUol5 

oU 

22 

9.449915 

9.982035 

9.467880 

10.532120 

10.017965 

10.550085 

38  | 

23 

9.450345 

9.981998 

9.468347 

10.531653 

10.018002 

10.549655 

37 

24 

9.450775 

9  981961 

9.468814 

10.531186 

10.018039 

10.549225 

36 

25 

9.451204 

9.981924 

9.469280 

10.530720 

10.018076 

10.548796 

35 

26 

9.451632 

9.981886 

9  460746 

10.B30254 

10.018114 

10.548368 

34 

27 

9.452060 

9.981849 

9.470211 

10.529789 

10.018151 

10.547940 

33 

28 

9.452488 

9.981812 

9  470676 

10.529324 

10.018188 

10.547512 

32 

29 

9.452915 

9.981774 

9.471141 

10.528859 

10.018226 

10.547085 

31 

30 

9.453342 

9.981737 

9.471605 

10.528395 

10.018263 

10.546658 

30 

31 

U.  453/08 

9.9817LO 

y.47ilO(J8 

10.52/932 

10.018300 

10.540232 

29 

32 

9.454194 

9.981662 

9.472532 

10.527468 

10.018338 

10.545806 

28 

33 

9.454619 

9.981625 

9.472995 

10.527005 

10.018375 

10.545381 

27 

34 

9.455044 

9.981587 

9.473457 

10.526543 

10.018413 

10.544956 

26 

35 

9.455469 

9.981549 

9.473919 

10.526081 

10.018451 

10.544531 

25 

3G 

9.455893 

9.981512 

9.474381 

10.525619 

10.018488 

10.544107 

24 

37 

9.45G316 

9  981474 

9.474842 

10.525158 

10.018526 

10.543684 

23 

38 

9.456739 

9.981436 

9.475303 

10.524697 

10.018564 

10.543261 

22 

39 

9.457162 

9.981399 

9.475763 

10.524237 

10.018601 

10.542838 

21 

|  40 

9.457584 

9.981361 

9.476223 

10.523777 

10.018639 

10.542416 

20 

41 

9.45bU06 

9.9813*3 

9  470083 

10.523317" 

1U.U18677 

10.541094 

19 

42 

9.458427 

9  981285 

9.477142 

10  522858 

10.018715 

10.541573 

18 

43 

9.458848 

9.981247 

9.477601 

10.522309 

10.018753 

10.541152 

17 

44 

9.459268 

9.981209 

9.478059 

10.521941 

10.018791 

10.540732 

16 

45 

9*.459C88 

9.981171 

9.478517 

10.  C2  1483 

10.018829 

10.540312 

15 

46 

9.460108 

9.981133 

9  478975 

10.521025 

10.018867 

10.539892 

14 

47 

9.460527 

9.981095 

9.479432 

10.520568 

10.018905 

10.539473 

13 

48 

9.460946 

9.981057 

9.479889 

10.520111 

10.018943 

10.539054 

12 

49 

9.461364 

9  981019 

9.480345 

10.519655 

10.018981' 

10.538636 

11 

50 

9  461782 

9.980981 

9  480801 

10.519199 

10.010019 

10.538218 

10 

51 

9.462199 

9  .  'JM,94-J 

9.481257 

1U.518743 

10.0lOUii8 

10.53<b01 

9 

52 

9.4G2616 

9  S80904 

9.481712 

10.518288 

10.019096 

10.537384 

8 

53 

9.463032 

9.C808C6 

9.4K2167 

10.517833 

10.019134 

10.536968 

7 

54 

9.463448 

9.980827 

9.482621 

10.517379 

10.019173 

10.536552 

6 

55 

9.4G3864 

9.9807S9 

9.483075 

10.516925 

10.019211 

10.536136 

5 

56 

9.464279 

9.980750 

9.483529 

10.516471 

10.019250 

10.535721 

4 

57 

9.464694 

9.980712 

9  483982 

10.516018 

10.019288 

10.535306 

3 

58 

9.465108 

9.880673 

9.484435 

10.515565 

10.019327 

10.534892 

2 

59 

9.465522 

9.980635 

9.484887 

10.515113 

10.019365 

10.534478 

1 

CO 

9.465935 

9.980596 

9.485339 

10.514661 

10.019404 

10.534065 

0 

M. 

Co-sine. 

bine.   |  Co-tang. 

Tangent.  |  Co-sec. 

Secant. 

M. 

73  .Degrees. 

160            '     TABLE  II. 

LOGARITHMIC  SIGNS,  TANGENTS  AND  SECANTS. 

17  Degrees. 

M. 

Sine. 

Co-sin  e.  (Tangent. 

Co-taug. 

Secant. 

Co-sec. 

M. 

0 

9.4Go935 

y.y.o-yjt; 

9.485^9 

10.ol4bol 

10.019404 

10.o34065 

GO 

1 

9.466348 

9  980558 

9  485791 

10.514209 

10.019442 

10.533652 

59 

•2 

9.4GG761 

9.9J0519 

9.486242 

10.513758 

10.019481 

10.533239 

58 

3 

9.467173 

9.930480 

9.486693 

10.513007 

10.019520 

10.532827 

57 

4 

9  467585 

9.980442 

9.487143 

10.512857 

10.019553 

10.532415 

56 

5 

9.467996 

9.980413 

9.487593 

10.512407 

10.019597 

10.532004 

55 

6 

9.468407 

9.980364 

9.483013 

10.511957 

10.019636 

10.531593 

54 

7 

9.468817 

9.980:25 

9.488492 

10.511508 

10.019G75 

10.531183 

53 

8 

9.469227 

9.930286 

9.488941 

10.511059 

10.019714 

10.530773 

52 

9 

9.469337 

9.980247 

9.489  90 

10.510610 

10.019753 

10  530363 

51 

10 

9.470046 

9.930208 

9.489833 

10.510162 

10.0197i>2 

10.529954 

50 

11 

9.4.0i55 

9  .  1)80109 

9.4902c6 

10.509/14 

100i9o31 

10.529545 

49 

12 

9.470883 

9.980130 

9  490733 

10.C09267 

10.019870 

10.529137 

48 

13 

9.471271 

9.930091 

9.491180 

10.508820 

10.019909 

10.528729 

47 

14 

9.471679 

9.980052 

9.491627 

10.508373 

10.019948 

10.528321 

46 

15 

9.472086 

9.980012 

9.492073 

10.507927 

10.01!988 

10.527914 

45 

1C 

9.472492 

9.979373 

9.492519 

10.507481 

10.020027 

10.527508 

44 

17 

9.472898 

9  979934 

9.492965 

10.507035 

10.02C066 

10.527102 

43 

18 

9.473304 

9.979895 

9.493410 

10.506590 

10.0201C5 

10.526696 

42 

19 

9.473710 

9.979355 

9.493854 

10.506146 

10.020145 

10.526290 

41 

20 

9.47-1115 

9  979316 

9.494299 

10.505701 

10.020184 

10.525885 

40 

21 

St.  474519 

9  97;;  /76 

9.4'J4743 

10.50u_57 

10.0^0:^4 

10.5zo4bl 

39 

22 

9  4749:3 

9.979737 

9.495186 

10.504814 

10  020263 

10.525077 

38 

23 

9.475327 

9  979G97 

9.495630 

10.501370 

10.020303 

10.524673 

37 

24 

9.475730 

9.979058 

9.496373 

10.503927 

10.020342 

10.524270 

30 

25 

9.476133 

9.979618 

9  49G515 

10.503485 

10.020382 

10.523867 

35 

26 

9  47G5:)6 

9.979579 

9  49G957 

10.503043 

10.020421 

10.523464 

34 

27 

9  47C938 

9.979539 

9  497399 

10.502601 

10.020461 

10.523062 

33 

28 

9  477310 

9.979499 

9  497841 

10.502159 

10  020501 

10.522660 

32 

29 

9.477741 

9.979459 

9.498282 

10.501718 

10.02C541 

10.522259 

31 

30 

9.478142 

9.97D420 

9.498722 

10.501278 

10.020580 

10.521858 

30 

31 

9  4vfio42 

9.979o80 

y.4'JJlo3 

10.500837 

10.0200*0 

10.5^1458 

29 

32 

9.478942 

9  979310 

9.499G03 

10.500397 

10.020660 

10.521058 

28 

33 

9.479342 

9  9793GO 

9.50U042 

10.409958 

10.020700 

10.520658 

27 

31 

9.479741 

9.979260 

9.500481 

10.499519 

10.020740 

10.520259 

26 

35 

9.480140 

9.979220 

9.500920 

10.499080 

10.020780 

10.519860 

25 

36 

9.480539 

9.979180 

9  501359 

10  498041 

10.020820 

10.519461 

24 

37 

9  480937 

9.979140 

9.501797 

10.498203 

10.020860 

10.519063 

23 

38 

9.481334 

9.979100 

9.502235 

10.497765 

10.020900 

10.518666 

22 

39 

9.481731 

9  .  979059 

9.502672 

10.497328 

10.020941 

10.518269 

21 

40 

9  482128 

9.979019 

9  503109 

10.496391 

10.020981 

10.517872 

20 

41 

9.48^525 

y  y?»9/y 

9.503546 

10.490454 

10.0210vil 

10.517475 

19 

42 

9.482921 

9.978939 

9.503982 

10.496018 

10.021061 

10.517079 

18 

43 

9.483316 

9.978898 

9.504418 

10.495582 

10.021102 

10.516684 

17 

44 

9.483712 

9.978858 

9.504854 

10.495146 

10.021142 

10.516288 

16 

45 

9.484107 

9.978817 

9.505289 

10494711 

10.021183 

10.51589S 

15 

4G 

9.484501 

9.978777 

9.505724 

10.494276 

10.021223 

10.515499 

14 

47 

9.481895 

9.978737 

9.506159 

10.493811 

10.021263 

10.515105 

13 

48 

9.485289 

9.978696 

9.506593 

10.493407 

10.021304 

10.514711 

12 

49 

9.435682 

9.978655 

9.507027 

10  492973 

10.021345 

10.514318 

11 

50 

9.48G075 

9.978615 

9.507460 

10.492540 

10  021385 

10.51S925 

10 

51 

9.486467 

9.978574 

9.  007  893 

1U.492107 

10.021426 

10.5135J3 

9 

52 

9.486860 

9.978533 

9  5l  '8326 

10.491G74 

10.021467 

10.513140 

8 

53 

9.487251 

9.978493 

9.508759 

10.491241 

10.021507 

10.512749 

7 

54 

9.487643 

9.978152 

9.509191 

10  490809 

10.021548 

10.512357 

6 

55 

9.488034 

9.978411 

9.509622 

10.490378 

10.021589 

10.511966 

5 

56 

9.488424 

9.978370 

9.510054 

10.489946 

10.021630 

10.511576 

4 

57 

9.488814 

9.978329 

9.510485 

10.489515 

10.021671 

10.511186 

3 

58 

9.489204 

9.978288 

9.510916 

10.489084 

10.021712 

10.510796 

2 

59 

9.489593 

9.978247 

9.511340 

10.488654 

10.021753 

10.510407 

1 

60 

9.489982 

9.978C06 

9  511776 

10.488224 

10.021794 

10.510018 

0 

M. 

Co-sine. 

Sine.   |  Co-tang. 

Tangent. 

Co-sec. 

Secant. 

H. 

7/4  JUejfrees. 

TABLE  II.                 161 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

18  Decrees. 

M. 

Sine. 

Co-sine.  Tangent. 

Co-tang. 

Secant. 

Co-sec.   M. 

0 

y.  489982 

9.978206 

9.511776 

10.488224 

10.0^1794 

10.510018 

GO 

1 

9.490371 

9.978165 

9.512206 

10.487794 

10.021835 

10.509629 

59 

2 

9.490759 

9.978124 

9.512635 

10.487365 

10.021876 

10.509241 

58 

3 

9.491147 

9.978083 

9.513064 

10.486936 

10.021917 

10.508853 

57 

4 

9  491535 

9.978042 

9.513493 

10.486507 

10.021958 

10.508465 

56 

5 

9.491922 

9.978U01 

9.513921 

10.486079 

10.  021999  *• 

10.508078 

55 

6 

9.492308 

9.977959 

9  514349 

10.485651 

10.022041 

10.507692 

54 

7 

9.492695 

9.977918 

9.514777 

10.485223 

10.022082 

10.507305 

53 

8 

9.493081 

9  977877 

9.515204 

10.484796 

10.022123 

10.506919 

52 

9 

9.493166 

9.977835 

9.515631 

10.484369 

10.022165 

10.506534 

51 

10 

9.493851 

9.977794 

9.516057 

ld.483943 

10.022206 

10.506149 

50 

11 

9.494236 

9  977752 

9.516484 

10.483516 

10.022248 

10.505764 

49 

12 

9.494621 

9.977711 

9.516910 

10.483090 

10.022289 

10.505379 

48 

13 

9.495005 

9.977669 

9.517335 

10.482665 

10.022331 

10.504995 

47 

14 

9.495388 

9.977628 

9.517761 

10.482239 

10.022372 

10.504612 

46 

15 

9.495772 

9.977586 

9.518185 

10.481815 

10.022414 

10.504228 

45 

16 

9.496154 

9.977544 

9.518610 

10.481390 

10.022456 

10.503846 

'44 

17 

9.496537 

9.977503 

9.519034 

10.480966 

10.022497 

10.503463 

43 

18 

9.496919 

9.977461 

9.519458 

10.480542 

10.022539 

10.503081 

42 

19 

9.497301 

9.977419 

9.519882 

10.480118 

10.022581 

10.502699 

41 

20 

9.497682 

9.977377 

9.520305 

10  479695 

10.022623 

10.502318 

40 

21 

9  498064 

9.977335 

9.520728 

10.479272 

10.022665 

10.501936 

39 

22 

9.498444 

9.977293 

9.521151 

10.478849 

10.022707 

10.501556 

38 

23 

9.498825 

9.977251 

9.521573 

10.478427 

10.022749 

10.501175 

37 

24 

9.499204 

9.977209 

9.521995 

10.478005 

10.022791 

10.500796 

36 

25 

9.499584 

9.977167 

9.522417 

10.477583 

10.022833 

10.500416 

35 

26 

9.499963 

9.977125 

9.522838 

10.477162 

10.022875 

10.500037 

34 

27 

9.500342 

9.977083 

9.523259 

10.476741 

10.022917 

10.499658 

33 

28 

9  500721 

9.977041 

9.523680 

10.476320 

10.022959 

10.499279 

32 

29 

9.501099 

9.976999 

9.524100 

10.475900 

10.023001 

10.498901 

31 

30 

9.501476 

9.976957 

9.524520 

10.475480 

10.023043 

10.498524 

30 

31 

9.501854 

9.976914 

9.524939 

10.475061 

10.023086 

10.498146 

29 

32 

9.502231 

9.976872 

9.525359 

10.474641 

10.023128 

10.497769 

28 

33 

9.502607 

9.976830 

9.525778 

10.474222 

10.023170 

10.497393 

27 

34 

9.502984 

9.976787 

9.526197 

10.473803 

10.023213 

10.497016 

26 

35 

9.503360 

9.976745 

9.526615 

10.473385 

10.023255 

10.496640 

25 

36 

9.503735 

9.976702 

9.527033 

10.472967 

10.023298 

10.496265 

24 

37 

9.504110 

9.976660 

9.527451 

10.472549 

10.023340 

10.495890 

23 

38 

9.504485 

9.976617 

9.527868 

10.472132 

10.023383 

10.495515 

22 

39 

9.504860 

9.976574 

9.528285 

10.471715 

10.023426 

10.495140 

21 

40 

9.505234 

9.976532 

9.528702 

10.471298 

10.023468 

10.494766 

20 

41 

9.505608 

9.976489 

9  529119 

10.470881 

10.023511 

10.494392 

19 

42 

9.505981 

9.976446 

9.529535 

10.470465 

10.023554 

10.494019 

18 

43 

9.506354 

9.976404 

9  529950 

10.470050 

10.023596 

10.493646 

17 

44 

9.506727 

9.976361 

9  530366 

10.469634 

10.023639 

10.493273 

16 

45 

9.507099 

9.976318 

9.530781 

10.469219 

10.023682 

10.492901 

15 

46 

9.507471 

9.976275 

9.531196 

10.468804 

10.023725 

10.492529 

14 

47 

9.507843 

9.976232 

9.531611 

10.468389 

10.023768 

10.492157 

13 

48 

9.508214 

9.976189 

9.532025 

10.467975 

10.023811 

10.491786 

12 

49 

9.508585 

9.976146 

9.532439 

10.467561 

10.023854 

10.491415 

11 

50 

9.508956 

9.976103 

9.532853 

10.467147 

10.023897 

10.491044 

10 

51 

9.509326 

9.976060 

9.533266 

10.466734 

10.023940 

10.490674 

9 

52 

9.509696 

9.976017 

9.533679 

10.466321 

10.023983 

10.490304 

8 

53 

9.510065 

9.975974 

9.534092 

10.465908 

10.024026 

10.489935 

7 

54 

9.510434 

9.975930 

9.534504 

10.465496 

10.024070 

10.489566 

6 

55 

9.510803 

9.975887 

9.534916 

10.465084 

10.024113 

10.489197 

5 

56 

9.511172 

9.975844 

9.535328 

10.464672 

10.024156 

10.488828 

4 

57 

9.511540 

9.975800 

9.535739 

10.464261 

10.024200 

10.488460 

3 

58 

9.511907 

9.975757 

9.536150 

10.463850 

10.024243 

10.488093 

2 

59 

9.512275 

9.975714 

9.536561 

10.463439 

10.024286 

10.487725 

1 

60 

9.512642 

9.975670 

9.536972 

10.463028 

10.024330 

10.487358 

0 

M. 

Co-sine. 

Sine.   |  Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

71  JJcjsrees. 

162                 TABLE  II. 

LOGAKITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

19  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-  tang. 

Secant. 

Co-sec. 

M. 

0 

9.512642 

9.975670 

9.5369/2 

10  463028 

10.0243oO 

10.487358 

60 

1 

9.513009 

9.975627 

9.537382 

10.462618 

10.024373 

10.486991 

59 

2 

9.513375 

9.975583 

9.537792 

10.462208 

10.024417 

10.486625 

58 

3 

9.513741 

9.975539 

9.538202 

10.461798 

10.024461 

10.486259 

57 

4 

9.514107 

9.975496 

9.538611 

10.461389 

10.024504 

10.485893 

56 

5 

9.514472 

9.975452 

9.539020 

10.460980 

10.024548 

10.485528 

55 

6 

9.514837 

9.975408 

9.539429 

10.460571 

10.024592 

10.485163 

54 

7 

9.515202 

9.975365 

9.539837 

10.460163 

10.024635 

10.484798 

53 

8 

9.515566 

9.975321 

9.540245 

10.459755 

10.024679 

10.484434 

52 

9 

9.515930 

9.975277 

9.540653 

10.459347 

10.024723 

10.484070 

51 

10 

9.516294 

9.975233 

9  541061 

10.458939 

10.024767 

10.483706 

50 

11 

9.510657 

9.975189 

9.541468 

10.458532 

10.024811 

10.483343 

49 

12 

9.517020 

9.975145 

9.541875 

10.458125 

10.024855 

10.482980 

48 

13 

9.517382 

9.975101 

9.542281 

10.457719 

10.024899 

10.482618 

47 

14 

9.517745 

9  975057 

9.542688 

10.457312' 

10.024943 

10.482255 

46 

15 

9  518107 

9.975013 

9.543094 

10.456906 

10.024987 

10.481893 

45 

16 

9.518468 

9.974969 

9.543499 

10.456501 

10.025031 

10.481532 

44 

17 

9.518829 

9  974925 

9.543905 

10.456095 

10.025075 

10.481171 

43 

18 

9.519190 

9.974880 

9.544310 

10.455690 

10.025120 

10.480810 

42 

19 

9.519551 

9.974836 

9.544715 

10.455285 

10.025164 

10.480449 

41 

20 

9.519911 

9.974792 

9.545119 

10.454881 

10.025208 

10.480089 

40 

21 

9.520271 

9.974748 

9.545524 

10.454476 

10.025252 

10.479729 

39 

22 

9.520634 

9.974703 

9.545928 

10.454072 

10.025297 

10.479369 

38 

23 

9.520990 

9.974659 

9.546331 

10.453669 

10.025341 

10.479010 

37 

24 

9  521349 

9.974614 

9.546735 

10.453265 

10.025386 

10.478651 

36 

25 

9.521707 

9  974570 

9.547138 

10.452862 

10.025430 

10.478293 

35 

26 

9.522066 

9.974525 

9.547540 

10.452460 

10.025475 

10.477934 

34 

27 

9.522424 

9.974481 

9.547943 

10.452057 

10.025519 

10.477576 

33 

28 

9.522781 

9.974436 

9.548345 

10.451655 

10.025564 

10.477219 

32 

29 

9.523138 

9.974391 

9.548747 

10.451253 

10.025609 

10.476862 

31 

30 

9.523495 

9.974347 

9.549149 

10.450851 

10.025653 

10.476505 

30 

31 

9  523852 

9.974302 

9.549550 

10.450450 

10.025698 

10.476148 

29 

32 

9  524208 

9  974257 

9.549951 

10.450049 

10.025743 

10.475792 

28 

33 

9.524564 

9.974212 

9.550352 

10.449648 

10.025788 

10.475436 

27 

34 

9.524920 

9.974167 

9.550752 

10.449248 

10.025833 

10.475080 

26 

35 

9  525275 

9.974122 

9.551152 

10.448848 

10.025878 

10.474725 

25 

36 

9  525630 

9.974077 

9.551552 

10.448448 

10.025923 

10.474370 

24 

37 

9.525984 

9  974032 

9.551952 

10.448048 

10.025968 

10.474016 

23 

38 

9.526339 

9.973987 

9.552351 

10.447649 

10.026013 

10.473661 

22 

39 

9.526693 

9.973942 

9.552750 

10.447250 

10.026058 

10.473307 

21 

40 

9.527046 

9.973897 

9.553149 

10.446851 

10.026103 

10.572954 

20 

41 

9.527400 

9.973852 

9.553548 

10.446452 

10.026148 

10.472600 

19 

42 

9.527753 

9.973807 

9.553946 

10.446054 

10.026193 

10.472247 

18 

43 

9.528105 

9.973761 

9.554344 

10.445656 

10.026239 

10.471895 

17 

44 

9.528458 

9.973716 

9.554741 

10.445259 

10.026284 

10.471542 

16 

45 

9.528810 

9.973671 

9.555139 

10.444861 

10.026329 

10.471190 

15 

46 

9.529161 

9.973625 

9.555536 

10.444464 

10.026375 

10.470839 

14 

47 

9  529513 

9.973580 

9.555933 

10.444067 

10.026420 

10.470487 

13 

48 

9.529864 

9.973535 

9.556329 

10.443671 

10.026465 

10.470136 

12 

49 

9.530215 

9.973489 

9.556725 

10.443275 

10.026511 

10.469785 

11 

50 

9.530565 

9.973444 

9.557121 

10.442879 

10.026556 

10.469435 

10 

51 

9.530915 

9.973398 

9.557517 

10.442483 

10.026602 

10.469085 

9 

52 

9.531265 

9.973352 

9.557913 

10.442087 

10.026648 

10.468735 

8 

53 

9.531614 

9.973307 

9.558308 

10.441692 

10.026693 

10.468386 

7 

54 

9.531963 

9.973261 

9.558702 

10.441298 

10.026739 

10.468037 

6 

55 

9  532312 

9.973215 

9.559097 

10.440903 

10.026785 

10.467688 

5 

56 

9.532661 

9.973169 

9.559491 

10.440509 

10.026831 

10.467339 

4 

57 

9.533009 

9.973124 

9.559885 

10.440115 

10.026876 

10.466991 

3 

58 

9.533357 

9.973078 

9.560279 

10.439721 

10.026922 

10.466643 

2 

59 

9.533704 

9.973032 

9.560673 

10.439327 

10.026968 

10.466296 

1 

60 

9.534052 

9.972986 

9.561066 

10.438934 

10.027014 

10.465948 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

7O  Degrees. 

TABLE  II.                 163 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

20  Degrees. 

M.  j  Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec.  |  M. 

u 

9.534052 

9.972986 

9.5ol066 

10.438934 

10.027014 

10.465948 

CO 

1 

9.534399 

9.972940 

9.561459 

10.438541 

10.027060 

10.465601 

E9 

2 

9.534745 

9.972894 

9.561851 

10.438149 

10.027106 

10.465255 

58 

3 

9.535092 

9.972848 

9.562244 

10.437756 

10.027152 

10.464908 

57 

4 

9.535438 

9.972802 

9.562636 

10.437364 

10.027198 

10.464562 

56 

5 

9.535783 

9.972755 

9.563028 

10.436972 

10.027245 

10.464217 

55 

6 

9.536129 

9.972709 

9.563419 

10.436581 

10.027291 

10.463871 

54 

7 

9.536474 

9.972663 

9.563811 

10.436189 

10.027337 

10.463526 

53 

8 

9.536818 

9.972617 

9.564202 

10.435798 

10.027383 

10.463182 

52 

9 

9.537163 

9.972570 

9.564592 

10.435408 

10.027430 

10.462837 

51 

10 

9.537507 

9.972524 

9.564983 

10.435017 

10.027476 

10.462493 

50 

11 

9.  537851 

9.972478 

9.565373 

10.434627 

10.027522 

10.462149 

49 

12 

9.538194 

9.972431 

9.565763 

10.434237 

10.027569 

10.461806 

48 

13 

9.538538 

9.972385 

9.566153 

10.433847 

10.027615 

10.461462 

47 

14 

9.538880 

9.972338 

9.566542 

10.433458 

10.027662 

10.461120 

46 

15 

9.539223 

9.972291 

9.566932 

10.433068 

10.027709 

10.460777 

45 

16 

9.539565 

9.972245 

9.567320 

10.432680 

10.027755 

10.460435 

44 

17 

9.539907 

9.972198 

9.5G7709 

10.432291 

10.027802 

10.460093 

43 

18 

9.540249 

9.972151 

9.568098 

10.431902 

10.027849 

10.459751 

42 

19 

9.540590 

9.972105 

9.568486 

10.431514 

10.027895 

10.459410 

41 

20 

9.540931 

9  .  972058 

9.568873 

10.431127 

10.027942 

10.459069 

40 

21 

9.541272 

9.972011 

9.569261 

10.430739 

10.027989 

10.458728 

39 

22 

9.541613 

9.971964 

9.569648 

10.430352 

10.028036 

10.458387 

38 

23 

9.541953 

9.971917 

9.570035 

10.429965 

10.028083 

10.458047 

37 

24 

9.542293 

9.971870 

9.570422 

10.429578 

10.028130 

10.457707 

36 

25 

9.542632 

9.971823 

9.570809 

10.429191 

10.028177 

10.457368 

35 

26 

9.542971 

9.971776 

9.571195 

10.428805 

10.028224 

10.457029 

34 

27 

9.543310 

9.971729 

9.571581 

10.428419 

10.028271 

10.456690 

33 

28 

9.543649 

9  971682 

9.571967 

10.428033 

10.028318 

10.456351 

32 

29 

9.543987 

9.971635 

9.572352 

10.427648 

10.028365 

10.456013 

31 

30 

9.544325 

9.971588 

9.572738 

10.427262 

10.028412 

10.455675 

30 

31 

9.544G63 

9.9/1540 

9.573123 

10.426877 

10.028460 

10.455337 

'z9 

32 

9.545000 

9.971493 

9.573507 

10.426493 

10.028507 

10.455000 

28 

33 

9.545338 

9.971446 

9.573892 

10.426108 

10.028554 

10.454662 

27 

31 

9.545674 

9.971398 

9.574276 

10.425724 

10.028602 

10.454326 

26 

35 

9.546011 

9.971351 

9.574660 

10.425340 

10.028649 

10.453989 

25 

36 

9.546347 

9.971303 

9.575044 

10.424956 

10.028697 

10.453653 

24 

37 

9.546683 

9.971256 

9.575127 

10.424573 

10.028744 

10.453317 

23 

38 

9.547019 

9.971208 

9.575810 

10.424190 

10.028792 

10.452981 

22 

39 

9.547354 

9.971161 

9.576193 

10.423807 

10.028839 

10.452646 

21 

40 

9.547689 

9.971113 

9.576576 

10.423424 

10.028887 

10.452311 

20 

41 

9.546024 

9.971066 

9.576958 

10.423012 

10.028934 

10.451976 

19 

42 

9.548359 

9.971018 

9  577341 

10.422659 

10.028982 

10.451641 

18 

43 

9.548693 

9.970970 

9.577723 

10.422277 

10.029030 

10.451307 

17 

44 

9.549027 

9.970922 

9.578104 

10.421896 

10.029078 

10.450973 

16 

45 

9.549360 

9.970874 

9.578486 

10.421514 

10.029126 

10.450640 

15 

46 

9.549693 

9.970827 

9.578867 

10.421133 

10.029173 

10.450307 

14 

47 

9.550026 

9.970779 

9.579248 

10.420752 

10.029221 

10.449974 

13 

48 

9.550359 

9.970731 

9.579629 

10.420371 

10.029269 

10.449641 

12 

49 

9.550692 

9.970683 

9.580009 

10.419991 

10.029317 

10.449308 

11 

SO 

9.551024 

9.970635 

9.580389 

10.419611 

10.029365 

10.448976 

10 

51 

9.551356 

9.970586 

9.580769 

10.419231 

10.029414 

10.448644 

9 

52 

9.551687 

9.970538 

9.581149 

10.418851 

10.029462 

10.448313 

8 

53 

9.552018 

9.970490 

9.581528 

10.418472 

10.029510 

10.447982 

7 

54 

9.552349 

9.970442 

9.581907 

10.418093 

10.029558 

10.447651 

6 

55 

9.552680 

9.970394 

9.582286 

10.417714 

10.029606 

10.447320 

5 

56 

9.553010 

9.970345 

9.582665 

10.417335 

10.029655 

10.446990 

4 

57 

9.553341 

9.970297 

9.583043 

10.416957 

10.029703 

10.446659 

3 

58 

9.553670 

9.970249 

9.583422 

10.416578 

10.029751 

10.446330 

2 

59 

9.554000 

9.970200 

9.583800 

10.416200 

10.029800 

10.446000 

1 

60 

9  554329 

9.  0701.-  -2 

9.584177 

10.415823 

10.029848 

10.445671 

0 

M. 

Co-sine. 

Sine.   |  Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

Ui>  Degrees. 

164                 TABLE  II. 

LOGAKITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

21  Degrees. 

M. 

Sine. 

Co-sine.  Tangent. 

Co-tang. 

Secant.   Co-sec. 

M. 

u 

9.554329 

9.9/0152 

9.584177 

10.415823 

10.029848 

10.44567  i 

(JO 

1 

9.554G58 

9.970103 

9.584555 

10.415445 

10.029897 

10.445342 

59 

2 

9  554987 

9.970055 

9.584932 

10.415068 

10.029945 

10.445013 

58 

3 

9.555315 

9.970006 

9.585309 

10.414691 

10.029994 

10.444685 

57 

4 

9.555643 

9.969957 

9.585686 

10.414314 

10.030043 

10.444357 

56 

5 

9.555971 

9.969909 

9.586062 

10.413938 

10.030091 

10.444029 

55 

G 

9.556299 

9.969860 

9.586439 

10.413561 

10.030140 

10.443701 

54 

7 

9.556626 

9.969811 

9.586815 

10.413185 

10.030189 

10.443374 

53 

8 

9.556953 

9.969762 

9.587190 

10.412810 

10.030238 

10.443047 

52 

9 

9.557280 

9.969714 

9.587566 

10.412434 

10.030286 

10.442720 

51 

10 

9.557606 

9.969665 

9.587941 

10.412059 

10.030335 

10.442394 

50 

11 

9.557932 

9.969616 

9.588316 

10.411684 

10.030384 

10.442068 

49 

12 

9.558258 

9.969567 

9.588691 

10.411309 

10.030433 

10.441742 

48 

13 

9.558583 

9.969518 

9.589066 

10.410934 

10.030482 

10.441417 

47 

14 

9.558909 

9.969469 

9.589440 

10.410560 

10.030531 

10.411091 

46 

15 

9.559234 

9.969420 

9.589814 

10.410186 

10.030580 

10.440766 

45 

1G 

9.559558 

9.969370 

9.590188 

10.409812 

10.030630 

10.440442 

44 

17 

9.559883 

9.969321 

9.590562 

10.409438 

10.030679 

10.440117 

43 

18 

9.560207 

9.969272 

9.590935 

10.409065 

10.030728 

10.439793 

42 

19 

9.560531 

9.969223 

9.591308 

10.408692 

10.030777 

10.439469 

41 

20 

9.560855 

9.969173 

9.591681 

10.408319 

10.030827 

10.439145 

40 

21 

9.561178 

9.969124 

9.592054 

10.407946 

10.030876 

10.43882'J 

39 

22 

9.561501 

9.969075 

9.592426 

10.407574 

10.030925 

10.438499 

38 

23 

9.561824 

9.969025 

9.592798 

10.407202 

10.030975 

10.438176 

37 

24 

9.562146 

9.968976 

9.593171 

10.406829 

10.031024 

10.437854 

36 

25 

9.562468 

9.968926 

9.593542 

10.406458 

10.031074 

10.437532 

35 

26 

9.562790 

9.968877 

9.593914 

10.406086 

10.031123 

10.437210 

34 

27 

9.563112 

9.968827 

9.594285 

10.405715 

10.031173 

10.436888 

33 

28 

9  563433 

9.968777 

9.594656 

10.405344 

10.031223 

10.436567 

32 

29 

9.563755 

9.968728 

9.595027 

10.404973 

10.031272 

10.436245 

31 

30 

9.564075 

9.968678 

9.595398 

10.404602 

10.031322 

10.435925 

30 

31 

9  564396 

9.968628 

9.595768 

10.404232 

10.031372 

10.435604 

W 

32 

9.564716 

9.968578 

9.596138 

10.403862 

10.031422 

10.435284 

28 

33 

9.565036 

9.968528 

9.596508 

10.403492 

10.031472 

10.434964 

27 

34 

9.565356 

9.968479 

9.596878 

10.403122 

10.031521 

10.434644 

26 

35 

9.56567G 

9.968429 

9.597247 

10.402753 

10.031571 

10.434324 

25 

36 

9.565995 

9.968379 

9.597616 

10.402384 

10.031621 

10.434005 

24 

37 

9.566314 

9.968329 

9.597985 

10.402015 

10.031671 

10.433686 

23 

38 

9.566632 

9.968278 

9.598354 

10.401646 

10.031722 

10.433368 

22 

39 

9.566951 

9.968228 

9.598722 

10.401278 

10.031772 

10.433049 

21 

40 

9.507269 

9.968178 

9.599091 

10.400909 

10.031822 

10.432731 

20 

41 

9  5U7587 

9.968128 

9.599459 

10.400541 

l'J.031872 

10.432413 

1U 

42 

9.567904 

9.968078 

9.599827 

10.400173 

10.031922 

10.432096 

18 

43 

9.568222 

9.968027 

9.600194 

10.399806 

10.031973 

10.431778 

17 

44 

9.568539 

9.967977 

9.600562 

10.399438 

10.032023 

10.431461 

16 

45 

9:568856 

9.967927 

9.600929 

10.399071 

10.032073 

10.431144 

15 

46 

9.569172 

9.967876 

9.601296 

10.398704 

10.032124 

10.430828 

14 

47 

9.569488 

9.967826 

9.601662 

10.398338 

10.032174 

10.430512 

13 

48 

9.569804 

9.967775 

9.602029 

10.397971 

10.032225 

10.430196 

12 

49 

9.570120 

9.967725 

9.602395 

10.397605 

10.032275 

10.429880 

11 

50 

9.570435 

9.967674 

9.602761 

10.397239 

10.032326 

10.429565 

10 

51 

9.57U751 

9.967624 

9.603127 

10.396873 

10.032376 

10.429249 

9 

52 

9.571066 

9.967573 

9.603493 

10.396507 

10.032427 

10.428934 

8 

53 

9.571380 

9.967522 

9.603858 

10.396142 

10.032478 

10.428620 

7 

54 

9.571695 

9.967471 

9.604223 

10.395777 

10.032529 

10.428305 

6 

55 

9.572009 

9.967421 

9.604588 

10.395412 

10.032579 

10.427991 

5 

56 

9.572323 

9.967370 

9.604953 

10.395047 

10.032630 

10.427677 

4 

57 

9.572636 

9.967319 

9.605317 

10.394683 

10.032681 

10.427364 

3 

58 

9.572950 

9.967268 

9.605682 

10.394318 

10.032732 

10.427050 

2 

59 

9.573263 

9.967217 

9.606046 

10.393954 

10.032783 

10.426737 

1 

CO 

9.573575 

9.967166 

9.606410 

10.393590 

10.032834 

10.426425 

0 

M.  )  Co-sine. 

Sine. 

3o-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

68  Degrees. 

TABLE  II.                 165 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

22  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec.   M. 

0 

9.573575 

9.907106 

9.G06410   10.393590 

10  032834 

10.4264^5 

60 

] 

9.573888 

9.967115 

9.606773 

10.393227 

10.032885 

10.426112 

59 

2 

9.574200 

9.967064 

9.607137 

10.392863 

10.032936 

10.425800 

58 

3 

9.574512 

9.967013 

9.607500 

10.392500 

10.032987 

10.425488 

57 

4 

9.574824 

9.966961 

9.607863 

10.392137 

10.033039 

10.425176 

56 

5 

9.575136 

9.966910 

9.608225 

10.391775 

10.033090 

10.424864 

55 

6 

9.575447 

9.966859 

9.608588 

10.391412 

10  033141 

10.424553 

54 

7 

9.575758 

9.966808 

9.608950 

10.391050 

10.033192 

10.424242 

53 

8 

9.576069 

9.966756 

9.609312 

10.390688 

10.033244 

10.423931 

52 

9 

9.576379 

9.966705 

9.609674 

10.390326 

10.033295 

10.423621 

51 

10 

9.576689 

9.966653 

9.610036 

10.389964 

10.033347 

10.423311 

50 

11 

9.57U999 

9.9GOC02 

9.610397 

10.389603 

10.033398 

10.423001 

49 

12 

9.577309 

9.966550 

9.610759 

10.389241 

10.033450 

10.422691 

48 

13 

9.577618 

9.966499 

9.611120 

10.388-880 

10.033501 

10.422382 

47 

14 

9.577927 

9.966447 

9.611480 

10.388520 

10.033553 

10.422073 

46 

15 

9.578236 

9.966395 

9.611841 

10.388159 

10.033605 

10.421764 

45 

1G 

9.578545 

9.966344 

9.612201 

10.387799 

10.033656 

10.421455 

44 

17 

9.578853 

9.966292 

9.612561 

10.387439 

10.033708 

10.421147 

43 

18 

9.579162 

9.966240 

9.612921 

10.387079 

10.033760 

10.420838  . 

42 

19 

9.579470 

9.966188 

9.613281 

10.386719 

10.033812 

10.420530 

41 

20 

9.579777 

9.966136 

9.613641 

10.386359 

10.033864 

10.420223 

40 

21 

9.  580085 

9.966085 

9.614000 

10.386000 

10.033915 

10.419915 

39 

22 

9.580392 

9.966033 

9.614359 

10.385641 

10.033967 

10.419608 

38 

23 

9.580699 

9.965981 

9.614718 

10.385282 

10.034019 

10.419301 

37 

24 

9.581005 

9.965929 

9.615077 

10.384923 

10.034071 

10.418995 

36 

25 

9.581312 

9.965876 

9.615435 

10.384565 

10.034124 

10.418688 

35 

26 

9.531618 

9.965824 

9.615793 

10.384207 

10.034176 

10.418382 

34 

27 

9.581924 

9.965772 

9.616151 

10.383849 

10.034228 

10.418076 

33 

28 

9.582229 

9  965720 

9.616509 

10.383491 

10.034280 

10.417771 

32 

29 

9.582535 

9  965668 

9.616867 

10.383133 

10.034332 

10.417465 

31 

30 

9  582840 

9  965615 

9.617224 

10.382776 

10.034385 

10.417160 

30 

31 

9.583145 

9.965563 

9.617582 

10.382418 

10.034437 

10.416855 

29 

32 

9.583449 

9.965511 

9.617939 

10.382061 

10.034489 

10.416551 

28 

33 

9.583754 

9  965458 

9.618295 

10.381705 

10.034542 

10.416246 

27 

34 

9.584058 

9  965406 

9.618652 

10.381348 

10.034594 

10.415942 

26 

35 

9.584361 

9.965353 

9.619008 

10.380992 

10.034647 

10.415639 

25 

36 

9.584665 

9  965301 

9.619364 

10.380636 

10.034699 

10.415335 

24 

37 

9.584968 

9.965248 

9.619721 

10.380279 

10.034752 

10.415032 

23 

38 

9.585272 

9.965195 

9.620076 

10.379924 

10.034805 

10.414728 

22 

39 

9.585574 

9.965143 

9.620432 

10.379568 

10.034857 

10.414426 

21 

40 

9.585877 

9.965090 

9.620787 

10.379213 

10.034910 

10.414123 

2u 

41 

9.5S6179 

9.965037 

9.621142 

10.378858 

10.034963 

10.413821 

19 

42 

9.586482 

9.964984 

9.621497 

10.378503 

10.035016 

10.413518 

18 

43 

9  586783 

9.964931 

9.621852 

10.378148 

10.035069 

10.413217 

17 

44 

9.587085 

9.964879 

9.622207 

10.377793 

10.035121 

10.412915 

16 

45 

9.587386 

9.964826 

9.622561 

10.377439 

10.035174 

10.412614 

15 

46 

9.587688 

9.964773 

9.622915 

10.377085 

10.035227 

10.412312 

14 

47 

9.587989 

9.964720 

9.623269 

10.376731 

10.035280 

10.412011 

13 

48 

9.588289 

9.964666 

9.623623 

10.376377 

10.035334 

10.411711 

12 

49 

9.588590 

9.964613 

9.623976 

10.376024 

10.035387 

10.411410 

11 

50 

9.588890 

9.964560 

9.624330 

10.375670 

10.035440 

10.411110 

10 

51 

9.589190 

9.904507 

9.624683 

10.375317 

10.035493 

10.410810 

9 

52 

9.589489 

9.964454 

9.625036 

10.374964 

10.035546 

10.410511 

8 

53 

9.589789 

9.964400 

9.625388 

10.374612 

10.033600 

10.410211 

7 

54 

9.590088 

9.964347 

9.625741 

10.374259 

10.035653 

10.409912 

6 

55 

9.590387 

9.964294 

9.626093 

10.373907 

10.035706 

10.409613 

5 

56 

9.590686 

9.964240 

9.626445 

10.373555 

10.035760 

10.409?14 

4 

57 

9.590984 

9.964187 

9.626797 

10.373203 

10.035813 

10.409016 

3 

58 

9.591282 

9.964133 

9.627149 

10.372851 

10.035867 

10.408718 

2 

59 

9.591580 

9.964080 

9.627501 

10.372499 

10.035920 

10.408420 

1 

60 

9.591878 

9.961026 

9.627852 

10.372148 

10.035974 

10.408122 

0 

M. 

Co-sine. 

Sine.   |  Co-tang.  |  Tangent. 

Co-sec. 

Secant.   M. 

O7  Degrees. 

166                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

23  Degrees. 

M. 

Sine. 

Co-sine.  |Tangent.|  Co-tang. 

Secant. 

Co-sec. 

M. 

0 
1 
2 
3 

4 
5 
6 
7 
8 
9 
10 

y.  5^1878 
9  592176 
9  592473 
9.592770 
9.593067 
9.593363 
9.593659 
9.593955 
9.594251 
9.594547 
9.594842 

9.904026 
9.963972 
9.963919 
9.963865 
9  963811 
9.963757 
9.963704 
9.963650 
9.963596 
9.963542 
9.963488 

9.6z7852 
9.628203 
9.628554 
9.628905 
9.629255 
9  629606 
9.629956 
9.630306 
9.630656 
9.631005 
9.631355 

10.37^148 
10.371797 
10.371446 
10.371095 
10.370745 
10.370394 
10.370044 
10.369694 
10.369344 
10.368995 
10.368645 

10.035974 
10.036028 
10.036081 
10.036135 
10.036189 
10.036243 
10.036296 
10.036350 
10.036404 
10.036458 
10.036512 

10.408122 
10.407824 
10.407527 
10.407230 
10.406933 
10.406637 
10.406341 
10.406045 
10.405749 
10.405453 
10.405158 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
-50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

9.59,3137 
9.595432 
9.595727 
9.596021 
9.596315 
9.596609 
9.596903 
9.597196 
9.597490 
9.597783 

9.963434 
9.963379 
9.963325 
9.963271 
9.963217 
9.963163 
9.963108 
9.963054 
9.962999 
9.962945 

9.631704 
9.632053 
9.632401 
9  632750 
9.633098 
9  633447 
9.633795 
9  634143 
9.634490 
9  634838 

10.368296 
10.367947 
10.367599 
10.367250 
10.366902 
10.366553 
10.366205 
10.365857 
10.365510 
10.365162 

10.036566 
10.036621 
10.036675 
10.036729 
10.036783 
10.036837 
10.036892 
10.036946 
10.037001 
10.037055 

10.404863 
10.404568 
10.404273 
10.403979 
10.403685 
10.403391 
10.403097 
10.402804 
10.402510 
10.402217 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

9.598075 
9.598368 
9.598660 
9.598952 
9.599244 
9.599536 
9.599827 
9.600118 
9.600409 
9.G00700 

9.962890 
9.962836 
9.962781 
9.962727 
9.962672 
9.962617 
9.962562 
9.962508 
9.962453 
9.962398 

9.635185 
9.635532 
9.635879 
9.636226 
9.636572 
9.636919 
9.637265 
9  637611 
9.637956 
9.638302 

10.364815 
10.364468 
10.364121 
10.363774 
10.363428 
10.363081 
10.362735 
10.362389 
10.362044 
10.361698 

10.037110 
10.037164 
10.037219 
10.037273 
10.037328 
10.037383 
10.037438 
10.037492 
10.037547 
10.037602 

10.401925 
10.401632 
10.401340 
10.401048 
10.400756 
10.400464 
10.400173 
10.399882 
10.399591 
10.399300 

3y 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

9.60U990 
9.601280 
9.C01570 
9.601860 
9.602150 
9.602439 
9.602728 
9.603017 
9.603305 
9.603594 

9.962343 
9.962288 
9.962233 
9.962178 
9.902123 
9.962067 
9  962012 
9.961957 
9.961902 
9.961846 

9.638647 
9.638992 
9.639337 
9.639682 
9.640027 
9.640371 
9.640716 
9.641060 
9.641404 
9.641747 

10.361353 
10.361008 
10.360663 
10.360318 
10.359973 
10.359629 
10.359284 
10.358940 
10.358596 
10.358253 

10.037657 
10.037712 
10.037767 
10.037822 
10.037877 
10.037933 
10.037988 
10.038043 
10.038098 
10.038154 

10.399010 
10.398720 
10.398430 
10.398140 
10.397850 
10.397561 
10.397272 
10.396983 
10.396695 
10.396406 

29 
28 
27 
26 
25 
24 
23 
2!2 
21 
20 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

U.  00388  2 
9.604170 
9.604457 
9.604745 
9.605032 
9.605319 
9.605606 
9.605892 
9.606179 
9  606465 

9.961791 
9  961735 
9.961680 
9.961624 
9.961569 
9.961513 
9.961458 
9.961402 
9.961346 
9.961290  • 

9.642091 
9.642434 
9.642777 
9.643120 
9.643463 
9  643806 
9.644148 
9.644490 
9.644832 
9  645174 

10.357909 
10.357566 
10.357223 
10.356880 
10.356537 
10.356194 
10.355852 
10.355510 
10.355168 
10.354826 

10.038209 
10.038265 
10.038320 
10.038376 
10.038431 
10.038487 
10.038542 
10.038598 
10.038654 
10038710 

10.396118 
10.395830 
10.395543 
10.395255 
10.394968 
10.394681 
10.394394 
10.394108 
10.393821 
10.393535 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

9.606751 
9.607036 
9.607322 
9.607607 
9.607892 
9.608177 
9.608461 
9.608745 
9.609029 
9.609313 

9.961235 
9.961179 
9.961123 
9.961067 
9.961011 
9.960955 
9.960899 
9.960843 
9.960786 
9.960730 

9.645516 
9.645857 
9.646199 
9.646540 
9.646881 
9.647222 
9  647562 
9.647903 
9.648243 
9.648583 

10.354484 
10.354143 
10.353801 
10.353460 
10.353119 
10.352778 
10.352438 
10.352097 
10.351757 
10.351417 

10.038765 
10.038821 
10.038877 
10.038933 
10.038989 
10.039045 
10.039101 
10.039157 
10.039214 
10.039270 

10.393249 
10.392964 
10.392678 
10.392393 
10.392108 
10.391823 
10.391539 
10.391255 
10.390971 
10.390687 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

M. 

Co-sine. 

Sine. 

Co-tahg. 

Tangent. 

Co-sec. 

Secant. 

M. 

66  Decrees. 

TABLE  H.                 1G7 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

24  Degrees. 

M. 

Sine. 

Co-sine.  (Tangent. 

Co-  tang. 

Secant. 

Co-sec. 

M. 

0 

1J.  609313 

9.9(50730 

9.648583 

10.351417 

10.039270 

10.390687 

60 

1 

9.609597 

9.960674 

9.648923 

10.351077 

10.039326 

10.390403 

59 

2 

9.609880 

9.960618 

9.649263 

10.350737 

10.039382 

10.390120 

58 

3 

9.610164 

9.960561 

9.649602 

10.350398 

10.039439 

10.389836 

57 

4 

9.610447 

9.960505 

9.649942 

10.350058 

10.039495 

10.389553 

56 

5 

9.610729 

9.960448 

9.650281 

10.349719 

10.039552 

10.389271 

55 

6 

9.611012 

9.960392 

9.650620 

10.349380 

10.039608 

10.388988 

54 

7 

9.611294 

9.960335 

9.650959 

10.349041 

10.039665 

10.388706 

53 

8 

9.611576 

9  960279 

9.651297 

10.348703 

10.039721 

10.388424 

52 

9 

9.611858 

9.960222 

9.651636 

10.348364 

10.039778 

10.388142 

51 

10 

9.612140 

9.960165 

9.651974 

10.348026 

10.039835 

10.387860 

50 

11 

9.6124-21 

9.960109 

9.652312 

10.347688 

10.039891 

10.387579 

49 

12 

9.612702 

9.960052 

9.652650 

10.347350 

10.039948 

10.387298 

48 

13 

9.612983 

9.959995 

9.652988 

10.347012 

10.040005 

10.387017 

47 

14 

9.613264 

9.959938 

9.653326 

10.346674 

10.040062 

10.386736 

46 

15 

9.613545 

9.959882 

9.653663 

10.346337 

10.040118 

10.386455 

45 

]6 

9.613825 

9.959825 

9.654000 

10.346000 

'10.040175 

10.386175 

44 

17 

9.614105 

9.959768 

9.654337 

10.345663 

10.040232 

10.385895 

43 

18 

9.614385 

9.959711 

9.654674 

10.345326 

10.04028y 

10.385615 

42 

19 

9.614665 

9.959654 

9.655011 

10.344989 

10.040346 

10.385335 

41 

20 

9  614944 

9.959596 

9.655348 

10.344652 

10.040404 

10.385056 

40 

21 

9.615223 

9.959539 

9.655684 

10.344316 

10.040461 

10.384777 

39 

22 

9.615502 

9.959482 

9.656020 

10.343980 

10.040518 

10.384498 

38 

23 

9.615781 

9.959425 

9.656356 

10.343644 

10.040575 

10.384219 

37 

24 

9.616060 

9.959368 

9.656692 

10.343308 

10.040632 

10.383940 

36 

25 

9.616338 

9.959310 

9.657028 

10.342972 

10.040690 

10.383662 

35 

26 

9.616616 

9.959253 

9.657364 

10.342636 

10.040747 

10.383384 

34 

27 

9.616894 

9.959195 

9.657699 

10.342301 

10.040805 

10.383106 

33 

28 

9  617172 

9.959138 

9.658034 

10.341966 

10.040862 

10.382828 

32 

29 

9.617450 

9.959080 

9.658369 

10.341631 

10.040919 

10.382550 

31 

30 

9  617727 

9.959023 

9.65.8704 

10.341296 

10.040977 

10.382273 

30 

31 

9.618004 

9.958965 

9.659039 

10.340961 

10.041035 

10.381996 

*9 

32 

9.618281 

9.958908 

9.659373 

10.340627 

10.041092 

10.381719 

28 

33 

9.618558 

9.958850 

9.659708 

10.340292 

10.041150 

10.381442 

27 

34 

9.618834 

9.958792 

9.660042 

10.339958 

10.041208 

10.381166 

26 

35 

9.619110 

9.958734 

9.660376 

10.339624 

10.041266 

10.380890 

25 

36 

9.619386 

9.958677 

9.660710 

10.339290 

10.041323 

10.380614 

24 

37 

9.619662 

9.958619 

9.661043 

10.338957 

10.041381 

10.380338 

23 

38 

9.619938 

9.958561 

9.661377 

10.338623 

10.041439 

10.380062 

22 

39 

9.620213 

9.958503 

9.661710 

10.338290 

10.041497 

10.379787 

21 

40 

9.620488 

9.958445 

9.662043 

10.337957 

10.041555 

10.379512 

'20 

41 

9.620763 

9.958387 

9.662376 

10.3376*4 

10.041613 

10.379237 

19 

42 

9.621038 

9.958329 

9.662709 

10.337291 

10.041671 

10.378962 

18 

43 

9.621313 

9.958271 

9.663042 

10.336958 

10.041729 

10.378687 

17 

44 

9.621587 

9.958213 

9  663375 

10.336625 

10.041787 

10.378413 

16 

45 

9.621861 

9.958154 

9.663707 

10.336293 

10.041846 

10.378139 

15 

46 

9.622135 

9.958096 

9.664039 

10.335961 

10.041904 

10.377865 

14 

47 

9.622409 

9.958038 

9.664371 

10.335629 

10.041962 

10.377591 

13 

48 

9.622682 

9.957979 

9.664703 

10.335297 

10.042021 

10.377318 

12 

49 

9.622956 

9.957921 

9.665035 

10.334965 

10.042079 

10.377044 

11 

50 

9.623229 

9.957863 

9.665366 

10.334634 

10.042137 

--«- 

10.376771 

10 

51 

9.623502 

9.957804 

9.665697 

10.334303 

10.042196 

10.376498 

9 

52 

9.623774 

9.957746 

9.666029 

10.333971 

10.042254 

10.376226 

8 

53 

9.624047 

9.957687 

9.666360 

10.333640 

10.042313 

10.375953 

7 

54 

9.624319 

9.957628 

9.666691 

10.333309 

10.042372 

10.375681 

6 

55 

9.624591 

9.957570 

9.667021 

10.332979 

10.042430 

10.375409 

5 

56 

9.624863 

9.957511 

9.667352 

10.332648 

10.042489 

10.375137 

4 

57 

9.625135 

9.957452 

9.667682 

10.332318 

10.042548 

10.374865 

3 

58 

9.625406 

9.957393 

9.668013 

10.331987 

10.042607 

10.374594 

2 

59 

9.625677 

9.957335 

9.668343 

10.331657 

10.042665 

10.374323 

1 

60 

9.G25948 

9.957270 

9.668672 

10.331328 

10.042724 

10.374052 

0 

M. 

Co-sine. 

Sine.   |  Co-tang.  Tangent. 

Co-sec. 

Secant. 

M. 

65  I)egre«H. 

108                 TABLE  II. 

LOGARITHMIC  SIGNS,  TANGENTS  AND  SECANTS. 

25  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

9.625948 

9.9-37^(5 

9.  (5(5867  J 

10.331327 

10.042724 

10.3740^ 

GO 

1 

9.626219 

9  957217 

9.669002 

10.330998 

10.042783 

10.373781 

59 

2 

9.626490 

9.957158 

9.669332 

10.330668 

10.042842 

10.373510 

58 

3 

9.620760 

9.957099 

9.669661 

10.330339 

10.042901 

10.373240 

57 

4 

9  627030 

9.957040 

9.669991 

10.330009 

10.042960 

10.372970 

56 

5 

9.627300 

9.956981 

9.670320 

10.329680 

10.043019 

10.372700 

55 

6 

9.627570 

9.956921 

9.670649 

10.329351 

10.043079 

10.372430 

54 

7 

9.627840 

9.956862 

9.670977 

10.329023 

10.043138 

10.372160 

53 

8 

9.628109 

9.956803 

9.671306 

10.328694 

10.043197 

10.371891 

52 

9 

9.628378 

9.956744 

9.671634 

10.328366 

10.043256 

10.371622 

51 

10 

9.628647 

9.956684 

9.671963 

10.328037 

10.043316 

10.371353 

50 

11 

9.028916 

9.956625 

9.672291 

10.327709 

10.043375 

10.371084 

49 

12 

9.629185 

9.956566 

9.672619 

10.327381 

10.043434 

10.370815 

48 

13 

9.629453 

9.956506 

9.672947 

10.327053 

10.043494 

10.370547 

47 

14 

9.629721 

9.956447 

9.673274 

10.326726 

10.043553 

10.370279 

46 

15 

9.629989 

9.956387 

9.673602 

10.326398 

10.043613 

10.370011 

45 

16 

9.630257 

9.956327 

9.673929 

10.326071 

10.043673 

10.369743 

44 

17 

9.630524 

9  956268 

9.674257 

10.325743 

10.043732 

10.369476 

43 

18 

9.630792 

9.956208 

9.674584 

10.325416 

10.043792 

10.369208 

42 

19 

9.631059 

9.956148 

9.674910 

10.325090 

10.043852 

10.368941 

41 

20 

9.631326 

9.956089 

9.675237 

10.324763 

10.043911 

10.368674 

40 

21 

9.631593 

9.956029 

9.675564 

10.324436 

10.043971 

10.368407 

39 

22 

9.631859 

9.955969 

9.675890 

10.324110 

10.044031 

10.368141 

38 

23 

9.632125 

9.955909 

9.676217 

10.323783 

10.044091 

10.367875 

37 

24 

9.632392 

9.955849 

9.676543 

10.323457 

10.044151 

10.367608 

3G 

25 

9.632658 

9.955789 

9.676869 

10.323131 

10.044211 

10.367342 

35 

26 

9  632923 

9.955729 

9.677194 

10.322806 

10.044271 

10.367077 

34 

27 

9.633189 

9.955669 

9  677520 

10.322480 

10.044331 

10.366811 

33 

28 

9.633454 

9.955609 

9.677846 

10.322154 

10.044391 

10.366546 

32 

29 

9.633719 

9.955548 

9.678171 

10.321829 

10.044452 

10.366281 

31 

30 

9.633984 

9.955488 

9.678496 

10.321504 

10.044512 

10.366016 

30 

31 

9.  (534249 

9.955428 

9.678821 

10.321179 

10.044572 

10.365751 

29 

32 

9.634514 

9.955368 

9.679146 

10.320854 

10.044632 

10.365486 

28 

33 

9.634778 

9.955307 

9.679471 

10.520529 

10.044693 

10.365222 

27 

34 

9.635042 

9.955247 

9.679795 

10.320205 

10.044753 

10.364958 

26 

35 

9.635306 

9.955186 

9.680120 

10.319880 

10.044814 

10.364694 

25 

36 

9.635570 

9.955126 

9.680444 

10.319556 

10.044874 

10.3644GO 

24 

37 

9.635834 

9.955065 

9.680768 

10.319232 

10.044935 

10.364166 

23 

38 

9.636097 

9.955005 

9.681092 

10.318908 

10.044995 

10.383903 

22 

39 

9.636360 

9.954944 

9.681416 

10.318584 

10.045056 

10.363640 

21 

40 

9.636623 

9.954883 

9.681740 

10.318260 

10.045117 

10.363377 

20 

41 

9.  63(5886 

9.954823 

9.  6S2063 

10.317937 

10.045177 

10.3(53114 

19 

42 

9.637148 

9.954762 

9.682387 

10.317613 

10.045238 

10.362852 

18 

43 

9.637411 

9.954701 

9.682710 

10.317290 

10.045299 

10.362589 

17 

44 

9.637673 

9.954640 

9.683033 

10.316967 

10.045360 

10.362327 

16 

45 

9.637935 

9.954579 

9.683356 

10.316644 

10.045421 

10.362065 

15 

46 

9.638197 

9.954518 

9.683679 

10.316321 

10.045482 

10.361803 

14 

47 

9.638458 

9.954457 

9.684001 

10.315999 

10.045543 

10.361542 

13 

48 

9.638720 

9.954396 

9.684324 

10.315676 

10.045604 

10.361280 

12 

49 

9.638981 

9.954335 

9.684646 

10.315354 

10.045665 

10.361019 

11 

50 

9.639242 

9.954274  . 

9.684968 

10.315032 

10.045726 

10.360758 

10 

51 

9.639503 

9.954213 

9.685290 

10.314710 

10.045787 

10.360497 

9 

52 

9.639764 

9.954152 

9.685612 

10.314388 

10.045848 

10.360236 

8 

53 

9.640024 

9.954090 

9.685934 

10.314066 

10.045910 

10.359976 

7 

54 

9.640284 

9.954029 

9.686255 

10.313745 

10.045971 

10.359716 

6 

55 

9.640544 

9.953968 

9.686577 

10.313423 

10.046032 

10.359456 

5 

56 

9.640804 

9.953906 

9.686898 

10.313102 

10.046094 

10.359196 

4 

57 

9.641064 

9.953845 

9.687219 

10.312781 

10.046155 

10.358936 

3 

58 

9.641324 

9.953783 

9.687540 

10.312460 

10.046217 

10.358676 

2 

59 

9.641583 

9.953722 

9.687861 

10.312139 

10.046278 

10.358417 

1 

60 

9.641842 

9.953660 

9.688182 

10.311818 

10.046340 

10.358158 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

O4  Degrees. 

TABLE  II.                 169 

Z/OGABITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

26  Decrees. 

M.  |  Sine. 

Co-sine.  Tangent. 

Co-tang.   Secant. 

Co-sec.  |  M. 

u 

9.641842 

9.953660 

9.688182 

1U.  311818 

10.04(3340 

10.35«158 

00 

1 

9.642101 

9.953599 

9.688502 

10.311498 

10.046401 

10.357899 

59 

2 

9.642360 

9.953537 

9.688823 

10.311177 

10.046463 

10.357640 

58 

3 

9.642618 

9.953475 

9.689143 

10.310857 

10.046525 

10.357382 

57 

4 

9.642877 

9.953413 

9.689463 

10.310537 

10.046587 

10.357123 

56 

3 

9.643135 

9.953352 

9.689783 

10.310217 

10.046648 

10.356865 

55 

6 

9.643393 

9.953290 

9.690103 

10.309897 

10.046710 

10.356607 

54 

7 

9.643650 

9.953228 

9.690423 

10.309577 

10.046772 

10.356350 

53 

8 

9.643908 

9.953166 

9.690742 

10.309258 

10.046834 

10.356092 

52 

9 

9.644165 

9.953104 

9.691062 

10.308938 

10.046896 

10.355835 

51 

10 

9  644423 

9.953042 

9.691381 

10.308619 

10.046958 

10.355577 

50 

11 

9.644680 

9.952980 

9.691700 

10.308300 

10.0470*0 

10.3553^:0 

49 

12 

9.644936 

9.952918 

9.692019 

10.307981 

10.047082 

10.355064 

48 

13 

9.645193 

9.952855 

9.692338 

10.307662 

10.047145 

10.354807 

47 

14 

9.645450 

9.952793 

9.692656 

10.307344 

10.047207 

10.354550 

46 

15 

9.645706 

9.952731 

9.692975 

10.307025 

10.047269 

10.354294 

45 

16 

9.645962 

9.952669 

9.693293 

10.306707 

10.047331 

10.354038 

44 

17 

9.646218 

9.952606 

9.693612 

10.306388 

10.047394 

10.353782 

43 

18 

9.646474 

9.952544 

9.693930 

10.306070 

10.047456 

10.353526 

42 

19 

9.646729 

9.952481 

9.694248 

10.305752 

10.047519 

10.353271 

41 

20 

9.646984 

9.952419 

9.694566 

10.305434 

10.047581 

10.353016 

40 

21 

9.647240 

9.952356 

9.694883 

10.305117 

10.047644 

10.35^700 

39 

22 

9.647494 

9.952294 

9.695201 

10.304799 

10.047706 

10.352506 

38 

23 

9.647749 

9.952231 

9.695518 

10.304482 

10.047769 

10.352251 

37 

24 

9.648004 

9.952168 

9.695836 

10.304164 

10.047832 

10.351996 

36 

25 

9.648258 

9.952106 

9.696153 

10.303847 

10.047894 

10.351742 

35 

26 

9.648512 

9.952043 

9.696470 

10.303530 

10.047957 

10.351488 

34 

27 

9.648766 

9.951980 

9  696787 

10.303213 

10.048020 

10.351234 

33 

28 

9.649020 

9.951917 

9.697103 

10.302897 

10.048083 

10.350980 

32 

29 

9.649274 

9.951854 

9.697420 

10.302580 

10.048146 

10.350726 

31 

30 

9.649527 

9.951791 

9.697736 

10.302264 

10.048209 

10.350473 

30 

31 

9  649781 

9.951728 

9.698053 

10.301947 

10.048272 

10.350219 

•29 

32 

9.650034 

9.951665 

9.698369 

10.301631 

10.048335 

10.349966 

28 

33 

9.650287 

9.951602 

9.698685 

10.301315 

10.048398 

10.349713 

27 

34 

9.650539 

9.951539 

9.699001 

10.300999 

10.048461 

10.349461 

26 

35 

9.650792 

9.951476 

9.699316 

10.300684 

10.048524 

10.349208 

25 

'  36 

9.651044 

9.951412 

9.699632 

10.300368 

10.048588 

10.348956 

24 

37 

9.651297 

9.951349 

9.699947 

10.300053 

10.048651 

10.348703 

23 

38 

9.651549 

9  951286 

9.700263 

10.299737 

10.048714 

10.348451 

22 

39 

9.651800 

9.951222 

9.700578 

10.299422 

10.048778 

10.348200 

21 

40 

9.652052 

9.951159 

9.700893 

10.299107 

10.048841 

10.347948 

20 

H~ 

9  652304 

9.951096 

9.701208 

10.298792 

10.048904 

10.347696 

iy 

42 

9.652555 

9.951032 

9.701523 

10.298477 

10.048968 

10.347445 

18 

43 

9  652806 

9.950968 

9.701837 

10.298163 

10.049032 

10.347194 

17 

44 

9.653057 

9.950905 

9.702152 

10.297848 

10.049095 

10.346943 

16 

45 

9.653308 

9.950841 

9.702466 

10.297534 

10.049159 

10.346692 

15 

46 

9.653558 

9.950778 

9.702780 

10.297220 

10.049222 

10.346442 

14 

47 

9.653808 

9.950714 

9.703095 

10.296905 

10.049286 

10.346192 

13 

48 

9.654059 

9.950650 

9.703409 

10.296591 

10.049350 

10.345941 

12 

49 

9.654309 

9.950586 

9.703723 

10.296277 

10.049414 

10.345691 

11 

50 

9.654558 

9.950522 

9.704036 

10.295964 

10.049478 

10.345442 

10 

51 

9.654808 

9.950458 

9.704350 

10.295650 

10.049542 

10.345192 

9 

52 

9.655058 

9.950394 

9.704663 

10.295337 

10.049606 

10.344942 

8 

53 

9.655307 

9.950330 

9.704977 

10.295023 

10.049670 

10.344693 

7 

54 

9.655556 

9.950266 

9.705290 

10.294710 

10.049734 

10.344444 

6 

55 

9.655805 

9.950202 

9.705603 

10.294397 

10.049798 

10.344195 

5 

56 

9.656054 

9.950138 

9.705916 

10.294084 

10.049862 

10.343946 

4 

57 

9.656302 

9.950074 

9.706228 

10.293772 

10.049926 

10.343698 

3 

58 

9.656551 

9.950010 

9.706541 

10.293459 

10.049990 

10.343449 

2 

59 

9.656799 

9.949945 

9.706854 

10.293146 

10.050055 

10.343201 

1 

60 

9.657047 

9.949881 

9.707166 

10.292834 

10.050119 

10.342953 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

O3  Degrees. 

170                 TABLE  II. 

LOGABITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

27  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

9.  667  047 

9.949881 

U.  707  106 

10.292831 

10.050119 

10.342953 

00 

1 

9.657295 

9.949816 

9.707478 

10.292522 

10.050184 

10.342705 

E9 

2 

9.657542 

9.949752 

9.707790 

10.292210 

10.050248 

10.342458 

58 

3 

9.657790 

9.949688 

9.708102 

10.291898 

10.050312 

10.342210 

57 

4 

9.658037 

9.949623 

9.708414 

10.291586 

10.050377 

10.341963 

56 

5 

9.658284 

9.949558 

9.708726 

10.291274 

10.050442 

10.341716 

55 

6 

9.658531 

9.949494 

9.709037 

10.290963 

10.050506 

10.341469 

54 

7 

9.658778 

9.949429 

9.709349 

10.290651 

10.050571 

10.341222 

53 

8 

9.659025 

9.949364 

9.709660 

10.290340 

10.050636 

10.340975 

52 

9 

9.659271 

9.949300 

9.709971 

10.290029 

10.050700 

10.340729 

51 

10 

9.659517 

9.949235 

9.710282 

10.289718 

10.050765 

10.340483 

50 

11 

9.059763 

9.949170 

9.710593 

10.289407 

10.050850 

10.340237 

49 

12 

9.660009 

9.949105 

9.710904 

10.289096 

10.050895 

10.339991 

48 

13 

9.66Q255 

9.949040 

9.711215 

10.288785 

10.050960 

10.339745 

47 

14 

9.660501 

9.948975 

9.711525 

10.288475 

10.051025 

10.339499 

46 

15 

9.660746 

9.948910 

9.711836 

10.288164 

10.051090 

10.339254 

45 

10 

9.660991 

9.948845 

9.712146 

10.287854 

10.051155 

10.339009 

44 

17 

9.661236 

9.948780 

9.712456 

10.287544 

10.051220 

10.338764 

43 

18 

9.661481 

9.948715 

9.712766 

10.287234 

10.051285 

10.338519 

42' 

19 

9.661726 

9.948650 

9.713076 

10.286924 

10.051350 

10.338274 

41 

20 

9.661970 

9.948584 

9.713386 

10.286614 

10.051416 

10.338030 

40 

21 

9.6(52214 

y.  948519 

9.  7  13690 

10.286304 

10.051481 

10.337780 

b9 

22 

9.662459 

9.948454 

9.714005 

10.285995 

10.051546 

10.337541 

38 

23 

9.662703 

9.948388 

9.714314 

10.285686 

10.051612 

10.337297 

37 

24 

9.662946 

9.948323 

9.714624 

10.285376 

10.051677 

10.337054 

36 

25 

9.663190 

9.948257 

9.714933 

10.285067 

10.051743 

10.336810 

35 

26 

9.663433 

9.948192 

9.715242 

10.284758 

10.051808 

10.336567 

34 

27 

9.663677 

9.948126 

9.715551 

10.284449 

10.051874 

10.336323 

33 

28 

9.663920 

9  948060 

9.715860 

10.284140 

10.051940 

10.336080 

32 

29 

9.664163 

9.947995 

9.716168 

10.283832 

10.052005 

10.335837 

31 

30 

9.664406 

9.947929 

9.716477 

10.283523 

10.052071 

10.335594 

30 

31 

9.  004048 

9.947803 

9.716785 

10.283215 

10.052137 

10.335352 

29 

32 

9.664891 

9.947797 

9.717093 

10.282907 

10.052203 

10.335109 

28 

33 

9.6G5133 

9.947731 

9.717401 

10.282599 

10.052269 

10.334867 

27 

34 

9.665375 

9.947605 

9.717709 

10.282291 

10.052335 

10.334625 

26 

35 

9.665617 

9.947600 

9.718017 

10.281983 

10.052400 

10.334383 

25 

36 

9.665859 

9.947533 

9.718325 

10.281675 

10.052467 

10.334141 

24 

37 

9.666100 

9.947467 

9.718633 

10.281367 

10.052533 

10.333900 

23 

38 

9.666342 

9.947401 

9.718940 

10.281060 

10.052599 

10.333658 

22 

39 

9.666583 

9.947335 

9.719248 

10.280752 

10.052665 

10.333417 

21 

40 

9.6G6824 

9.947269 

9.719555 

10.280445 

10.052731 

10.333176 

20 

41 

9.007065 

9.947203 

9.719862 

10.280138 

10.052797 

10.332935 

19 

42 

9.6G7305 

9.947136 

9  720169 

10.279831 

10.052864 

10.332695 

18 

43 

9.667546 

9.947070 

9.720476 

10.279524 

10.052930 

10.332454 

17 

44 

9.667786 

9.947004 

9  720783 

10.279217 

10.052996 

10.332214 

10 

45 

9.668027 

9  946937 

9.721089 

10.278911 

10.053063 

10.331973 

15 

46 

9.638267 

9.946871 

9  721396 

10.278604 

10.053129 

10.331733 

14 

47 

9.668506 

9.946804 

9.721702 

10.278298 

10.053196 

10.331494 

13 

48 

9.668746 

9.946738 

9.722009 

10.277991 

10.053262 

10.331254 

12 

49 

9.668986 

9.946671 

9.722315 

10.277685 

10.053329 

10.331014 

11 

50 

9.669225 

9.946604 

9.722621 

10.277379 

10.053396 

10.330775 

10 

51 

9.669464 

9.946538 

9.722927 

10.277073 

10.053462 

10.330536 

y 

52 

9.669703 

9.946471 

9.723232 

10.276768 

10.053529 

10.330297 

8 

53 

9.669942 

9.946404 

9.723538 

10.276462 

10.053596 

10.330058 

7 

54 

9.670181 

9.946337 

9.723844 

10.276156 

10.053663 

10.329819 

6 

55 

9.670419 

9.946270 

9.724149 

10.275851 

10.053730 

10.329581 

5 

56 

9.670658 

9.946203 

9.724454 

10.275546 

10.053797 

10.329342 

4 

57 

9.670896 

9.946136 

9.724759 

10.275241 

10.053864 

10.329104 

3 

58 

9.671134 

9.946069 

9.725065 

10.274935 

10.053931 

10.328866 

2 

59 

9.671372 

9.946002 

9.725369 

10.274631 

10.053998 

10.328628 

1 

60 

9.671609 

9  915935 

9.725674 

10.274326 

10.054065 

10.328391 

0 

M. 

Co-sine. 

Sine.   |  Co-tan.?. 

Tangent. 

Co-sec.    Secant. 

M. 

W$  Degrees. 

TABLE  II.                 171 

LOGABITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

28  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

1 

2 
3 

4 
5 
6 
7 
8 
9 
10 

9.6716U9 
9.671847 
9.672084 
9.672321 
9.672558 
9.672795 
9.673032 
9.673268 
9.673505- 
9.673741 
9  673977 

9.945935 
9.945868 
9.945800 
9.945733 
9.945666 
9.945598 
9.945531 
9.945464 
9.945396 
9.945328 
9.945261 

9.725674 
9.725979 
9.726284 
9.726588 
9.726892 
9.727197 
9.727501 
9.727805 
9.728109 
9.728412 
9  728716 

10  274326 
10.274021 
10.273716 
10.273412 
10.273108 
10.272803 
10.272499 
10.272195 
10.271891 
10.271588 
10.271284 

10.054065 
10.054132 
10.054200 
10.054267 
10.054334 
10.054402 
10.054469 
10.054536 
10.054604 
10.054672 
10.054739 

10.328391 
10.328153 
10.327916 
10.327679 
10.327442 
10.327205 
10.326968 
10.326732 
10.326495 
10.326259 
10.326023 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

9.674213 
9  674448 
9.674684 
9.674919 
9  675155 
9.675390 
9.675624 
9.675859 
9.676094 
9.676328 

9.945193 
9.945125 
9.945058 
9  944990 
9.944922 
9.944854 
9  944786 
9.944718 
9  944650 
9.944582 

9.729020 
9.729323 
9.729626 
9.729929 
9.730233 
9.730535 
9.730838 
9.731141 
9.731444 
9.731746 

10.270980 
10.270677 
10.270374 
10.270071 
10.269767 
10.269465 
10.269162 
10.268859 
10.268556 
10.268254 

10.054807 
10.054875 
10.054942 
10.055010 
10.055078 
10.055146 
10.055214 
10.055282 
10.055350 
10.055418 

10.325787 
10.325552 
10.325316 
10.325081 
10.324845 
10.324610 
10.324376 
10.324141 
10.323906 
10.323672 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 

25 
26 

27 
28 
29 
30 

9.676562 
9.676796 
9.677030 
9.677264 
9.677498 
9.677731 
9.677964 
9.678197 
9.678430 
9.678663 

9.944514 
9.944446 
9.944377 
9.944309 
9  944241 
9.944172 
9.944104 
9.944036 
9.943967 
9.943899 

9.732048 
9.732351 
9.732653 
9.732955 
9.733257 
9.733558 
9.733860 
9.734162 
9.734463 
9.734764 

10.267952 
10.267649 
10.267347 
10.267045 
10.266743 
10.266442 
10.266140 
10.265838 
10.265537 
10.265236 

10.055486 
10.055554 
10.055623 
10.055691 
10.055759 
10.055828 
10.055896 
10.055964 
10.056033 
10.056101 

10.323438 
10.323204 
10.322970 
10.322736 
10.322502 
10.322269 
10.322036 
10.321803 
10.321570 
10.321337 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

9.678895 
9.679128 
9.679360 
9.679592 
9  679824 
9  680056 
9.680288 
9.680519 
9.680750 
9.680982 

9.943830 
9.943761 
9.943693 
9.943624 
9.943555 
9.943486 
9  943417 
9.943348 
9.943279 
9.943210 

9.735056 
9  735367 
9.735668 
9.735969 
9.736269 
9.736570 
9.736871 
9.737171 
9.737471 
9.737771 

10.264934 
10.264633 
10.264332 
10.264031 
10.263731 
10.263430 
10.263129 
10.262829 
10.262529 
10.262229 

10.056170 
10.056239 
10.056307 
10.056376 
10.056445 
10.056514 
10.056583 
10.056652 
10.056721 
10.056790 

10.321105 
10.320872 
10.320640 
10.320408 
10.320176 
10.319944 
10.319712 
10.319481 
10.319250 
10.319018 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 

41 

42 
43 
44 
45 

46 
47 
48 
49 
50 

9.681213 
9.681443 
9.681674 
9.681905 
9.682135 
9.682365 
9.682595 
9.682825 
9.683055 
9.683284 

9.943141 
9.943072 
9.943003 
9.942934 
9.942864 
9.942795 
9.942726 
9.942656 
9.942587 
9.942517 

9.738071 
9.738371 
9.738671 
9.738971 
9.739271 
9.739570 
9.739870 
9.740169 
9.740468 
9.740767 

10.261929 
10.261629 
10.261329 
10.261029 
10.260729 
10.260430 
10.260130 
10.259831 
10.259532 
10.259233 

10.056859 
10.056928 
10.056997 
10.057066 
10.057136 
10.057205 
10.057274 
10.057344 
10.057413 
10.057483 

10.318787 
10.318557 
10.318326 
10.318095 
10.317865 
10.317635 
10.317405 
10.317175 
10.316945 
10.316716 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52- 
53 
54 
55 
56 
57 
58 
59 
60 

9.683514 
9.683743 
9.683972 
9.684201 
9  684430 
9.684658 
9.684887 
9.685115 
9.685343 
9.685571 

9.942448 
9.942378 
9.942308 
9.942239 
9.942169 
9.942099 
9  942029 
9.941959 
9.941889 
9.941819 

9.741066 
9.741365 
9.741664 
9.741962 
9.742261 
9.742559 
9.742858 
9.743156 
9.743454 
9.743752 

10.258934 
10.258635 
10.258336 
10.258038 
10.257739 
10.257441 
10.257142 
10.256844 
10.256546 
10.256248 

10.057552 
10.057622 
10.057692 
10.057761 
10.057831 
10.057901 
10.057971 
10.058041 
10.058111 
10.058181 

10.316486 
10.316257 
10.316028 
10.315799 
10.315570 
10.315342 
10.315113 
10.314885 
10.314657 
10.314429 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

M.  |  Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

til  Degrees. 

172                 TABLE  II. 

LOGARITHMIC  SIXES,  TANGENTS',  AND  SECANTS. 

29  Degrees. 

M. 

Sine. 

Co-sine.  [Tangent. 

Co-tang. 

Secant. 

(Jo-sec. 

M. 

0 

i 

2 
3 

4 
5 
6 
7 
8 
9 
10 

9.685571 
9.685799 
9  686027 
9.686254 
9.686482 
9.686709 
9.68G936 
9.6871G3 
9.687389 
9.687616 
9.687843 

9.  941819 
9.941749 
9.941679 
9.941609 
9.941539 
9.941469 
9.941398 
9.941328 
9.941258 
9.941187 
9.941117 

9.743752 
9.744050 
9.744348 
9.744645 
9.744943 
9.745240 
9.745538 
9.745835 
9.746132 
9.746429 
9.746726 

10.256248 
10.255950 
10.255652 
10.255355 
10.255057 
10.254760 
10.254462 
10.254165 
10.253868 
10.253571 
10.253274 

10.0o«lSl 
10.058251 
10.058321 
10.058391 
10.058461 
10.058531 
10.058602 
10.058672 
10.058742 
10.058813 
10.058883 

10.3144J9 
10.314201 
10.313973 
10.313746 
10.313518 
10.313291 
10.313064 
10.31--837 
10.312611 
10.312384 
10.312157 

bU 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

9.688069 
9.688295 
9.688521 
9.688747 
9.688972 
9.689198 
9.689423 
9.689648 
9.689873 
9.690098 

9.941046 
9.940975 
9.940905 
9.940834 
9.940763 
9.940693 
9.940622 
9.940551 
9.940480 
9.940409 

9.747023 
9.747319 
9.747616 
9.747913 
9.748209 
9.748505 
9.748801 
9.749097 
9.749393 
9.749689 

10.252977 
10.252681 
10.252384 
10.252087 
10.251791 
10.251495 
10.251199 
10.250903 
10.250607 
10.250311 

10.058954 
10.059025 
10.059095 
10.059166 
10.059237 
10.059307 
10.059378 
10.059449 
10.059520 
10.059591 

10.311931 
10.311705 
10.311479 
10.311253 
10.311028 
10.310802 
10.310577 
10.310352 
10.310127 
10.309902 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

9.69J323 
9.690548 
9.690772 
9.690996 
9.691220 
9.691444 
9.691668 
9.691892 
9.692115 
9  692339 

9.940338 
9.940267 
9.940196 
9.940125 
9.940054 
9.939982 
9.939911 
9  939840 
9.939768 
9.939697 

9.749985 
9.750281 
9.750576 
9.750872 
9.751167 
9.751462 
9.751757 
9.752052 
9.752347 
9.752642 

10.250015 
10.249719 
10.249424 
10.249128 
10.248833 
10.248538 
10.248243 
10.247948 
10.247653 
10.247358 

10.059662 
10.059733 
10.059804 
10.059875 
10.059946 
10.060018 
10.060089 
10.060160 
10.060232 
10.060303 

10.309677 
10.309452 
10.309228 
10.309004 
10.308780 
10.308556 
10.308332 
10.308108 
10.307885 
10.307661 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
33 
36 
37 
38 
39 
40 

9.692562 
9.692785 
9.693008 
9.693231 
9.693453 
9.693676 
9.693898 
9.694120 
9.694342 
9.694564 

9.939625 
9.939554 
9.939482 
9.939410 
9.939339 
9.939267 
9.939195 
9.939123 
9.939052 
9.938980 

9.752937 
9.753231 
9.753526 
9.753820 
9.754115 
9.754409 
9.754703 
9.754997 
9.755291 
9.755585 

10.247063 
10.246769 
10.246474 
10.246180 
10.245885 
10.245591 
10.245297 
10.245003 
10.244709 
10.244415 

10.060b75 
10.060446 
10.060518 
10.060590 
10.060661 
10.060733 
10.060805 
10.060877 
10.060948 
10.061020 

10.307438 
10.307215 
10.306992 
10.306769 
10.306547 
10  306324 
10.306102 
10.305880 
10.305658 
10  305436 

29 

28 
27 
26 
25 
24 
23 
22 
21 
20 

41 

42 
43 
44 
45 
46 
47 
48 
49 
50 

9.G94786 
9.695007 
9  .  695229 
9.695450 
9.695G71 
9.695892 
9.696113 
9.G96334 
9.696554 
9.696775 

9.938908 
9.938836 
9.938763 
9.938691 
9.938619 
9.938547 
9.938475 
9.938402 
9.938330 
9.938258 

9.755878 
9.756172 
9.756465 
9.756759 
9.757052 
9.757345 
9.757638 
9.757931 
9.758224 
9.758517 

10.244122 
10.243828 
10.243535 
10.243241 
10.242948 
10.242655 
10.242362 
10.242069 
10.241776 
10.241483 

10.061092 
10  061164 
10.061237 
10.061309 
10.061381 
10.061453 
10.061525 
10.061598 
10.061670 
10.061742 

10.305^14 
10.304993 
10.304771 
10.304550 
10.304329 
10.304108 
10.303887 
10.303666 
10.303446 
10.303225 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

9.696995 
9.697215 
9.697435 
9.697654 
9.697874 
9.698094 
9.698313 
9.698532 
9.698751 
9.698970 

9.938185 
9.938113 
9.938040 
9.937967 
9.937895 
9.937822 
9.937749 
9.937676 
9.937604 
9.937531 

9.758810 
9.759102 
9.759395 
9.759687 
9.759979 
9.760272 
9.760564 
9.760856 
9.761148 
9.761439 

10.241190 
10.240898 
10.240605 
10.240313 
10.240021 
10.239728 
10.239436 
10.239144 
10.238852 
10.2385G1 

10.001815 
10.061887 
10.061960 
10.062033 
10.062105 
10.062178 
10.062251 
10.062324 
10.062396 
10.062469 

10.303005 
10.302785 
10.302565 
10.302346 
10.302126 
10.301906 
10.301687 
10.301468 
10.301249 
10.301030 

9 
'  8 
7 
6 
5 
4 
3 
2 
1 
0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant.   M. 

GO  Degrees. 

TABLE  II.                 173 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

30  Degrees. 

M. 

Sine.   Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

y.6d»97u 

9.  93  <  531 

9.7(31439 

10.238561 

10.0(324(39 

10.301030 

60 

1 

9.G99189 

9.937458 

9.761731 

10.238269 

10.062542 

10.300811 

59 

2 

9.699407 

9.937385 

9.762023 

10.237977 

10.062615 

10.300593 

58 

3 

9.699626 

9.937312 

9.762314 

10.237686 

10.062688 

10.300374 

57 

4 

9.699844 

9.937238 

9.762606 

10.237394 

10.062762 

10.300156 

56 

5 

9.700062 

9.937165 

9.762897 

10.237103 

10.062835 

10.299938 

55 

6 

9.700280 

9.937092 

9.763188 

10.236812 

10.062908 

10.299720 

54 

7 

9.700498 

9.937019 

9.763479 

10.236521 

10.062981 

10.299502 

53 

8 

9.700716 

9.936946 

9.763770 

10.236230 

10.063054 

10.299284 

52 

9 

9.700933 

9.936872 

9.764061 

10.235939 

10.063128 

10.299067 

51 

10 

9.701151 

9.936799 

9.764352 

10.235648 

10.063201 

10.298849 

50 

11 

9.7013(38 

9.936725 

9.764643 

10.235357 

10.063275 

10.298632 

49 

12 

9.701585 

9.936652 

9.764933 

10.235067 

10.063348 

10.298415 

48 

13 

9.701802 

9.936578 

9.765224 

10.234776 

10.063422 

10.298198 

47 

14 

9.702019 

9.936505 

9.765514 

10.234486 

10.063495 

10.297981 

46 

15 

9.702236 

9.936431 

9.765805 

10.234195 

10.063569 

10.297764 

45 

16 

9.702452 

9.936357 

9.766095 

10.233905 

10.063643 

10.297548 

44 

17 

9.702669 

9.936284 

9.766385 

10.233615 

10.063716 

10.297331 

43 

18 

9.702885 

9.936210 

9.766675 

10.233325 

10.063790 

10.297115 

42 

19 

9.703101 

9.936136 

9.766965 

10.233035 

10.063864 

10.296899 

41 

20 

9.703317 

9.936062 

9.767255 

10.232745 

10.063938 

10.296683 

40 

21 

9.703533 

9.9J5988 

9,767545 

10.232455 

10.0(34012 

10.296407 

39 

22 

9.703749 

9.935914 

9.767834 

10.232166 

10.064086 

10.296251 

38 

23 

9.703964 

9.935840 

9.768124 

10.231876 

10.064160 

10.296036 

37 

24 

9.704179 

9.935766 

9.768414 

10.231586 

10.064234 

10.295821 

36 

25 

9.704395 

9.935692 

9.768703 

10.231297 

10.064308 

10.295605 

35 

26 

9.704610 

9.935618 

9.768992 

10.231008 

10.064382 

10.295390 

34 

27 

9.704825 

9.935543 

9.769281 

10.230719 

10.064457 

10.295175 

33 

28 

9.705040 

9.935469 

9.769570 

10.230430 

10.064531 

10.294960 

32 

29 

9.705254 

9.935395 

9.769860 

10.230140 

10.064605 

10.294746 

31 

30 

9.705469 

9.935320 

9.770148 

10.229852 

10.064680 

10.294531 

30 

31 

9.705683 

9.935246 

9.770437 

10.229563 

10.064754 

10.294317 

29 

32 

9.705898 

9.935171 

9.770726 

10.229274 

10.064829 

10.294102 

28 

33 

9.706112 

9.935097 

9.771015 

10.228985 

10.064903 

10.293888 

27 

34 

9.706326 

9.935022 

9.771303 

10.228697 

10.064978 

10.293674 

26 

35 

9.706539 

9.934948 

9.771592 

10.228408 

10.065052 

10.293461 

25 

36 

9.706753 

9.934873 

9.771880 

10.228120 

10.065127 

10.293247 

24 

37 

9.706967 

9.934798 

9.772168 

10.227832 

10.065202 

10.293033 

23 

38 

9.707180 

9.934723 

9.772457 

10.227543 

10.065277 

10.292820 

22 

39 

9.707393 

9.934649 

9.772745 

10.227255 

10.065351 

10.292607 

21 

40 

9.707606 

9.934574 

9.773033 

10.226967 

10.065426 

10.292394 

20 

41 

9.707819 

9.934499 

9  773321 

10.226679 

10.065501 

10.29/1«1 

19 

42 

9.708032 

9.934424 

9.773608 

10.226392 

10.065576 

10.291968 

18 

43 

9.708245 

9.934349 

9  773896 

10.226104 

10.065651 

10.291755 

17 

44 

9.708458 

9.934274 

9  774184 

10.225816 

10.065726 

10.291542 

16 

45 

9.708670 

9.934199 

9.774471 

10.225529 

10.065801 

10.291330 

15 

46 

9.708882 

9.934123 

9.774759 

10.225241 

10.065877 

10.291118 

14 

47 

9.709094 

9.934048 

9.775046 

10.224954 

10.065952 

10.290906 

13 

48 

9.709306 

9.933973 

9.775333 

10.224667 

10.066027 

10.290694 

12 

49 

9.709518 

9.933898 

9.775621 

10.224379 

10.066102 

10.290482 

11 

50 

9.709730 

9.933822 

9.775908 

10.224092 

10.066178 

10.290270 

10 

51 

9.709941 

9.933747 

9.776195 

10.223805 

10.066253 

10.290059 

9. 

52 

9.710153 

9.933671 

9.776482 

10.223518 

10.066329 

10.289847 

8 

53 

9.710364 

9.933596 

9.776769 

10.223231 

10.066404 

10.289636 

7 

54 

9.710575 

9.933520 

9.777055 

10.222945 

10.066480 

10.289425 

6 

55 

9.710786 

9.933445 

9.777342 

10.222658 

10.066555 

10.289214 

5 

56 

9.710997 

9.933369 

9.777628 

10.222372 

10.066631 

10.289003 

4 

57 

9.711208 

9.933293 

9.777915 

10.222085 

10.066707 

10.288792 

3 

58 

9.711419 

9.933217 

9.778201 

10.221790 

10.066783 

10.288581 

2 

59 

9.711629 

9.933141 

9.778487 

10.221513 

10.066859 

10.288371 

1 

GO 

9.711839 

9.933066 

9.778774 

10.221226 

10.066934 

10.288161 

0 

M. 

Co-sine. 

Sine.   |  Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

Gi)  Degrees. 

174                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

31  Degrees. 

M. 

Sine. 

Co-sine.  Tangent.)  Co-tang. 

Secant. 

Co-sec. 

M. 

0 

9.711839 

9.9b30b6 

9.7/8774 

10.221226 

10.0(J0934 

10.288161 

60 

1 

9.712050 

9.932990 

9.779060 

10.220940 

10.067010 

10.287950 

59 

2 

9  712260 

9.932914 

9.779346 

10.220654 

10.067086 

10.287740 

58 

3 

9.712469 

9.932838 

9.779632 

10.220368 

10.067162 

10.287531 

57 

4 

9.712679 

9  932762 

9.779918 

10.220082 

10.067238 

10.287321 

56 

5 

9.712889 

9.932685 

9  780203 

10.219797 

10.067315 

10.287111 

55 

6 

9.713098 

9.932609 

9.780489 

10.219511 

10.067391 

10.286902 

54 

7 

9.713308 

9.932533 

9.780775 

10.219225 

10.067467 

10.286692 

53 

8 

9.713517 

9.932457 

9.781060 

10.218940 

10.067543 

10.286483 

52 

9 

9.713726 

9.932380 

9.781346 

10.218654 

10.067620 

10.286274 

51 

10 

9.713935 

9.932304 

9.781631 

10.218369 

10.067696 

10.286065 

50 

11 

9.714144 

9.932228 

9.781916 

10.218084 

10.007772 

10.285856 

49 

12 

9.714352 

9.932151 

9.782201 

10.217799 

10.067849 

10.285648 

48 

13 

9.714561 

9.932075 

9.782486 

10.217514 

10.067925 

10.285439 

47 

14 

9.714769 

9.931998 

9  782771 

10.217229 

10.068002 

10.285231 

46 

15 

9.714978 

9.931921 

9.783056 

10.216944 

10.068079 

10.285022 

45 

16 

9.715186 

9.931845 

9  783341 

10.216659 

10.068155 

10.284814 

44 

17 

9.715394 

9.931768 

9.783626 

10.216374 

10.068232 

10.284606 

43 

18 

9.715602 

9.931691 

9  783910 

10.216090 

10.068309 

10.284398 

42 

19 

9.715809 

9.931614 

9.784195 

10.215805 

10.068386 

10.284191 

41 

20 

9.716017 

9.931537 

9  784479 

10.215521 

10.068463 

10.283983 

40 

21 

9.716224 

9.931460 

y.  784764 

10.215236 

10.00*540 

10.283776 

by 

22 

9.716432 

9.931383 

9.785048 

10.214952 

10.068617 

10.283568 

38 

23 

9.716639 

9.931306 

9.7d5332 

10.214668 

10.068694 

10.283361 

37 

24 

9.716846 

9.931229 

9.785616 

10.214384 

10.068771 

10.283154 

36 

25 

9.717053 

9.931152 

9.785900 

10.214100 

10.068848 

10.282947 

35 

26 

9.717259 

9.931075 

9.786184 

10.213816 

10.068925 

10.282741 

34 

27 

9.717466 

9.930998 

9.786468 

10.213532 

10.069002 

10.282534 

33 

28 

9.717673 

9.930921 

9.786752 

10.213248 

10.069079 

10.282327 

32 

29 

9.717879 

9.930843 

9.787036 

10.212964 

10.069157 

10.282121 

31 

30 

9.718085 

9.930766 

9.787319 

10.212681 

10.069234 

10.281915 

30 

31 

9.718291 

9.930688 

y.  787603 

10.212397 

10.069312 

10.2817U9 

29 

32 

9.718497 

9.930611 

9.787886 

10.212114 

10.069389 

10.281503 

28 

33 

9.718703 

9.930533 

9.788170 

10.211830 

10.069467 

10.281297 

27 

34 

9.718909 

9.930456 

9.788453 

10.211547 

10.069544 

10.281091 

26 

35 

9.719114 

9.930378 

9.788736 

10.211264 

10.069622 

10.280886 

25 

36 

9.719320 

9.930300 

9.789019 

10.210981 

10.069700 

10.280680 

24 

37 

9.719525 

9  930223 

9.789302 

10.210698 

10.069777 

10.280475 

23 

38 

9.719730 

9.930145 

9.789585 

10.210415 

10.069855 

10.280270 

22 

39 

9.719935 

9.930067 

9.789868 

10.210132 

10.069933 

10.280065 

21 

40 

9.720140 

9.929989 

9.790151 

10.209849 

10.070011 

10.279860 

20 

41 

9.720345 

9.92i;911 

9.790433 

10.209567 

10.07  OU89 

10.279655 

19 

42 

9.720549 

9  929833 

9.790716 

10.209284 

10.070167 

10.279451 

18 

43 

9.720754 

9.929755 

9.790999 

10.209001 

10.070245 

10.279246 

17 

44 

9.720958 

9.929677 

9.791281 

10.208719 

10.070323 

10.279042 

16 

45 

9.721162 

9.929599 

9.791563 

10.208437 

10.070401 

10.278838 

15  , 

46 

9.721366 

9.929521 

9.791846 

10.208154 

10.070479 

10.278634 

14 

47 

9.721570 

9.929442 

9.792128 

10.207872 

10.070558 

10.278430 

13 

48 

9.721774 

9.929364 

9.792410 

10.207590 

10.070636 

10.278226 

12 

49 

9.721978 

9.929286 

9.792692 

10.207308 

10.070714 

10.278022 

11 

50 

9  722181 

9.929207 

9  792974 

10.207026 

10.070793 

10.277819 

10 

51 

9.722385 

9.929129 

9.793256 

10.206744 

10.070871 

10.277615 

9 

52 

9.722588 

9.929050 

9.793538 

10.206462 

10.070950 

10.277412 

8 

53 

9.722791 

9.928972 

9.793819 

10.206181 

10.071028 

10.277209 

7 

54 

9.722994 

9.928893 

9.794101 

10.205899 

10.071107 

10.277006 

6 

55 

9.723197 

9.928815 

9.794383 

10.205617 

10.071185 

10.276803 

5 

56 

9.723400 

9.928736 

9.794664 

10.205336 

10.071264 

10.276600 

4 

57 

9.723603 

9.928657 

9.794945 

10.205055 

10.071343 

10.276397 

3 

58 

9.723805 

9.928578 

9.795227 

10.204773 

10.071422 

10.276195 

2 

59 

9.724007 

9.928499 

9.795508 

10.204492 

10.071501 

10.275993 

1 

60 

9.724210 

9.928420 

9.795789 

10.204211 

10.071580 

10.275790 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec.   Secant. 

M. 

58  Degrees. 

TABLE  II.                 175 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

32  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-  tang. 

Secant. 

Co-sec. 

M. 

u 

y.  724210 

9.928420 

9.795789 

10.204211 

10.071080 

10.275790 

GO 

1 

9.724412 

9.928342 

9.796070 

10.203930 

10.071658 

10.275588 

59 

2 

9.724614 

9.928263 

9.796351 

10.203649 

10.071737 

10.275386 

58 

3 

9.724816 

9.928183 

9.796632 

10.203368 

10.071817 

10.275184 

57 

4 

9.725017 

9.928104 

9.796913 

10.203087 

10.071896 

10.274983 

56 

5 

9.725219 

9.928025 

9.797194 

10.202806 

10.071975 

10.274781 

55 

6 

9.725420 

9.927946 

9  797475 

10.202525 

10.072054 

10.274580 

54 

7 

9.725622 

9.927867 

9.797755 

10.202245 

10.072133 

10.274378 

53 

8 

9.725823 

9  927787 

9.79803G 

10.201964 

10.072213 

10.274177 

52 

9 

9.726024 

9.927708 

9.798316 

10.201684 

10.072292 

10.273976 

51 

10 

9.726225 

9.927629 

9.798596 

10.201404 

10.072371 

10.273775 

50 

11 

y.  7264*6 

9  927549 

9.798877 

10.2U1123 

10.072451 

10.273574 

49 

12 

9.726626 

9.927470 

9.799157 

10.200843 

10.072530 

10.273374 

48 

13 

9.726827 

9.927390 

9.799437 

10.200563 

10.072610 

10.273173 

47 

14 

9.727027 

9.927310 

9.799717 

10.200283 

10.072690 

10.272973 

46 

15 

9.727228 

9.927231 

9.799997 

10.200003 

10.072769 

10.272772 

45 

16 

9.727428 

9.927151 

9.800277 

10.199723 

10.072849 

10.272572 

44 

17 

9.727628 

9.927071 

9.800557 

10.199443 

10.072929 

10.272372 

43 

18 

9.727828 

9.926991 

9.800836 

10.199164 

10.073009 

10.272172 

42 

19 

9.728027 

9.926911 

9.801116 

10.198884 

10.073089 

10.271973 

41 

20 

9.728227 

9.926831 

9.801396 

10  198604 

10.073169 

10.271773 

40 

21 

9.728427 

9.926751 

9  801U75 

10.19c>325 

10.073249 

10.271573 

31J 

22 

9.728626 

9.926671 

9.801955 

10.198045 

10.073329 

10.271374 

38 

23 

9.728825 

9.926591 

9.802234 

10.197766 

10.073409 

10.271175 

37 

24 

9.729024 

9.926511 

9.802513 

10.197487 

10.073489 

10.270976 

36 

25 

9.729223 

9.926431 

9.802792 

10.197208 

10.073569 

10.270777 

35 

26 

9.729422 

9.926351 

9.803072 

10.196928 

10.073649 

10.270578 

34 

27 

9.729621 

9.926270 

9  803351 

10.19G649 

10.073730 

10.270379 

33 

28 

9  729820 

9.926190 

9.803630 

10.19G370 

10.073810 

10.270180 

32 

29 

9.730018 

9.92G110 

9.803908 

10.196092 

10.073890 

10.269982 

31 

30 

9.730217 

9.92G029 

9.804187 

10.195813 

10.073971 

10.269783 

30 

31 

9  730415 

9.  925949 

9.8044G6 

10.195534 

10.074051 

10.209585 

29 

32 

9.730613 

9.925868 

9.804745 

10.195255 

10.074132 

10.269387 

28 

33 

9.730811 

9.925788 

9.805023 

10.194977 

10.074212 

10.269189 

27 

34 

9.731009 

9.925707 

9.805302 

10.194698 

10.074293 

10.268991 

26 

35 

9.731206 

9.925626 

9.805580 

10.194420 

10.074374 

10.268794 

25 

3G 

9.731404 

9.925545 

9.805859 

10.194141 

10.074455 

10.268596 

24 

37 

9.731602 

9.925465 

9.806137 

10.193863 

10.074535 

10.268398 

23 

38 

9.731799 

9  925384 

9.806415 

10.193585 

10.074616 

10.268201 

22 

33 

9.731996 

9.925303 

9.806693 

10.193307 

10.074697 

10.268004 

21 

40 

9.732193 

9.925222 

9.806971 

10.193029 

10.074778 

10.267807 

•20 

41 

9  732390 

9  925141 

9.807249 

10.1U2751 

l'J.074859 

10.267610 

19 

42 

9.732587 

9.925060 

9.807527 

10.192473 

10.074940 

10.267413 

18 

43 

9.732784 

9.924979 

9.807805 

10.192195 

10.075021 

10.267216 

17 

44 

9.732980 

9.924897 

9.808083 

10.191917 

10.075103  • 

10.267020 

16 

45 

9.733177 

9.924816 

9.808361 

10.191639 

10.075184 

10.266823 

15 

46 

9.733373 

9.924735 

9.808638 

10.191362 

10.075265 

10.266627 

14 

.47 

9.733569 

9.924654 

9.808916 

10.191084 

10.075346 

10.266431 

13 

48 

9.733765 

9.924572 

9.809193 

10.190807 

10.075428 

10.266235 

12 

49 

9.733961 

9.924491 

9.809471 

10.190529 

10.075509 

10.266039 

11 

50 

9.734157 

9.924409 

9.809748 

10.190252 

10.075591 

10.265843 

10 

51 

9.734353 

9.  9243*8 

9.810025 

10.189975 

10.075672 

10.265647 

9 

52 

9.734549 

9.924246 

9.810302 

10.189698 

10.075754 

10.265451 

8 

53 

9.734744 

9.924164 

9.810580 

10.189420 

10.075836 

10.265256 

7 

54 

9.734939 

9.924083 

9.810857 

10.189143 

10.075917 

10.265061 

6 

55 

9.735135 

9.924001 

9.811134 

10.188866 

10.075999 

10.264865 

5 

56 

9.735330 

9.923919 

9.811410 

10.188590 

10.076081 

10.264670 

4 

57 

9.735525 

9.923837 

9.811687 

10.188313 

10.076163 

10.264475 

3 

58 

9.735719 

9.923755 

9.8119G4 

10.188036 

10.076245 

10.264281 

2 

59 

9.735914 

9.923673 

9.812241 

10.187759 

10.076327 

10.264086 

1 

GO 

9.736109 

9.923591 

9.812517 

10.187483 

10.076409 

10.263891 

0 

M. 

Co-sine. 

Sine.   |  Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

57  Degrees. 

176                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

33  Decrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

9.736109 
9.736303 
9.736498 
9.736692 
9  736886 
9.737080 
9.737274 
9.737467 
9.737661 
9.737855 
9.738048 

9.923591 
9.923509 
9.923427 
9.923345 
9.923263 
9.923181 
9.923098 
9  923016 
9.922933 
9.922851 
9  922768 

9.812517 
9.812794 
9.813070 
9.813347 
9.813623 
9.813899 
9.814175 
9.814452 
9.814728 
9.815U04 
9.815279 

10.187483 
10.187206 
10.186930 
10.186653 
10.186377 
10.186101 
10.185825 
10.185548 
10.185272 
10.184996 
10.184721 

10.076409 
10.076491 
10.076573 
10.076655 
10.076737 
10.076819 
10.076902 
10.076984 
10.077067 
10.077149 
10.077232 

10.263891 
10.263697 
10.263502 
10.263308 
10.263114 
10.262920 
10.262726 
10.262533 
10.262339 
10.262145 
10.261952 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 

15 
16 
17 

18 
19 
20 

22 
23 
24 
25 
26 
27 
28 
29 
30 

9.738241 
9.738434 
9.738627 
9.738820 
9.739013 
9.739206 
9.739398 
9.739590' 
9.739783 
9.739975 

9.922086 
9.922603" 
9.922520 
9.922438 
9  922355 
9.922272 
9.922189 
9.922106 
9.922023 
9.921940 

9.815555 
9.815831 
9  816107 
9.816382 
9.816658 
9.816933 
9.817209 
9.817484 
9.817759 
9  818035 

10.184445 
10.184169 
10.183893 
10.183618 
10.183342 
10.183067 
10.182791 
10.182516 
10.182241 
10.181965 

10!077397 
10.077480 
10.077562 
10.077645 
10.077728 
10.077811 
10.077894 
10.077977 
10.078060 

I0.'2617o9 
10.261566 
10.261373 
10.261180 
10.260987 
10.260794 
10.260602 
10.260410 
10.260217 
10.260025 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

9.740107 
9.740359 
9.740550 
9.740742 
9.740934 
9.741125 
9.741316 
9.741508 
9.741699 
9.741889 

9.921857 
9.921774 
9.921691 
9.921G07 
9.921524 
9.921441 
9.921357 
9.921274 
9.921190 
9.921107 

9.818310 
9.818585 
9.818860 
9.819135 
9.819410 
9.819884 
9.819959 
9.820234 
9.820508 
9  820783 

10.181690 
10.181415 
10.181140 
10.180865 
10.180590 
10.180316 
10.180041 
10.179766 
10.179492 
10.179217 

10.0*8143 
10.078226 
30.078309 
lu.078393 

10.078476 
10.078559 
10.078643 
10.078726 
10.078810 
10.078893 

10.259833 
10.259641 
10.259450 
10.259258 
10.259066 
10.258875 
10.258684 
10.258492 
10.258301 
10.258111 

38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

9.742080 
9.742271 
9.742462 
9.742652 
9.742842 
9.743033 
9.743223 
9.743413 
9.743602 
9.743792 

9.921023 
9.920939 
9.920856 
9.920772 
•9.920688 
9.920604 
9  920520 
9.920436 
9.920352 
9.920268 

9.821057 
9.821332 
9.821606 
9.821880 
9.822154 
9.822429 
9.822703 
9.822977 
9.823250 
9.823524 

10.178943 
10.178668 
10.178394 
10.178120 
10.177846 
10.177571 
10.177297 
10.177023 
10.176750 
10.176476 

I0.07o977 
10.079061 
10.079144 
10.079228 
10.079312 
10.079396 
10.079480 
10.079564 
10.079648 
10.079732 

10.257920 
10.257729 
10.257538 
10.257348 
10.257158 
10.256967 
10.256777 
10.256587 
10.256398 
10.256208 

28 
27 
26 
25 
24 
23 
22 
21 
20 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

9.743982 
9.744171 
9.744361 
9.744550 
9.744739 
9.744928 
9.745117 
9.745306 
9.745494 
9.745683 

9.920184 
9.920099 
9.920015 
9.919931 
9.919846 
9.919762 
9.919677 
9.919593 
9.919508 
9.919424 

9  !  824072 
9.824345 
9.824619 
9  824893 
9.825166 
9.825439 
9.825713 
9.825986 
9.826259 

10.176202 
10.175928 
10.175655 
10.175381 
10.175107 
10.174834 
10.174561 
10.174287 
10174014 
10.173741 

10.079816 
10.079901 
10.079985 
10.080069 
10.080154 
10.080238 
10.080323 
10.080407 
10.080492 
10080576 

10.256018 
10.255829 
10.255639 
10.255450 
10.255261 
10.255072 
10.254883 
10.254694 
10.254506 
10.254317 

19 
18 
17 
18 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

9.745871 
9.746060 
9.746248 
9.746436 
9.746624 
9.746812 
9.746999 
9.747187 
9.747374 
9.747562 

9.919339 
9.919254 
9.919169 
9.919085 
9.919000 
9.918915 
9.918830 
9.918745 
9.918659 
9.918574 

9.826532 
9.826805 
9.827078 
9.827351 
9.827624 
9.827897 
9.828170 
9.828442 
9.828715 
9.828987 

10.173468 
10.173195 
10.172922 
10.172649 
10.172376 
10.172103 
10.171830 
10.171558 
10.171285 
10.171013 

10.080661 
10.080746 
10.080831 
10.080915 
10.081000 
10.081085 
10.081170 
10.081255 
10.081341 
10.081426 

10.254129 
10.253940 
10.253752 
10.253564 
10.253376 
10.253188 
10.253001 
10.252813 
10.252626 
10.252438 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

56  Degrees. 

TABLE  II.                 177 

LOGAEITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

34  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent 

Co-tang. 

Secant. 

Co-sec. 

M. 

u 

9.747562 

9.  9  J  8574 

9.8289»7 

10.171013 

10.081426 

10.252438 

60 

1 

9.747749 

9.918489 

9.829260 

10.170740 

10.081511 

10.252251 

£9 

2  9.747936 

9.918404 

9.829532 

10.170468 

10.081596 

10.252064 

58 

3  9.748123 

9.918318 

9.829805 

10.170195 

10.081682 

10.251877 

57 

4  9.748310 

9.918233 

9.830077 

10.169923 

10.081767 

10.251690 

56 

5  9.748497 

9.918147 

9.830349 

10.169651 

10.081853 

10.251503 

55 

6  9.748683 

9.918062 

9.830621 

10.169379 

10.081938 

10.251317 

54 

7  9.748870 

9.917976 

9.830893 

10.169107 

10.082024 

10.251130 

53 

8 

9.749056 

9.917891 

9.831165 

10.168835 

10.082109 

10.250944 

52 

9 

9.749243 

9.917805 

9.831437 

10.168563 

10.082195 

10.250757 

51 

10 

9.749429 

9.917719 

9.831709 

10.168291 

10.082281 

10.250571 

50 

11 

9.749615 

9.9)7634 

9.831981 

10.168019 

10  08*366 

10.250385 

49 

12 

9.749801 

9.917548 

9.832253 

10.167747 

10.082452 

10.250199 

48 

13 

9.749987 

9.917462 

9.832525 

10.167475 

10.082538 

10.250013 

47 

14 

9.750172 

9.917376 

9.832796 

10.167204 

10.082624 

10.249828 

46 

15 

9.750358 

9.917290 

9.833068 

10.166932 

10.082710 

10.219642 

45 

16 

9.750543 

9.917204 

9.833339 

10.166661 

10.082796 

10.249457 

44 

17 

9.750729 

9.917118 

9.833611 

10.166389 

10.082882 

10.249271 

43 

18 

9.750914 

9.917032 

9.833882 

10.166118 

10.082968 

10.249086 

42 

19 

9.751099 

9.916946 

9.834154 

10.165846 

10.083054 

10.248901 

41 

20 

9.751284 

9.91C859 

9.834425 

10.165575 

10.083141 

10.248716 

40 

21 

1).  75  1469 

9.916773 

9.834696 

10.165304 

10.033227 

10.248531 

39 

22 

9.751654 

9.916687 

9.834967 

10.165033 

10.083313 

10.248346 

38 

23 

9.751839 

9.916600 

9.835238 

10.164762 

10.083400 

10.248161 

37 

24 

9.752023 

9.916514 

9.835509 

10.164491 

10.083486 

10.247977 

36 

25  |  9.752208 

9.916427 

9.835780 

10.164220 

10.083573 

10.247792 

35 

26 

9.752392 

9.916341 

9.836051 

10.163949 

10.083659 

10.247608 

34 

27 

9.752576 

9.916254 

9.836322 

10.163678 

10.083746 

10.247424 

33 

28 

9.752760 

9  916167 

9.836593 

10  163407 

10.083833 

10.247240 

32 

29 

9.752944 

9.916081 

9.836864 

10.163136 

10.083919 

10.247056 

31 

30 

9.753128 

9.915994 

9.837134 

10.162866 

10.084006 

10.246872 

30 

31 

9.753312 

9.915907 

9.837405 

10.162595 

10.084093 

10.246688 

k9 

32 

9.753495 

9.915820 

9  837675 

10.162325 

10.084180 

10.246505 

28 

33 

9.753679 

9.915733 

9.837946 

10.162054 

10.084267 

10.246321 

27 

34 

9.753862 

9.915646 

9.838216 

10.161784 

10.084354 

10.246138 

26 

35 

9.754046 

9.915559 

9.838487 

10.161513 

10.084441 

10.245954 

25 

36 

9.754229 

9.915472 

9.838757 

10.161243 

10.084528 

10.245771 

24 

37 

9.754412 

9.915385 

9.839027 

10.160973 

10.084615 

10.245588 

23 

38 

9.754595 

9.915297 

9.839297 

10.160703 

10.084703 

10.245405 

22 

39 

9.754778 

9.915210 

9  839568 

10.160432 

10.084790 

10.245222 

21 

40  |  9.754960 

9.915123 

9.839838 

10.160162 

10.084877 

10.245040 

20 

41 

9.755143 

9.915035 

9.840108 

10.159892 

10.084965 

10.244857 

19 

42 

9.755326 

9.914948 

9  840378 

10.159622 

10.085052 

10.244674 

18 

43 

9  .  755508 

9.914860 

9.840647 

10.159353 

10.085140 

10.244492 

17 

44 

9  755690 

9.914773 

9  840917 

10.159083 

10.085227 

10.244310 

16 

45 

9.755872 

9.914685 

9.841187 

10.158813 

10.085315 

10.244128 

15 

46 

9.756054 

9.914598 

9  841457 

10.158543 

10.085402 

10.243946 

14 

47 

9.756236 

9.914510 

9.841726 

10.158274 

10.085490 

10.243764 

13 

48 

9.756418 

9.914422 

9.841996 

10.158004 

10.085578 

10.243582 

12 

49 

9.756600 

9.914334 

9.842266 

10.157734 

10.085666 

10.243400 

11 

50 

9.756782 

9.914246 

9.842535 

10.157465 

10.085754 

10.243218 

10 

51 

9.756963 

9.914158 

9.842805 

10.157195 

10.085842 

10.243037 

9 

52 

9.757144 

9.914070 

9.843074 

10.156926 

10.085930 

10.242856 

8 

53 

9.757326 

9.913982 

9.843343 

10.156657 

10.086018 

10.242674 

7 

54 

9.757507 

9.913894 

9.843612 

10.156388 

10.086106 

10.242493 

6 

55 

9.757688 

9.913806 

9.843882 

10.156118 

10.086194 

10.242312 

5 

56 

9.757869 

9.913718 

9.844151 

10.155849 

10.086282 

10.242131 

4 

57 

9.758050 

9.913630 

9.841420 

10.155580 

10.086370 

10.241950 

3 

58 

9.758230 

9.913541 

9.844689 

10.155311 

10.086459 

10.241770 

2 

59 

9.758411 

9.913453 

9.844958 

10.155042 

10.086547 

10.243589 

1 

60 

9  758591 

9  913365 

9.845227 

10.154773 

10.086635 

10.241409 

0 

M. 

Co-sine. 

Sine.   |  Co-tang. 

Tangent.   Co-sec. 

Secant. 

M. 

55  Degrees. 

178                 TABLE  II. 

LOGARITHMIC  SIGNS,  TANGENTS  AND  SECANTS. 

35  Degrees. 

II. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

9.758591 

9.913365 

9.845227 

10.154773 

10.086635 

10.241409 

60 

1 

9.758772 

9  913276 

9.845496 

10.154504 

10.086724 

10.241228 

59 

2 

9.758952 

9.913187 

9.845764 

10.154236 

10.086813 

10.241048 

58 

3 

9.759132 

9.913099 

9.846033 

10.153967 

10.086901 

10.240868 

57 

4 

9  759312 

9.913010 

9.846302 

10.153698 

10.086990 

10.240688 

56 

5 

9.759492 

9.912922 

9.846570 

10.153430 

10.087078 

10.240508 

55 

6 

9.759672 

9.912833 

9.846839 

10.153161 

10.087167 

10.240328 

54 

7 

9.759852 

9.912744 

9.847107 

10.152893 

10.087256 

10.240148 

53 

8 

9.760031 

9.912655 

9.847376 

10.152624 

10.087345 

10.239969 

52 

9 

9.760211 

9.912566 

9.847644 

10.152356 

10.087434 

10.239789 

51 

10 

9.760390 

9.912477 

9.847913 

10.152087 

10.087523 

10.239610 

50 

11 

9.760569 

9.912388 

9.848181 

10.151819 

10.0S7612 

10.239431 

49 

12 

9.760748 

9.912299 

9.848449 

10.151551 

10.087701 

10.239252 

48 

13 

9.760927 

9.912210 

9.848717 

10.151283 

10.087790 

10.239073 

47 

14 

9.761106 

9.912121 

9.848986 

10.151014 

10.087879 

10.238894 

46 

15 

9.761285 

9.912031 

9.849254 

10.150746 

10.087969 

10.238715 

45 

16 

9.761464 

9.911942 

9.849522 

10.150478 

10.088058 

10.238536 

44 

17 

9.761642 

9  911853 

9.849790 

10.150210 

10.088147 

10.238358 

43 

]8 

9.761821 

9.911763 

9.850058 

10.149942 

10.088237 

10.238179 

42 

19 

9.761999 

9.911674 

9.850325 

10.149675 

10.088326 

10.238001 

41 

20 

9.762177 

9.911584 

9.850593 

10.149407 

10.088416 

10.237823 

40 

21 

9.762356 

9.911495 

9.850861 

10.149139 

10.0S8505 

10.237644 

39 

22 

9.762534 

9.911405 

9.851129 

10.148871 

10.088595 

10.237466 

38 

23 

9.762712 

9  911315 

9.851396 

10.148604 

10.088685 

10.237288 

37 

24 

9.762889 

9.91J226 

9.851664 

10.148336 

10.088774 

10.237111 

36 

25 

9.763067 

9.911136 

9  851931 

10.148069 

10.088864 

10.236933 

35 

26 

9  763245 

9.911046 

9  852199 

10.147801 

10.088954 

10.236755 

34 

27 

9.763422 

9.910956 

9  852466 

10.147534 

10.089044 

10.236578 

33 

28 

9.763600 

9.910866 

9.852733 

10.147267 

10.089134 

10.236400 

32 

29 

9.763777 

9.910776 

9.853001 

10.146999 

10.089224 

10.236223 

31 

30 

9.763954 

9.910686 

9.853268 

10.146732 

10.089314 

10.236046 

30 

31 

9.764131 

9.910596 

9.853535 

10.1464(35 

10.089404 

10.235b(5lJ 

29 

32 

9.764308 

9.910506 

9.853802 

10.146198 

10.089494 

10.235692 

28 

33 

9.764485 

9.910415 

9.854069 

10.145931 

10.089585 

10.235515 

27 

34 

9.764662 

9.910325 

9.854336 

10.145664 

10.089675 

10.235338 

26 

35 

9.764838 

9.910235 

9.854603 

10.145397 

10.089765 

10.235162 

25 

36 

9.765015 

9.910144 

9.854870 

10.145130 

10.089856 

10.234985 

24 

37 

9.765191 

9.910054 

9.855137 

10.144863 

10.089946 

10.234809 

23 

38 

9.765367 

9.909963 

9.855404 

10.144596 

10.090037 

10.234833 

22 

39 

9.765544 

9.909873 

9.855671 

10.144329 

10.090127 

10.234456 

21 

40 

9.765720 

9.909782 

9.855938 

10.144062 

10.090218 

10.234280 

20 

41 

9.765896 

9.909691 

9.856204 

10.143796 

10.090309 

10.234104 

19 

42 

9.766072 

9.909601 

9.856471 

10.143529 

10.09,0399 

10.233928 

18 

43 

9.766247 

9.909510 

9.856737 

10.143263 

10.090490 

10.233753 

17 

44 

9.766423 

9.909419 

9.857004 

10.142996 

10.090581 

10.233577 

16 

45 

9.766598 

9.909328 

9.857270 

10.142730 

10.090672 

10.233402 

15 

46 

9.766774 

9.909237 

9.857537 

10.142463 

10.090763 

10.233226 

14 

47 

9.766949 

9.909146 

9.857803 

10.142197 

10.090854 

10.233051 

13 

48 

9.767124 

9.909055 

9.858069 

10.141931 

10.090945 

10.232876 

12 

49 

9.767300 

9.908964 

9.858336 

10.141664 

10.091036 

10.232700 

11 

50 

9.767475 

9.908873 

9.858602 

10.141398 

10.091127 

10.232525 

10 

51 

9.767649 

9.908781 

9.858868 

10.141132 

10.091219 

10.232351 

9 

52 

9.767824 

9.908690 

9.859134 

10.140866 

10.091310 

10.232176 

8 

53 

9.767999 

9.908599 

9.859400 

10.140600 

10.091401 

10.232001 

7 

54. 

9.768173 

9.908507 

9.859666 

10.140334 

10.091493 

10.231827 

6 

55 

9.768348 

9.908416 

9.859932 

10.140068 

10.091584 

10.231652 

5 

56 

9.768522 

9.908324 

9.860198 

10.139802 

10.091676 

10.231478 

4 

57 

9.768697 

9.908233 

9.860464 

10.139536 

10.091767 

10.231303 

3 

58 

9.768871 

9.908141 

9.860730 

10.139270 

10.091859 

10.231129 

2 

59 

9.769045 

9.908049 

9.860995 

10.139005 

10.091951 

10.230955 

1 

60 

9.769219 

9  907958 

9.861261 

10.138739 

10.092042 

10.230781 

0 

M.  1  Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

54  Degrees. 

TABLE  II.                 179 

LOGARITHMIC  SIXES,  TANGENTS,  AND  SECANTS. 

36  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec.   M. 

0 

y.  7692  19 

9.907958 

9.861261 

10.138739 

10.092042 

10.23U761 

60 

1 

9.769393 

9.9078G6 

9.861527 

10.138473 

10.092134 

10.230607 

59 

2 

9.769566 

9.907774 

9.861792 

10.138208 

10.092226 

10.230434 

58 

3 

9.769740 

9.907682 

9.862058 

10.137942 

10.092318 

10.230260 

57 

4 

9.769913 

9.907590 

9.862323 

10.137677 

10.092410 

10.230087 

56 

5 

9.770087 

9.907498 

9.862589 

10.137411 

10.092502 

10.229913 

55 

6 

9.770260 

9.907406 

9.862854 

10.137146 

10.092594 

10.229740 

54 

7 

9.770433 

9.907314 

9.863119 

10.136881 

10.092686 

10.229567 

53 

8 

9.770G06 

9.907222 

9.863385 

10.136615 

10.092778 

10.229394 

52 

9 

9.770779 

9.907129 

9.863650 

10.136350 

10.092871 

10.229221 

51 

10 

9.770952 

9.907037 

9.863915 

10.136085 

10.092963 

10.229048 

50 

11 

9.  771125 

9.906945 

9.864180 

10.135820 

10.093055 

10.228875 

49 

12 

9.771298 

9.906852 

9.864445 

10.135555 

10.093148 

10.228702 

48 

13 

9.771470 

9.906760 

9.864710 

10.135290 

10.093240 

10.228530 

47 

14 

9.771643 

9.906667 

9.864975 

10.135025 

10.093333 

10.228357 

46 

15 

9.771815 

9.906575 

9.865240 

10.134760 

10.093425 

10.228185 

45 

16 

9.771987 

9.906482 

9.865505 

10.134495 

10.093518 

10.228013 

44 

17 

9.772159 

9.906389 

9.865770 

10.134230 

10.093611 

10.227841 

43 

18 

9.772331 

9.906296 

9.866035 

10.133965 

10.093704 

10.227669 

42 

19 

9.772503 

9.906204 

9.866300 

10.133700 

10.093796 

10.227497 

41 

20 

9.772675 

9.906111 

9.866564 

10.133436 

10.093889 

10.227325 

40 

21 

9.772847 

9.90U018 

9.8G6829 

10.133171 

10.093982 

10.227153 

39 

22 

9.773018 

9.905925 

9.867094 

10.132906 

10.094075 

10.226982 

38 

23 

9.773190 

9.905832 

9.867358 

10.132642 

10.094168 

10.226810 

37 

24 

9.773361 

9.905739 

9  867623 

10.132377 

10.094261 

10.226639 

36 

25 

9.773533 

9.905645 

9.867887 

10.132113 

10.094355 

10.226467 

35 

26 

9.773704 

9.905552 

9.868152 

10.131848 

10.094448 

10.226296 

34 

27 

9.773875 

9.905459 

9.868416 

10.131584 

10.094541 

10.226125 

33 

28 

9.774046 

9.905366 

9.8686SO 

10.131320 

10.094634 

10.225954 

32 

29 

9.774217 

9.905272 

9.868945 

10.131055 

10.094728 

10.225783 

31 

30 

9.774388 

9.905179 

9.869209 

10.130791 

10.094821 

10.225612 

30 

31 

9.774558 

9.905U85 

9.869473 

10.130527 

10.094915 

10.225442 

*9 

32 

9.774729 

9.904992 

9.869737 

10.130263 

10.095008 

10.225271 

28 

33 

9.774899 

9.904898 

9.870001 

10.129999 

10.095102 

10.225101 

27 

34 

9.775070 

9.904804 

9.870265 

10.129735 

10.095196 

10.224930 

26 

35 

9.775240 

9.904711 

9.870529 

10.129471 

10.095289 

10.224760 

25 

36 

9.775410 

9.904617 

9.870793 

10.129207 

10.095383 

10.224590 

24 

37 

9.775580 

9.904523 

9.871057 

10.128943 

10.095477 

10.224420 

23 

38 

9.775750 

9T904429 

9.871321 

10.128679 

10.095571 

10.224250 

22 

39 

9.775920 

9.904335 

9.871585 

10.128415 

10.095665 

10.224030 

21 

40 

9.776090 

9.904241 

9.871849 

10.128151 

10.095759 

10.223910 

20 

41 

9.  7  76259 

9.904147 

9.872112 

10.127888 

10.095853 

10.223741 

19 

42 

9.776429 

9.904053 

9.872376 

10.127624 

10.095947 

10.223571 

18 

43 

9.776598 

9.903959 

9  872640 

10.127360 

10.09G041 

10.223402 

17 

44 

9.776768 

9.903864 

9  872903 

10.127097 

10.096136 

10.223232 

16 

45 

9.776937 

9.903770 

9.873167 

10.126833 

10.096230 

10.223063 

15 

46 

9.777106 

9.903676 

9.873430 

10.126570 

10.096324 

10.222894 

14 

47 

9.777275 

9.903581 

9.873694 

10.126306 

10.096419 

10.222725 

13 

48 

9.777444 

9.903487 

9.873957 

10.126043 

10.096513 

10.222556 

12 

49 

9.777613 

9.903392 

9.874220 

10.125780 

10.096608 

10.222387 

11 

50 

9.777781 

9.903298 

9.874484 

10.125516 

10.096702 

10.222219 

10 

51 

9.  77  7950 

9.903203 

9.874747 

10.125253 

10.096797 

10.222050 

y 

52 

9.778119 

9.903108 

9.875010 

10.124990 

10.096892 

10.221881 

8 

53 

9.778287 

9.903014 

9.875273 

10.124727 

10.096986 

10.221713 

7 

54 

9.778455 

9.902919 

9.875536 

10.124464 

10.097081 

10.221545 

6 

55 

9.778G24 

9.902824 

9.875800 

10.124200 

10.097176 

10.221376 

5 

56 

9.778792 

9.902729 

9.876063 

10.123937 

10.097271 

10.221208 

4 

57 

9.778960 

9.902634 

9.876326 

10.123674 

10.097366 

10.221040 

3 

58 

9.779128 

9.902539 

9.876589 

10.123411 

10.097461 

10.220872 

2 

59 

9.779295 

9.902444 

9.876851 

10.123149 

10.097556 

10.220705 

1 

60 

9.7794G3 

9.902349 

9.877114 

10.122886 

10.097651 

10.220537 

0 

M. 

Co-sine. 

Sine.   |  Co-taug. 

Tangent. 

Co-sec.   Secant. 

M. 

53  Degrees. 

180                  TABLE  II. 

LOGAKITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

37  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-  tang. 

Secant. 

Co-sec. 

M. 

0 

9.  779463 

9.902349 

9.877114 

10  122886 

10.097051 

10.220537 

60 

1 

9.779631 

9.902253 

9.877377 

10.122623 

10.097747 

10.220369 

59 

2 

9.779798 

9.902158 

9.877640 

10.122360 

10.097842 

10.220202 

58 

3 

9.779966 

9.902063 

9.877903 

10.122097 

10.097937 

10.220034 

57 

4 

9  780133 

9.901967 

9.878165 

10.121835 

10.098033 

10.219867 

56 

5 

9.780300 

9.901872 

9.878428 

10.121572 

10.098128 

10.219700 

55 

6 

9.780467 

9.901776 

9.878691 

10.121309 

10.098224 

10.219533 

54 

7 

9.780634 

9.901681 

9.878953 

10.121047 

10.098319 

10.219366 

53 

8 

9.780801 

9.901585 

9.879216 

10.120784 

10.098415 

10.219199 

52 

9 

9.780968 

9.901490 

9.879478 

10.120522 

10.098510 

10.219032 

51 

10 

9.781134 

9.901394 

9  879741 

10.120259 

10.098606 

10.218866 

50 

11 

9.781301 

9  901298 

9.880003 

10.  119997 

10.098702 

10.218699 

49 

12 

9  781468 

9.901202 

9.880265 

10.119735 

10.098798 

10.218532 

48 

13 

9.781G34 

9.9C1106 

9.880528 

10.119472 

10.098894 

10.218366 

47 

14 

9.781800 

9  901010 

9.880790 

10.119210 

10.098990 

10.218200 

46 

15 

9  781  966 

9.900914 

9.881052 

10.118948 

10.099086 

10.218034 

45 

16 

9.782132 

9.900818 

9.881314 

10.118686 

10.099182 

10.217868 

44 

17 

9.782298 

9  900722 

9.881576 

10.118424 

10.099278 

10.217702 

43 

18 

9.782464 

9.900626 

9.881839 

10.118161 

10.099374 

10.217536 

42 

19 

9.782630 

9.900529 

9.882101 

10.117899 

10.099471 

10.217370 

41 

20 

9.782796 

9.900433 

9.882363 

10.117637 

10.099567 

10.217204 

40 

21 

9.  782961 

9.900337 

9.882625 

10.117375 

10.0996G3 

10.217039 

39 

22 

9.783127 

9.900240 

9.882887 

10.117113 

10.099760 

10.216873 

38 

23 

9.783292 

9.900144 

9.883148 

10.116852 

10.099856 

10.216708 

37 

24 

9  783458 

9.900047 

9.883410 

10.116590 

10.099953 

10.216542 

36 

25 

9.783623 

9  899951 

9.883672 

10.116328 

10.100049 

10.216377 

35 

26 

9.783788 

9.899854 

9.883934 

10.116066 

10.100146 

10.216212 

34 

27 

9.783953 

9.899757 

9.884196 

10.115804 

10.100243 

10.216047 

33 

28 

9.784118 

9.899660 

9.884457 

10.115543 

10.100340 

10.215882 

32 

29 

9.784282 

9.899564 

9.884719 

10.115281 

10.100436 

10.215718 

31 

30 

9.784447 

9.899467 

9.884980 

10.115020 

10.100533 

10.215553 

30 

31 

9.784612 

9.899370 

9.885242 

10.114758 

10.100630 

10.215388 

29 

32 

9.784776 

9.899273 

9  855503 

10.114497 

10.100727 

10.215224 

28 

33 

9.784941 

9.899176 

9.885765 

10.114235 

10.100824 

10.215059 

27 

34 

9.785105 

9.899078 

9.886026 

10.113974 

10.100922 

10.214895 

26 

35 

9  785269 

9.898981 

9.886288 

10.113712 

10.101019 

10.214731 

25 

36 

9.785433 

9.898884 

9.886549 

10.113451 

10.101116 

10.214567 

24 

37 

9.785597 

9  898787 

9.886810 

10.113190 

10.101213 

10.214403 

23 

38 

9.785761 

9.898689 

9.887072 

10.112928 

10.101311 

10.214239 

22 

39 

9.785925 

9.898592 

9.887333 

10.112667 

10.101408 

10.214075 

21 

40 

9.786089 

9.898494 

9.887594 

10.112406 

10.101506 

10.213911 

20 

41 

9.786252 

9.898397 

9.887855 

10.112145 

10.101603 

10.213748 

19 

42 

9.786416 

9.898299 

9.888116 

10.111884 

10.101701 

10.213584 

18 

43 

9.786579 

9.898202 

9.888377 

10.111623 

10.101798 

10.213421 

17 

44 

9.786742 

9.898104 

9  888639 

10.111361 

10.101896 

10.213258 

16 

45 

9.786906 

9.898006 

9.888900 

10.111100 

10.101994 

10.213094 

15 

46 

9.787069 

9.897908 

9.889160 

10.110840 

10.102092 

10.212931 

14 

47 

9.787232 

9.897810 

9.889421 

10.110579 

10.102190 

10.212768 

13 

48 

9.787395 

9.897712 

9.889682 

10.110318 

10.102288 

10.212605 

12 

49 

9.787557 

9.897614 

9.889943 

10.110057 

10.102386 

10.212443 

11 

50 

9.787720 

9.897516 

9.890204 

10.109796 

10.102484 

10.212280 

10 

51 

9.787883 

9.897418 

9.890465 

10.109535 

10.102582 

10.212117 

9 

52 

9.788045 

9.897320 

9.890725 

10.109275 

10.102680 

10.211955 

8 

53 

9.788208 

9.897222 

9.890986 

10.109014 

10.102778 

10.211792 

7 

54 

9.788370 

9.897123 

9.891247 

10.108753 

10.102877 

10.211630 

6 

55 

9.788532 

9.897025 

9.891507 

10.108493 

10.102975 

10.211468 

5 

56 

9.788694 

9.896926 

9.891768 

10.108232 

10.103074 

10.211306 

4 

57 

9.788856 

9  896828 

9.892028 

10.107972 

10.103172 

10.211144 

3 

58 

9.789018 

9.896729 

9.832289 

10.107711 

10.103271 

10.210982 

2 

59 

9.789180 

9.896631 

9.892549 

10.107451 

10.103369 

10.210820 

1 

GO 

9.789342 

9.896532 

9.892810 

10.107190 

10.103468 

10.210658 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

52  l>cgrees. 

TABLE  II.                 181 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

38  Degrees. 

M. 

Sine.   Co-sine.  [Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

9.78934a 

9.89o532 

9.81)2810 

10.107J90 

10.103468 

10.210658 

60 

1 

9.7S9504 

9.896433 

9.893070 

10.106930 

10.103567 

10.210496 

59 

2 

9.789G65 

9.896335 

9.893331 

10.106669 

10.103665 

10.210335 

58 

3 

9.789827 

9.896236 

9.893591 

10.10(5409 

10.103764 

10.210173 

57 

•  4 

9.789988 

9.896137 

9.893851 

10.106149 

10.103863 

10.210012 

56 

5 

9.790149 

9.896038 

9.894111 

10.105889 

10.103962 

10.209851 

55 

6 

9.790310 

9.895939 

9.894371 

10.105629 

10.104061 

10.209690 

54 

7 

9.790471 

9.895840 

9.894632 

10.105368 

10.104160 

10.209529 

53 

8 

9.790632 

9  895741 

9.8)4892 

10.105108 

10.104259 

10.209368 

52 

9 

9.790793 

9.895641 

9.895152 

10.104848 

10.104359 

10.209207 

51 

1U 

9.790954 

9.895542 

9.895412 

10.104588 

10.104458 

10.209046 

50 

11 

9.791115 

9  895443 

9.895672 

10.104328 

10.104557 

10.208885 

49 

12 

9.791275 

9.895343 

9.895932 

10.104068 

10.104657 

10.208725 

48 

13 

9.791436 

9.895244 

9.896192 

10.103808 

10.104756 

10.208564 

47 

14 

9.791596 

9.895145 

9.896452 

10.103548 

10.104855 

10.208404 

46 

15 

9.791757 

9.895045 

9.896712 

10.103288 

10.104955 

10.208243 

45 

16 

9.791917 

9.894945 

9.S96971 

10.103029 

10.105055 

10.208083 

44 

17 

9.792077 

9.894846 

9.897231 

10.102769 

10.105154 

10.207923 

43 

18 

9.792237 

9.894746 

9.897491 

10.102509 

10.105254 

10.207763 

42 

19 

9.792397 

9.894646 

9.8U7751 

10.102249 

10.105354 

10.207603 

41 

20 

9.792557 

9.891546 

9.898010 

10.101990 

10.105454 

10.207443 

40 

21 

9.793716 

9.894446 

9.898270 

10.101730 

10.105554 

10.207284 

39 

22 

9.792876 

9.894346 

9.898530 

10.101470 

10.105654 

10.207124 

38 

23 

9.793035 

9.894246 

9.898789 

10.101211 

10.105754 

10.206965 

37 

24 

9.793195 

9.894146 

9.899049 

10.100951 

10.105854 

10.206805 

36 

25 

9.793354 

9.894046 

9.899308 

10.100692 

10.105954 

10.206646 

35 

2(5 

9.793514 

9.893946 

9.899568 

10.100432 

10.106054 

10.206486 

34 

27 

9.793673 

9.893846 

9  899827 

10.100173 

10.106154 

10.206327 

33 

28 

9  793832 

9.893745 

9.900086 

10.099914 

10.106255 

10.206168 

32 

29 

9.793991 

9.893645 

9.900346 

10.099654 

10.106355 

10.206009 

31 

30 

9.794150 

9.893544 

9.900605 

10.099395 

10.106456 

10.205850 

30 

31 

9  794308 

9.893444 

9.900864 

10.099136 

10.106556 

10.205692 

29 

32 

9.794467 

9.893343 

9.901124 

10.098876 

10.106657 

10.205533 

28 

33 

9.794626 

9.893243 

9.901383 

10.098617 

10.106757 

10.205374 

27 

34 

9.794784 

9.893142 

9.901642 

10.098358 

10.106858 

10.205216 

26 

35 

9.794942 

9.893041 

9.901901 

10.098099 

10.106959 

10.205058 

25 

36 

9.795101 

9.892940 

9.902160 

10.097840 

10.107060 

10.204899 

24 

37 

9.795259 

9.892839 

9.902419 

10.097581 

10.107161 

10.204741 

23 

38 

9.795417 

9.892739 

9.902679 

10.097321 

10.107261 

10.204583 

22 

33 

9.795575 

9.892638 

9.902938 

10.097062 

10.107362 

10.204425 

21 

40 

9.795733 

9.892536 

9.903197 

10.096803 

10.107464 

10.204267 

20 

41 

9  795891 

9.892435 

9.903455 

10.096545 

1'J.  107565 

10.204109 

19 

42 

9.796049 

9.892334 

9.903714 

10.096286 

10.107666 

10.203951 

18 

43 

9.796206 

9.892233 

9.903973 

10.096027 

10.107767 

10.203794 

17 

44 

9.796364 

9.892132 

9.904232 

10.095768 

10.107868 

10.203636 

16 

45 

9.796521 

9.892030 

9.904491 

10.095509 

10.107970 

10.203479 

15 

46 

9.796679 

9.891929 

9.904750 

10.095250 

10.108071 

10.203321 

14 

47 

9.796836 

9.891827 

9.905008 

10.094992 

10.108173 

10.203164 

13 

48 

9.796993 

9.891726 

9.905267 

10.094733 

10.108274 

10.203007 

12 

49 

9.797150 

9.891624 

9.905526 

10.094474 

10.108376 

10.202850 

11 

50 

9.797307 

9.891523 

9.905784 

10.094216 

10.108477 

10.202693 

10 

51 

9.797464 

9.891421 

9.906043 

10.093957 

10.1U8579 

10.202536 

9 

52 

9.797621 

9.891319 

9.906302 

10.093698 

10.108681 

10.202379 

8 

53 

9.797777 

9.891217 

9.906560 

10.093440 

10.108783 

10.202223 

7 

54 

9.797934 

9.891115 

9.906819 

10.093181 

10.108885 

10.202066 

6 

55 

9.798091 

9.891013 

9.907077 

10.092923 

10.108987 

10.201909 

5 

56 

9.798247 

9.890911 

9.907336 

10.092664 

10.109089 

10.201753 

4 

57 

9.798403 

9.890809 

9.907594 

10.092406 

10.109191 

10.201597 

3 

58 

9.798560 

9.890707 

9.907852 

10.092148 

10.109293 

10.201440 

2 

59 

9.798716 

9.890605 

9.908111 

10.091889 

10.109395 

10.201284 

1 

60 

9.798872 

9.890503 

9,908369 

10.091631 

10.109497 

10.201128 

0 

M.  j  Co-sine,  j  Sine.   |  Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

51  Degrees. 

182                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

39  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

9.798872 

9.89U503 

9.908369 

10.091631 

10.109497 

10.201128 

60 

l 

9.799028 

9.890400 

9.908628 

10.091372 

10.109600 

10.200972 

.59 

2 

9  799184 

9.890298 

9.908886 

10.091114 

10.109702 

10.200816 

58 

3 

9.799339 

9.890195 

9.909144 

10.090856 

10.109805 

10.200661 

57 

4 

9  799495 

9  890093 

9.909402 

10.090598 

10.109907 

10.200505 

56 

5 

9.799651 

9.889990 

9  909660 

10.090340 

10.110010 

10.200349 

55 

6 

9.799806 

9.889888 

9.909918 

10.090082 

10.110112 

10.200194 

54 

7 

9.799962 

9.889785 

9.910177 

10.089823 

10.110215 

10.200038 

53 

8 

9.800117 

9.889682 

9.910435 

10.089565 

10.110318 

10.199883 

52 

9 

9.800272 

9.889579 

9.910693 

10.089307 

10.110421 

10.199728 

51 

10 

9.800427 

9.889477 

9.910951 

10.089049 

10.110523 

10.199573 

50 

11 

9.800582 

9.889374 

9.911209 

10.088791 

10.110626 

10.199418 

49 

12 

9.800737 

9.889271 

9.911467 

10.088533 

10.110729 

10.199263 

48 

13 

9.800892 

9.889168 

9.911724 

10.088276 

10.110832 

10.199108 

47 

14 

9.801047 

9.889064 

9  911982 

10.088018 

10.110936 

10.198953 

46 

15 

9.801201 

9.888961 

9.912240 

10.087760 

10.111039 

10.198799 

45 

16 

9.801356 

9.888858 

9.912498 

10.087502 

10.111142 

10.198644 

44 

17 

9.801511 

9.888755 

9.912756 

10.087244 

10.111245 

10.198489 

43 

18 

9.801C65 

9.888G51 

9  913014 

10.086986 

10.111349 

10.198335 

42 

19 

9.801819 

9.888548 

9.913271 

10.086729 

10.111452 

10.198181 

41 

20 

9.801973 

9.888444 

9  913529 

10.086471 

10.111556 

10.198027 

40 

21 

9.802128 

9.888341 

9.913787 

10.086213 

10.111659 

10.197672 

i*9 

22 

9.802282 

9.888237 

9.914044 

10.085956 

10.111763 

10.197718 

38 

23 

9.802436 

9.888134 

9.914302 

10.085698 

10.111866 

10.197564 

37 

24 

9.802589 

9.888030 

9.914560 

10.085440 

10.111970 

10.197411 

36 

25 

9.802743 

9.887926 

9.914817 

10.085183 

10.112074 

10.197257 

35 

26 

9.802897 

9.887822 

9.915075 

10.084925 

10.112178 

10.197103 

34 

27 

9.803050 

9.887718 

9.915332 

10.084668 

10.112282 

10.196950 

33 

28 

9.803204 

9.887614 

9.9115590 

10.084410 

10.112386 

10.196796 

32 

29 

9.803357 

9.887510 

9.915847 

10.084153 

10.112490 

10.196643 

31 

30 

9.803511 

9.887406 

9.916104 

10.083896 

10.112594 

10.196489 

30 

31 

9.803664 

9.887302 

9.916362 

10.083638 

10.112698 

10.196336 

29 

32 

9.803817 

9.887198 

9.916619 

10.083381 

10.112802 

10.196183 

28 

33 

9.803970 

9.887093 

9.916877 

10.083123 

10.112907 

10.196030 

27 

34 

9.804123 

9.886989 

9.917134 

10.082866 

10.113011 

10.195877 

26 

35 

9.804276 

9.886885 

9.917391 

10.082609 

10.113115 

10.195724 

25 

36 

9.804428 

9.886780 

9.917648 

10.082352 

10.113220 

10.195572 

24 

37 

9.804581 

9  886676 

9.917905 

10.082095 

10.113324 

10.195419 

23 

38 

9.804734 

9.886571 

9.918163 

10.081837 

10.113429 

10.195266 

22 

39 

9.804886 

9.886466 

9.918420 

10.081580 

10.113534 

10.195114 

21 

40 

9.805039 

9.886362 

9.918677 

10.081323 

10.113638 

10.194961 

20 

41 

9.805191 

9.886257 

9.918934 

10.081066 

10.113743 

10.1948U9 

19 

42 

9.805343 

9  886152 

9.919191 

10.080809 

10.113848 

10.194657 

18 

43 

9.805495 

9.886047 

9.919448 

10.080552 

10.113953 

10.194505 

17 

44 

9.805647 

9.885942 

9.919705 

10.080295 

10.114058 

10.194353 

16 

45 

9.805799 

9.885837 

9.919962 

10.080038 

10.114163 

10.194201 

15 

46 

9.805951 

9.885732 

9.920219 

10.079781 

10.114268 

10.194049 

14 

47 

9.806103 

9.885627 

9.920476 

10.079524 

10.114373 

10.193897 

13 

48 

9.806254 

9.885522 

9.920733 

10.079267 

10.114478 

10.193746 

12 

49 

9.806406 

9.885416 

9.920990 

10.079010 

10.114584 

10.193594 

11 

50 

9  806557 

9.885311 

9.921247 

10.078753 

10.114689 

10.193443 

10 

51 

9.806709 

9.885205 

9.921503 

10.078497 

10.114795 

10.193291 

9 

52 

9.806860 

9.885100 

9.921760 

10.078240 

10.114900 

10.193140 

8 

53 

9.807011 

9.884994 

9.922017 

10.077983 

10.115006 

10.192989 

7 

54 

9.807163 

9.884889 

9.922274 

10.077726 

10.115111 

10.192837 

6 

55 

9.807314 

9.884783 

9.922530 

10.077470 

10.115217 

10.192686 

5 

56 

9.807465 

9.884677 

9.922787 

10.077213 

10.115323 

10.192535 

4 

57 

9.807615 

9.884572 

9  923044 

10.076956 

10.115428 

10.192385 

3 

58 

9.807766 

9.884466 

9.923300 

10.076700 

10.115534 

'  10.192234 

2 

59 

9.807917 

9.884360 

9.923557 

10.076443 

10.115640 

10.192083 

1 

60 

9.808067 

9.884254 

9.923813 

10.076187 

10.115746 

10.191933 

0 

M. 

Co-sine. 

Sine. 

Co-tang,  j  Tangent. 

Co-sec.    Secant. 

M. 

SO  l>«?grees. 

TABLE  II.                 183 

LOOAEITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

40  Degrees. 

M.   Sine. 

Co-sine.  jTangeni 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

9.80S067 

9.884254 

9.923813 

10.076167 

10.115746 

10.191933 

60 

1 

9.808218 

9.884148 

9.924070 

10.075930 

10.115852 

10.191782 

£Q 
cj 

2 

9.808368 

9.884042 

9.924327 

10.075673 

10.115958 

10.191632 

58 

3 

9.808519 

9.883936 

9.924583 

10.075417 

10.116064 

10.191481 

57 

4 

9.8086G9 

9.883829 

9.924840 

10.075160 

10.116171 

10.191331 

56 

5 

9.808819 

9.883723 

9.925096 

10.074904 

10  116277 

10.191181 

55 

6 

9.808969 

9.883617 

9.925352 

10.074648 

10.116383 

10.191031 

54 

7 

9.809119 

9.883510 

9.925609 

10.074391 

10.116490 

10.190881 

53 

8 

9.809269 

9.883404 

9.925865 

10.074135 

10.116596 

10.190731 

52 

9 

9.809419 

9.883297 

9.926122 

10.073878 

10.116703 

10.190581 

51 

10 

9.809569 

9.883191 

9.926378 

10.073622 

10.116809 

10.190431 

50 

11 

9.809718 

9.883U84 

9.926634 

10.073366 

10.116916 

10.190282 

49 

12 

9.809868 

9.882977 

9.926890 

10.073110 

10.117023 

10.190132 

48 

13 

9.810017 

9.882871 

9.927147 

10.072853 

10.117129 

10.189983 

47 

14 

9.810167 

9.882764 

9.927403 

10.072597 

10.117236 

10.189833 

46 

15 

9.810316 

9.882657 

9.927659 

10.072341 

10.117343 

10.189684 

45 

16 

9.810465 

9.882550 

9.927915 

10.072085 

10.117450 

10.189535 

44 

17 

9.810614 

9.882443 

9.928171 

10.071829 

10.117557 

10.189386 

43 

18 

9.810763 

9.882336 

9.928427 

10.071573 

10.117664 

10.189237 

42 

19 

9.810912 

9.882229 

9.928683 

10.071317 

10.117771 

10.189088 

41 

20 

9.811061 

9.882121 

9.928940 

10.071060 

10.117879 

10.188939 

40 

•11 

9.811210 

9.882014 

9.9*9196 

10.07U804 

10.117U86 

10.188790 

39 

22 

9.811358 

9.881907 

9.929452 

10.070548 

10.118093 

10.188642 

38 

23 

9.811507 

9.881799 

9.929708 

10.070292 

10.118201 

10.188493 

37 

24 

9.811655 

9.881692 

9.929964 

10.070036 

10.118308 

10.188345 

36 

25 

9.811804 

9.881584 

9.930220 

10.069780 

10.118416 

10.188196 

35 

26 

9.811952 

9.881477 

9.930475 

10.069525 

10.118523 

10.188048 

34 

27 

9.812100 

9.881369 

9.930731 

10.0G9269 

10.118631 

10.187900 

33 

28 

9.812248 

9.881261 

9.930987 

10069013 

10.118739 

10.187752 

32 

29 

9.812396 

9.881153 

9.931243 

10.068757 

10.118847 

10.187604 

31 

30 

9.812544 

9.881046 

9.931499 

10  068501 

10.118954 

10.187456 

30 

31 

9.812694 

9.880958 

9.931755 

10.068245 

10.119062 

10.187308 

£9 

32 

9.812840 

9.880830 

9.932010 

10.067990 

10.119170 

10.187160 

28 

33 

9  812988 

9.880722 

9.932266 

10.067734 

10.119278 

10.187012 

27 

34 

9.813135 

9.880613 

9.932522 

10.067478 

10.119387 

10.186865 

26 

35 

9.813283 

9.880505 

9.932778 

10.067222 

10.119495 

10.186717 

25 

36 

9.813430 

9.880397 

9.933033 

10.066967 

10.119603 

10.186570 

24 

37 

9.813578 

9.880289 

9.933289 

10.066711 

10.119711 

10.186422 

23 

38 

9.813725 

9.880180 

9.933545 

10.066455 

10.119820 

10.186275 

22 

39 

9.813872 

9.880072 

9.933800 

10.066200 

10.119928 

10.186128 

21 

40 

9.814019 

9.879963 

9.934056 

10.065944 

10.120037 

10.185981 

20 

41 

9.  8  14166 

9.879855 

9.934311 

10.065089 

10.120145 

10.185834 

19 

42 

9.814313 

9.879746 

9  934567 

10.065433 

10.120254 

10.185687 

18 

43 

9.814460 

9.879637 

9.934823 

10.065177 

10.120363 

10.185540 

17 

44 

9  814607 

9.879529 

9  935078 

10.064922 

10.120471 

10.185393 

16 

45 

9.814753 

9.879420 

9.935333 

10.064667 

10.120580 

10.185247 

15 

46 

9.814900 

9.879311 

9  935589 

10.064411 

10.120689 

10.185100 

14 

47 

9.815046 

9.879202 

9.935844 

10.064156 

10.120798 

10.184954 

13 

48 

9.815193 

9.879093 

9.936100 

10.063900 

10.120907 

10.184807 

12 

49 

9.815339 

9.878984 

9.936355 

10.063645 

10.121016 

10.184661 

11 

50 

9.815485 

9.878875 

9.936610 

10.063390 

10.121125 

10.184515 

10 

51 

9  .  815632 

9.878766 

9.936866 

10.063134 

10.121234 

10.184308 

9 

52 

9.815778 

9.878656 

9.937121 

10.062879 

10.121344 

10.184222 

8 

53 

9.815924 

9.878547 

9.937376 

10.062624 

10.121453 

10.184076 

7 

54 

9.816069 

9.878438 

9.937632 

10.062368 

10.121562 

10.183931 

8 

55 

9.816215 

9.878328 

9.937887 

10.062113 

10.121672 

10.183785 

5 

56 

9.816361 

9.878219 

9.938142 

10.061858 

10.121781 

10.183639 

4 

57 

9.816507 

9.878109 

9.938398 

10.061602 

10.121891 

10.183493 

3 

58 

9.816652 

9.877999 

9.938653 

10.061347 

10.122001 

10.183348 

2 

59 

9.816798 

9.877890 

9.938908 

10.061092 

10.122110 

10.183202 

1 

60 

9  816943 

9  877780 

9.939163 

10.060837 

10.122220 

10.183057 

0 

M.  Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

49  Degrees. 

184:                 TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

41  Decrees. 

M. 

Sine. 

Co-sine. 

Tangent.  Co-tang. 

Secant. 

Co-sec. 

M. 

0 

y.  816943 

9.877780 

9.939163 

10.060837 

10.1222*0 

10.183057 

60 

1 

9.817088 

9.877670 

9.939418 

10.060582 

10.122330 

10.182912 

59 

2 

9.817233 

9.877560 

9.939673 

10.060327 

10.122440 

10.182767 

58 

3 

9.817379 

9.877450 

9.939928 

10.060072 

10.122550 

10.182621 

57 

4 

9.817524 

9.877340 

9.940183 

10.059817 

10.122660 

10.182476 

56 

5 

9.817668 

9.877230 

9.940438 

10.059562 

10.122770 

10.182332 

55 

6 

9.817813 

9.877120 

9.940694 

10.059306 

10.122880 

10.182187 

54 

7 

9.817958 

9.877010 

9.940949 

10.059051 

10.122990 

10.182042 

53 

8 

9.818103 

9.876899 

9.941204 

10.058796 

10.123101 

10.181897 

52 

9 

9.818247 

9.876789 

9.941458 

10.058542 

10.123211 

10.181753 

51 

10 

9.818392 

9.876678 

9.941714 

10.058286 

10.123322 

10.181608 

50 

11 

9.818536 

9.876568 

9.941968 

10.058032 

10.  123432 

10.181464 

49 

12 

9.818681 

9.876457 

9.942223 

10.057777 

10.123543 

10.181319 

48 

13 

9.818825 

9.876347 

9.942478 

10.057522 

10.123653 

10.181175 

47 

14 

9.818969 

9.876236 

9.942733 

10.057267 

10.123764 

10.181031 

46 

15 

9.819113 

9.876125 

9.942988 

10.057012 

10.123875 

10.180887 

45 

16 

9.819257 

9.876014 

9.943243 

10.056757 

10.123986 

10.180743 

44 

17 

9.819401 

9.875904 

9.943498 

10.056502 

10.124096 

10.180599 

43 

18 

9.819545 

9.875793 

9.943752 

10.056248 

10.124207 

10.180455 

42 

19 

9.819689 

9  875682 

9.944007 

10.055993 

10.124318 

10.180311 

41 

20 

9.819832 

9  875571 

9  944262 

10.055738 

10.124429 

10.180168 

40 

21 

9.81997(5 

9.875459 

9.944517 

10.055483 

10.124541 

I0.18u0ki4 

39 

22 

9.820120 

9.875348 

9.944771 

10.055229 

10.124652 

10.179880 

38 

23 

9.820263 

9.875237 

9.945026 

10.054974 

10.124763 

10.179737 

37 

24 

9.820406 

9.875126 

9.945281 

10.054719 

10.124874 

10.179594 

36 

25 

9.820550 

9.875014 

9.945535 

10.054465 

10.124986 

10.179450 

35 

26 

9.820693 

9.874903 

9.945790 

10.054210 

10.125097 

10.179307 

34 

27 

9.820836 

9.874791 

9.946045 

10.053955 

10.125209 

10.179164 

33 

28 

9.820979 

9.874680 

9.946299 

10.053701 

10.125320 

10.179021 

32 

29 

9.821122 

9.874568 

9.946554 

10.053446 

10.125432 

10.178878 

31 

30 

9.821265 

9.874456 

9.946808 

10.053192 

10.125544 

10.178735 

30 

31 

9.821407 

9.874344 

9.947003 

10.052937 

10.125656 

10.178593 

'29 

32 

9.821550 

9.874232 

9.947318 

10.052682 

10.125768 

10.178450 

28 

33 

9.821693 

9.874121 

9.947572 

10.052428 

10.125879 

10.178307 

27 

34 

9.821835 

9.874009 

9.947826 

10.052174 

10.125991 

10.178165 

26 

35 

9.821977 

9.873896 

9.948081 

10.051919 

10.126104 

10.178023 

25 

36 

9.822120 

9.873784 

9.948336 

10.051664 

10.126216 

10.177880 

24 

37 

9.822262 

9.873672 

9.948590 

10.051410 

10.126328 

10.177738 

23 

38 

9.822404 

9.873560 

9.948844 

10.051156 

10.126440 

10.177596 

22 

39 

9.822546 

9.873448 

9.949099 

10.050901 

10.126552 

10.177454 

21 

40 

9.822688 

9.873335 

9.949353 

10.050647 

10.126665 

10.177312 

20 

41 

9.822831) 

9.873223 

9.949607 

10.050393 

10.126777 

10.177170 

19 

42 

9.822972 

9.873110 

9.949862 

10.050138 

10.126890 

10.177028 

18 

43 

9.823114 

9.872998 

9.950116 

10.049884 

10.127002 

10.176886 

17 

44 

9.823255 

9.872885 

9.950370 

10.049630 

10.127115 

10.176745 

16 

45 

9.823397 

9.872772 

9.950625 

10.049375 

10.127228 

10.176603 

15 

46 

9.823539 

9.872659 

9.950879 

10.049121 

10.127341 

10.176461 

14 

47 

9.823680 

9.872547 

9.951133 

10.048867 

10.127453 

10.176320 

13 

48 

9.823821 

9.872434 

9.951388 

10.048612 

10.127566 

10.176179 

12 

49 

9.823963 

9.872321 

9.951642 

10.048358 

10.127679 

10.176037 

11 

50 

9.824104 

9.872208 

9.951896 

10.048104 

10.127792 

10.175896 

10 

51 

9.824245 

9.8720U5 

9.952150 

10.047850 

10.127905 

10.175755 

9 

52 

9.824386 

9.871981 

9.952405 

10.047595 

10.128019 

10.175614 

8 

53 

9.824527 

9.871868 

9.952659 

10.047341 

10.128132 

10.175473 

7 

54 

9.824668 

9.871755 

9.952913 

10.047087 

10.128245 

10.175332 

6 

55 

9.824808 

9.871641 

9.953167 

10.046833 

10.128359 

10.175192 

5 

56 

9.824949 

9.871528 

9.953421 

10.046579 

10.128472 

10.175051 

4 

57 

9.825090 

9.871414 

9.953675 

10.046325 

10.128586 

10.174910 

3 

58 

9.825230 

9.871301 

9.953929 

10.046071 

10.128699 

10.174770 

2 

59 

9.825371 

9.871187 

9.954183 

10.045817 

10.128813 

10.174629 

1 

60 

9.825511 

9.871073 

9.954437 

10.015563 

10.128927 

10.174489 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

48  Decrees. 

TABLE  H.                 185 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

42  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

9.825511 

9.871073 

9.954437 

10.045563 

10.128927 

10.174489 

60 

1 

9.825651 

9.870960 

9.954691 

10.045309 

10.129040 

10.174349 

59 

2 

9  825791 

9  870846 

9.954945 

10.045055 

10.129154 

10.174209 

58 

3 

9.825931 

9.870732 

9.955200 

10.044800 

10.129268 

10.174069 

57 

4 

9.826071 

9.870618 

9  955454 

10.044546 

10.129382 

10.173929 

56 

5 

9.826211 

9.870504 

9  955707 

10.044293 

10.129496 

10.173789 

55 

6 

9.826351 

9.870390 

9.955961 

10.044039 

10.129610 

10.173649 

54 

7 

9.826491 

9.870276 

9.956215 

10.043785 

10.129724 

10.173509 

53 

8 

9.826631 

9.870161 

9.956469 

10.043531 

10.129839 

10.173369 

52 

9 

9.826770 

9.870047 

9.956723 

10.043277 

]0.  129953 

10.173230 

51 

10 

9.826910 

9.869933 

9.956977 

10.043023 

10.13U067 

10.173090 

50 

11 

9.837049 

9.869818 

9.95/231 

10.042769 

10.130182 

10.17iJ951 

49 

12 

9.827189 

9.869704 

9.957485 

10.042515 

10.130296 

10.172811 

48 

13 

9.827328 

9.869589 

9.957739 

10.042261 

10.130411 

10.172672 

47 

H 

9.827467 

9.869474 

9.957993 

10.042007 

10.130526 

10.172533 

46 

15 

9.827606 

9.869360 

9.958246 

10.041754 

10.130640 

10.172394 

45 

16 

9.827745 

9.869245 

9.958500 

10.041500 

10.130755 

10.172255 

44 

17 

9.827884 

9.869130 

9.958754 

10.041246 

10.130870 

10.172116 

43 

18 

9.828023 

9.869015 

9.959008 

10.040992 

10.130925 

10.171977 

42 

19 

9.828162 

9.868900 

9.959262 

10.040738 

10.131100 

10.171838 

41 

20 

9.828301 

9.868785 

9.959516 

10.040484 

10.131215 

10.171699 

40 

21 

9.8^8439 

9.868670 

9.959769 

10.040231 

10.131330 

10.171501 

39 

22 

9.828578 

9.868555 

9.960023 

10.039977 

10.131445 

10.171422 

38 

23 

9.828716 

9.868440 

9.960277 

10.039723 

10.131560 

10.171284 

37 

24 

9.828855 

9.868324 

9.960531 

10.039469 

10.131676 

10.171145 

36 

25 

9.828993 

9.868209 

9.960784 

10.039216 

10.131791 

10.171007 

35 

26 

9.829131 

9.868093 

9.961038 

10.038962 

10.131907 

10.170869 

34 

27 

9.829269 

9.867978 

9.961291 

10.038709 

10.132022 

10.170731 

33 

28 

9.829407 

9  867862 

9.961545 

10.038455 

10.132138 

10.170593 

32 

29 

9.829545 

9.867747 

9.961799 

10.038201 

10.132253 

10.170455 

31 

30 

9  829683 

9.867631 

9.962052 

10.037948 

10.132369 

10.170317 

30 

31 

9.8298^1 

9.867515 

9.962306 

10.057694 

10.132485 

10.170179 

29 

32 

9.829959 

9.867399 

9.962560 

10.037440 

10.132601 

10.170041 

28 

33 

9.830097 

9.867283 

9.962813 

10.037187 

10.132717 

10.169903 

27 

34 

9.830234 

9.867167 

9.963067 

10.036933 

10.132833 

10.169766 

26 

35 

9.830372 

9.867051 

9.963320 

10.036680 

10.132949 

10.169628 

25 

36 

9.830509 

9.866935 

9.963574 

10.036426 

10.133065 

10.169491 

24 

37 

9.830646 

9.866819 

9.963827 

10.036173 

10.133181 

10.169354 

23 

38 

9.830784 

9.866703 

9.964081 

10.035919 

10.133297 

10.169216 

22 

39 

9.830921 

9.866586 

9.964335 

10.035665 

10.133414 

10.169079 

21 

40 

9.831058 

9.866470 

9.964588 

10.035412 

10.133530 

10.168942 

20 

41 

9.831195 

9.866353 

9.964842 

10.035158 

10.133647 

10.108805 

19 

42 

9.831332 

9.866237 

9.965095 

10.034905 

10.133763 

10.168668 

18 

43 

9.831469 

9.866120 

9.965349 

10.034651 

10.133880 

10.168531 

17 

44 

9.831606 

9.866004 

9.965602 

10.034398 

10.133996 

10.168394 

16 

45 

9.831742 

9.865887 

9.965855 

10.034145 

10.134113 

10.168258 

15 

46 

9.831879 

9.865770 

9.966109 

10.033891 

10.134230 

10.168121 

14 

47 

9.832015 

9.865653 

9.966362 

10.033638 

10.134347 

10.167985 

13 

48 

9.832152 

9.865536 

9.966616 

10.033384 

10.134464 

10.167848 

12 

49 

9.832288 

9.865419 

9.966869 

10.033131 

10.134581 

10.167712 

11 

50 

9.832425 

9.865302 

9.967123 

10.032877 

10.134698 

10.167575 

10 

51 

9.832561 

9.865185 

9.967376 

10.032624 

10.134815 

10.167439 

9 

52 

9.832697 

9.865068 

9.967629 

10.032371 

10.134932 

10.167303 

8 

53 

9.832833 

9.864950 

9.967883 

10.032117 

10.135050 

10.167167 

7 

54 

9.832969 

9.864833 

9.968136 

10.031864 

10.135167 

10.167031 

6 

55 

9.833105 

9.864716 

9.968389 

10.031611 

10.135284 

10.166895 

5 

56 

9.833241 

9.864598 

9.968643 

10.031357 

10.135402 

10.166759 

4 

57 

9.833377 

9.864481 

9.968896 

10.031104 

10.135519 

10.166623 

3 

58 

9.833512 

9.864363 

9.969149 

10.030851 

10.135637 

10.166488 

2 

59 

9.833648 

9.864245 

9.969403 

10.030597 

10.135755 

10.166352 

1 

60 

9.833783 

9.864127 

9.969656 

10.030344 

10.135873 

10.166217 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

47  Degrees. 

186                  TABLE  II. 

LOGARITHMIC  SINES,  TANGENTS,  AND  SECANTS. 

43  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-sec. 

M. 

0 

y.  633783 

9.864127 

y.'jiwooo 

10  030344 

10.135873 

10.166217 

60 

1 

9.833919 

9.864010 

9.969909 

10.030091 

10.135990 

10.166081 

59 

2 

9.831054 

9.863892 

9  970162 

10.029838 

10.136108 

10.165946 

58 

3 

9.834189 

9.863774 

9.970416 

10.029584 

10.136226 

10.165811 

57 

4 

9  834325 

9.863656 

9.9706G9 

10.029331 

10.136344 

10.165675 

56 

5 

9.831460 

9.863538 

9.970922 

10.029078 

10.136462 

10.165540 

55 

6 

9.834595 

9.863419 

9.971175 

10.028825 

10.136581 

10.165405 

54 

7 

9.834730 

9.863301 

9.971429 

10.028571 

10.136699 

10.165270 

53 

8 

9.834865 

9.863183 

9.971682 

10.028318 

10.136817 

10.165135 

52 

9 

9.834999 

9.863064 

9.971935 

10.028065 

10.136936 

10.165001 

51 

10 

9  835134 

9.862946 

9  972188 

10.027812 

10.137054 

10.164866 

50 

11 

9.8352G(J 

y  .  862827 

9.972441 

10.0^:7559 

10.137173 

10.164731 

49 

12 

9  835403 

9.862709 

9.972694 

10.027306 

10.137291 

10.164597 

48 

13 

9.835538 

9.862590 

9.972948 

10.027052 

10.137410 

10.164462 

47 

14 

9.835672 

9  862471 

9.973201 

10.026799 

10.137529 

10.164328 

46 

15 

9  835S07 

9.862353 

9.973454 

10.026546 

10.137647 

10.164193 

45 

16 

9.835941 

9.862234 

9.973707 

10.026293 

10.137766 

10.164059 

44 

17 

9.836075 

9  862115 

9.973960 

10.026040 

10.137885 

10.163925 

43 

18 

9.836209 

9.861996 

9.974213 

10.025787 

10.138004 

10.163791 

42 

19 

9.836343 

9  861877 

9  974466 

10.025534 

10.138123 

10.163657 

41 

20 

9.836477 

9.861758 

9.974719 

10.025281 

10.138242 

10.163523 

40 

21 

9.8J6611 

9.8ol638 

9.y/jy/3 

10.025027 

10.138362 

10.103369 

39 

22 

9.836745 

9.861519 

9.975226 

10.024774 

10.138181 

10.163255 

38 

23 

9.836878 

9.861400 

9.975479 

10.024521 

10.138600 

10.163122 

37 

24 

9  837012 

9.861280 

9.975732 

10.024268 

10.138720 

10.162988 

36 

25 

9.837146 

9  861161 

9.975985 

10.024015 

10.138839 

10.162854 

35 

26 

9.837279 

9.861041 

9.976238 

10.023762 

10.138959 

10.162721 

34 

27 

9.837412 

9.860922 

9.976491 

10.023509 

10.139078 

10.162588 

33 

28 

9.837546 

9.860802 

9.976744 

10.023256 

10.139198 

10.162454 

32 

29 

9.837679 

9.860682 

9.976997 

10.023003 

10.139318 

10.162321 

31 

30 

9.837812 

9.860562 

9.977250 

10.022750 

10.139438 

10.162188 

30 

31 

9.«37945 

9.8(30442 

9.9/7503 

10.022497 

10.139558 

10.102055 

29 

32 

9  833078 

9.860322 

9  977756 

10.022244 

10.139678 

10.161922 

28 

33 

9.838211 

9.860202 

9.978009 

10.021991 

10.139798 

10.161789 

27 

34 

9.838344 

9.860082 

9.978262 

10.021738 

10.139918 

10.161656 

26 

35 

9  838477 

9.859962 

9.978515 

10.021485 

10.140038 

10.161523 

25 

36 

9  838310 

9.859842 

9.978768 

10.021232 

10.140158 

10.161390 

24 

37 

9.838742 

9  859721 

9.979021 

10.020979 

10.140279 

10.161258 

23 

38 

9.838875 

9.859601 

9.979274 

10.020726 

10.140399 

10.161125 

22 

39 

9.839007 

9.859480 

9.979527 

10.020473 

10.140520 

10.160993 

21 

40 

9.839140 

9.859360 

9.979780 

10.020220 

10.140640 

10.160860 

20 

41 

9.8.J92/2 

9.859239 

9.960033 

lo.oiyyo7 

10.140761 

10.1GO/28 

19 

42 

9.839404 

9.859119 

9.980286 

10.019714 

10.140881 

10.160596 

18 

43 

9.839536 

9.858998 

9.980538 

10.019462 

10.141002 

10.160464 

17 

44 

9.839668 

9.858877 

9  980791 

10.019209 

10.141123 

10.160332 

16 

45 

9.839800 

9.858756 

9.981044 

10.018956 

10.141244 

10.160200 

15 

46 

9.839932 

9.858635 

9.981297 

10.018703 

10.141365 

10.160068 

14 

47 

9.840064 

9.858514 

9.931550 

10.018450 

10.141486 

10.159936 

13 

48 

9.840196 

9.858393 

9.981803 

10.018197 

10.141607 

10.159804 

12 

49 

9.840328 

9.858272 

9.982056 

10.017944 

10.141728 

10.159672 

11 

50 

9.840459 

9.858151 

9.982309 

10.017691 

10.141849 

10.159541 

10 

51 

9.840591 

9.  658029 

9.9»25U2 

10.017438 

10.141971 

10.159409 

9 

52 

9.840722 

9.&57908 

9.982814 

10.017186 

10.142092 

10.159278 

8 

53 

9.840854 

9.857786 

9.983067 

10.016933 

10.142214 

10.159146 

7 

54 

9.840985 

9.857665 

9.983320 

10.016680 

10.  142335 

10.159015 

6 

55 

9  8U116 

9.857543 

9.983573 

10.016427 

10.142457 

10.158884 

5 

56 

9.841247 

9.857422 

9.983826 

10.016174 

10.142578 

10.158753 

4 

57 

9.841378 

9  857300 

9.984079 

10.015921 

10.142700 

10.158622 

3 

58 

9.841509 

9.857178 

9.984331 

10.015669 

10.142822 

10.158491 

2 

59 

9.841640 

9.857056 

9.984584 

10.015416 

10.142944 

10.158360 

1 

60 

9.841771 

9.856934 

9.981837 

10.015163 

10.143066 

10.158229 

0 

M. 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sec. 

Secant. 

M. 

4O  Degrees. 

TABLE  II.                187 

LOGARITHMIC  SIGNS,  TANGENTS  AND  SECANTS. 

44  Degrees. 

M. 

Sine. 

Co-sine. 

Tangent.  Co-tang. 

Secant.   Co-sec. 

If. 

0 

9.841771 

9.850934 

9.984»37 

10.015103 

10.14oOOO 

•  10.168229 

00 

l 

9.841902 

9  856812 

9  985090 

10.014910 

10.143188 

10.158098 

59 

'2 

9.842033 

9.856690 

9.985343 

10.014657 

10.143310 

10.157967 

58 

3 

9.842163 

9.856568 

9.985596 

10.014404 

10.143432 

10.157837 

57 

4 

9  842294 

9.856446 

9.985848 

10.014152 

10.143554 

10.157706 

56 

5 

9.S42424 

9.85G323 

9.986101 

10.013899 

10.143677 

10.157576 

55 

6 

9.842555 

9.856201 

9.986354 

10.013646 

10.143799 

10.157445 

54 

7 

9.842685 

9.856078 

9.986607 

10.013393 

10.143922 

10.157315 

53 

8 

9.842815 

9.855956 

9.986860 

10.013140 

10.144044 

10.157185 

52 

9 

9.842946 

9.855833 

9.987112 

10.012888 

10.144167 

10.157054 

51 

10 

9.843076 

9.855711 

9.987365 

10.012635 

10.144289 

10.150924 

50 

11 

9.843206 

9.85,3588 

9.987018 

10.012382 

10.144412 

10.1567U4 

49 

12 

9.843336 

9.855465 

9  987871 

10.012129 

10.144535 

10.150664 

48 

13 

9.843466 

9.855342 

9.988123 

10.011877 

10.144658 

10.156534 

47 

14 

9.843595 

9.855219 

9.988376 

10.011624 

10.144781 

10.156405 

46 

15 

9.843725 

9.855096 

9.988629 

10.011371 

10.144904 

10.156275 

45 

16 

9.843855 

9.854973 

9.S88882 

10.011118 

10.145027 

10.156145 

44 

17 

9.843984 

9  854850 

9.989134 

10.010866 

10.145150 

10.156016 

43 

18 

9.844114 

9.854727 

9.989387 

10.010613 

10.145273 

10.155886 

42 

19 

9.844243 

9.854603 

9.989640 

10.010360 

10.145397 

10.155757 

41 

20 

9.844372 

9.854480 

9.989893 

10.010107 

10.145520 

10.155628 

40 

21 

9.844502 

9.854356 

9.990145 

10.009*55 

I0.14a044 

10.155498 

39 

22 

9  844631 

9.854233 

9.990398 

10.009602 

10.145767 

10.155369 

38 

23 

9.8447CO 

9  854109 

9.990651 

10.009349 

10.145891 

10.155240 

37 

24 

9.844889 

9.853986 

9.990903 

10.009097 

10.146014 

10.155111 

36 

25 

9.845018 

9.853862 

9  991156 

10.008844 

10.146138 

10.154982 

35 

26 

9  845147 

9.853738 

9.991409 

10.008591 

10.146262 

10.154853 

34 

27 

9  845276 

9.853614 

9  991662 

10.008338 

10.146386 

10.154724 

33 

28 

9.845405 

9.853490 

9  991914 

10.008086 

10.146510 

10.154595 

32 

29 

9.845533 

9.853366 

9.992167 

10.007833 

10.146634 

10.154467 

31 

30 

9.845662 

9.853242 

9.992420 

10.007580 

10.146758 

10.154338 

30 

31 

9.845790 

9.853118 

9.992G72 

10.0073*8 

10.1408S2 

10.154210 

29 

82 

9.845919 

9.852994 

9.992925 

10.007075 

10.147006 

10.154081 

28 

33 

9.846047 

9.852869 

9.993178 

10.006822 

10.147131 

10.153953 

27 

34 

9.846175 

9.852745 

9.993430 

10.006570 

10.147255 

10.153825 

26 

35 

9.84G304 

9.852620 

9.993683 

10.006317 

10.147380 

10.153696 

25 

36 

9.846432 

9.852496 

9.993936 

10.006064 

10.147504 

10.153568 

24 

37 

9.846560 

9.852371 

9.994189 

10.005811 

10.147629 

10.153440 

23 

38 

9.846688 

9.852247 

9.994441 

10.005559 

10.147753 

10.153312 

22 

39 

9.846816 

9.852122 

9.994G94 

10.005306 

10.147878 

10.153184 

21 

40 

9.846944 

9.851997 

9.994947 

10.005053 

10.148003 

10.153056 

20 

41 

9.847071 

9.851872 

9.995199 

10.004801 

10.148128 

10.15*929 

19 

42 

9.847199 

9.851747 

9.995452 

10.004548 

10.148253 

10.152801 

18 

43 

9.847327 

9.851622 

9.995705 

10.004295 

10.148378 

10.152673 

17 

44 

9.847454 

9.851497 

9.995957 

10.004043 

10.148503 

10.152546 

16 

45 

9.847582 

9.851372 

9.996210 

10.003790 

10.148628 

10.152418 

15 

46 

9.847709 

9.851246 

9.996463 

10.003537 

10.148754 

10.152291 

14 

47 

9.847836 

9.851121 

9.996715 

10.003285 

10.148879 

10.152164 

13 

48 

9.847964 

9.850996 

9.996968 

10.003032 

10.149004 

10.152036 

12 

49 

9.848091 

9.850870 

9.997221 

10.002779 

10.149130 

10.151909 

11 

50 

9.848218 

9.850745 

9.997473 

10.002527 

10.149255 

10.151782 

10 

51 

9.848345 

9.  8500  19 

9.997726 

10.002274 

10.149381 

10.151655 

9 

52 

9.848472 

9.850493 

9.997979 

10.002021 

10.149507 

10.151528 

8 

53 

9.848599 

9.850368 

9.998231 

10.001769 

10.149632 

10.151401 

7 

54 

9.848726 

9.850242 

9.998484 

10.001516 

10.149758 

10.151274 

6 

55 

9.848852 

9.850116 

9.998737 

10.001263 

10.149884 

10.151148 

5 

56 

9.848979 

9.849990 

9.998989 

10.001011 

10.150010 

10.151021 

4 

57 

9.849106 

9  849864 

9.999242 

10.000758 

10.150136 

10.150894 

3 

58 

9.849232 

9  849738 

9.999495 

10.000505 

10.150262 

10.150708 

2 

59 

9.849359 

9.849611 

9.999747 

10.000253 

10.150389 

10.150641 

1 

60 

9.849485 

9.849485 

0.000000 

10.000000 

10.150515 

10.150515 

0 

M.  |  Co-sine. 

Sine. 

Co-tang. 

Tangent.   Co-sec. 

Secant.   M. 

45  1  >•••.;  r<-.--.. 

188                                         TABLE  III. 

DIFFERENCE    OF   LATITUDE    AND    DEPARTURE   FOR   ^   POINT. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

l 

01.0 

00.0 

61 

60.9 

03.0 

121 

120.9 

05.9 

181 

180.8 

08.9 

241 

240.7 

11.8 

2 

02.0 

00.1 

62 

61.9 

03.0 

122 

121.9 

06.0 

182 

181.8 

08.9 

242 

241.7 

11.9 

3 

03.0 

00.1 

63 

62.9 

03.1 

123 

122.9 

06.0 

183 

182.8 

09.0 

243 

242  7 

11.9 

4 

04.0 

00.2 

64 

63.9 

03.1 

124 

123.9 

06.1 

184 

183.8 

09.0 

244 

243.7 

12,0 

5 

05.0 

00.2 

65 

64.9 

03.2 

125 

124.9 

06.1 

185 

184.8 

09.1 

245 

244.7 

12.0 

6 

06.0 

00.3 

66 

65.9 

03.2 

126 

125.8 

06.2 

186 

185.8 

09.1 

246 

245.7 

12.1 

7 

07.0 

00.3 

67 

66.9 

03.3 

127 

126.8 

06.2 

187 

186.8 

09.2 

247 

246.7 

12.1 

8 

08.0 

00.4 

68 

67.9 

03.3 

128 

127.8 

06.3 

188 

187.8 

09.2 

248 

247.7 

12.2 

9 

09  0 

00.4 

69 

68.9 

03.4 

129 

128.8 

06.3 

189 

188.8 

09.3 

249 

248.7 

12.2 

10 

10.0 

00.5 

70 

69.9 

03.4 

130 

129.8 

06.4 

190 

189.8 

09.3 

250 

249.7 

12.3 

11 

11.0 

00.5 

71 

70.9 

03.5 

131 

130.8 

06.4 

191 

190.8 

09.4 

251 

250.7 

12.3 

12 

12.0 

00.6 

72 

71.9 

03.5 

132 

131.8 

06.5 

192 

191.8 

09.4 

252 

251.7 

12.4 

13 

13.0 

00.  G 

73 

72.9 

03.6 

133 

132.6 

06.5 

193 

192.8 

09.5 

253 

252.7 

12.4 

14 

14.0 

00.7 

74 

73.9 

03.6 

134 

133.8 

06.6 

194 

193  8 

09.5 

254 

253.7 

12.5 

15 

15.0 

00.7 

75 

74.9 

03.7 

135 

134.8 

06.6 

195 

194.8 

09.6 

255 

254.7 

12.5 

16 

16.0 

00.8 

76 

75.9 

03.7 

136 

135.8 

06.7 

196 

195.8 

09.6 

256 

255.7 

12.6 

17 

17.0 

00.8 

77 

76.9 

03.8 

137 

136.8 

06.7 

197 

196.8 

09.7 

257 

256.7 

12.6 

18 

18.0 

00.9 

78 

77.9 

03.8 

138 

137.8 

06.8 

198 

197.8 

09.7 

258 

257.7 

12.7 

19 

19.0 

00.9 

79 

78  9 

03.9 

139 

138.8 

06.8 

199 

198.8 

09.8 

259 

258.7 

12.7 

20 

20.0 

01.0 

80 

79.  < 

03  9 

140 

139.8 

06.9 

200 

199.8 

09.8 

260 

259.7 

12.8 

21 

21.0 

01.0 

81 

80.9 

04.0 

141 

140.  b 

06.9 

201 

200.8 

09.9 

261 

260.7 

12.8 

22 

22.0 

01.1 

82 

81.9 

04.0 

142 

141.8 

07.0 

202 

201.8 

09.9 

262 

261.7 

12.9 

23 

23.0 

01.1 

83 

82.9 

04.1 

143 

142.8 

07.0 

203 

202.8 

10.0 

263 

262.7 

12.9 

24 

24.0 

01.2 

84 

83.9 

04.1 

144 

143.8 

07.1 

204 

203.8 

10.0 

264 

263.7 

13.0 

25 

25.0 

01.2 

85 

84.9 

04.2 

145 

144.8 

07.1 

205 

204.8 

10.1 

265 

264.7 

13.0 

26 

26.0 

01.3 

86 

85.9 

04.2 

146 

145.8 

07.2 

206 

205.8 

10.1 

266 

265.7 

13.1 

27 

27.0 

01.3 

87 

86.9 

04.3 

147 

146.8 

07.2 

207 

206.8 

10.2 

267 

266.7 

13.1 

28 

28.0 

01.4 

88 

87.9 

04.3 

148 

147.8 

07.3 

208 

207.8 

10.2 

268 

267.7 

13.2 

29 

29.0 

01.4 

89 

88.9 

04.4 

149 

148.8 

07.3 

209 

208.8 

10.3 

269 

268.7 

13.2 

30 

30.0 

01.5 

90 

89.9 

04.4 

150 

149.8 

07.4 

210 

209.8 

10.3 

270 

269.7 

13.3 

31 

31.0 

01.5 

91 

90.9 

04.5 

151 

150.8 

07.4 

211 

210.7 

10.4 

271 

270.7 

13.3 

32 

32.0 

01.6 

92 

91.9 

04.5 

152 

151.8 

07.5 

212 

211.7 

10.4 

272 

271.7 

13.3 

33 

33.0 

01.6 

93 

92.9 

04.6 

153 

152.8 

07.5 

213 

212.7 

10.5 

273 

272.7 

13.4 

34 

34.0 

01.7 

94 

93.9 

04.6 

154 

153.8 

07.6 

214 

213.7 

10.5 

274 

273.7 

13.4 

35 

35.0 

01.7 

95 

94.9 

04.7 

155 

154.8 

07.6 

215 

214.7 

10.6 

275 

274.7 

13.5 

36 

36  0 

01.8 

96 

95.9 

04.7 

156 

155.8 

07.7 

216 

215.7 

10.6 

276 

275.7 

13.5 

37 

37.0 

01.8 

97 

96.9 

04.8 

157 

156.8 

07.7 

217 

216.7 

10.7 

277 

276.7 

13.6 

38 

38.0 

01.9 

98 

97.9 

04.8 

158 

157.8 

07.8 

218 

217.7 

10.7 

278 

277.7 

13.6 

39 

39.0 

01.9 

99 

98.9 

04.9 

159 

158.8 

07.8 

219 

218.7 

10.8 

279 

278.7 

13.7 

40 

40.0 

02.0 

101 

99.  CJ 

04.9 

160 

159.8 

07.9 

220 

219.7 

10.8 

280 

279.7 

13.7 

41 

41.0 

02.0 

101 

100.9 

05.0 

161 

160.8 

07.9 

221 

220.7 

10.8 

281 

280.7 

13.8 

42 

41.9 

02.1 

102 

101.9 

05.0 

162 

161.8 

08.0 

222 

221.7 

10.9 

282 

281.7 

13.8 

43 

42.9 

02.1 

103 

102.9 

05.1 

163 

162.8 

08.0 

223 

222.7 

10.9 

283 

282.7 

13.9 

44 

43.9 

02.2 

104 

103  9 

05.1 

164 

163  8 

08.1 

224 

223.7 

11.0 

284 

283.7 

13.9 

45 

44.902.2 

105 

104.9 

05.2 

165 

164.8 

08.1 

225 

224.7 

11.0 

285 

284.7 

14.0 

46 

45.9 

02.3 

106 

105.9 

05.2 

166 

165  8 

08.2 

226 

225.7 

11.1 

286 

285.7 

14.0 

47 

46.9 

02.3 

107 

106.9 

05.3 

167 

166.8 

08.2 

227 

226.7 

11.1 

287 

286.7 

14.1 

48 

47.9 

02.4 

108 

107.9 

05.3 

168 

167.8 

08.2 

228 

227.7 

11.2 

288 

287.7 

14.1 

49 

48.902.4 

109 

108.9 

05.4 

169 

168.8 

08.3 

229 

228.7 

11.2 

289 

288.7 

14.2 

50 

49.902.5 

110 

109.9 

05.4 

170 

169  8 

08.3 

230 

229.7 

11.3 

290 

289.7 

14.2 

51 

50.902  5 

111 

110.9 

05.5 

171 

170.8 

08.4 

231 

230.7 

11.3 

291 

290.7 

14.3 

52 

51.902.6 

112 

111.9 

05.5 

172 

171.8 

08.4 

232 

231.7 

11.4 

292 

291  7 

14.3 

53 

52.902.6 

113 

112.9 

05.5 

173 

172.8 

08.5 

233 

232.7 

11.4 

293 

292.7 

14.4 

54 

53.902.7 

114 

113.9 

05.6 

174 

173.8 

08.5 

234 

233.7 

11.5 

294 

293.6 

14.4 

55 

54.902.7 

115 

114.9 

05.6 

175 

174.8 

08.6 

235 

234.7 

11.5 

295 

294.6 

14.5 

56 

55.902.8 

116 

115.9 

05.7 

176 

175.8 

08.6 

236 

235.7 

11.6 

296 

295.6 

14.5 

57 

56.902.8 

117 

116.9 

05.7 

177 

176.8 

08.7 

237 

236.7 

11.6 

297 

296.6 

14.6 

58 

57.902.9 

118 

117.9 

05.8 

178 

177.8 

08.7 

238 

237.7 

11.7 

298 

497.6 

14.6 

59 

58.902.9 

119 

118  9 

05.8 

179 

178.8 

08.8 

239 

238.7 

11.7 

299 

298.6 

14.7 

60 

59.9 

02  9 

120 

119.9 

05.9 

180 

179.8 

08.8 

240 

239.7 

11.8 

300 

299.6 

14.7 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dcp. 

Lat. 

Dist.1  Dep. 

Lat. 

For  7f  Points. 

TABLE  III.                                          189 

DIFFERENCE    OF   LATITUDE   AND   DEPARTURE   FOR   ^   POINT. 

Dist. 

Lat.  Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1 

01.000.1 

61 

60.7 

06.0 

121 

120.4 

11.9 

181 

180.1 

17.7 

241 

239.8 

23.6 

2 

02.0 

00.2 

62 

61  7 

06  1 

122 

121.4 

12.0 

182 

181.1 

17.8 

242 

240.8 

23.7 

3 

03.0 

00.3 

63 

62.7 

06.2 

123 

122.4 

12.1 

183 

182.1 

17.9 

243 

241.8 

23.8 

4 

04.0 

00.4 

64 

63.7 

06.3 

124 

123.4 

12.2 

184 

183.1 

18.0 

244 

242.8 

23.9 

5 

05.  G 

00.5 

65 

64.7 

06.4 

125 

124.4 

12.3 

185 

184.1 

18.1 

245 

243.8 

24.0 

6 

06.0 

00.6 

66 

65.7 

06.5 

126 

125.4 

12.3 

186 

185.1 

18.2 

246 

244.8 

24.1 

7 

07.  G 

00.7 

67 

66.7 

06  6 

127 

126.4 

12.4 

187 

186.1 

18.3 

247 

245.8 

24.2 

8 

08.0 

00.8 

68 

67.7 

06.7 

128 

127.4 

12.5 

188 

187.1 

18.4 

248 

246  8 

24.3 

9 

09.  G 

00.9 

69 

68.7 

06  8 

129 

128.4 

12.6 

189 

188.1 

18.5 

249 

247.3 

24.4 

Id 

10.  G 

01.  G 

70 

69.7 

06.9 

130 

129.4 

12.7 

19( 

189.1 

18.6 

250 

248.8 

24.5 

11 

10.9 

01.1 

71 

70.7 

07.0 

131 

130.4 

12.8 

191 

190.1 

18.7 

251 

249.8 

24.6 

12 

11.9 

01.2 

72 

71.7 

07.1 

132 

131.4 

12.9 

192 

191.1 

18.8 

252 

250.8 

24.7 

13 

12.9 

01.3 

73 

72.6 

07.2 

133 

132.4 

13.0 

193 

192.1 

18.9 

253 

251.  b 

24.8 

14 

13  9 

01.4 

74 

73.6 

07.3 

134 

133.4 

13.1 

194 

193.1 

19.0 

254 

252.8 

24.9 

15 

14.9 

01.5 

75 

74.6 

07.4 

135 

134. 

13.2 

195 

194.1 

19.1 

255 

253.8 

25.0 

16 

15.9 

01.6 

76 

75.6 

07.4 

136 

135. 

13.3 

196 

195.x 

19.2 

256 

254.8 

25.1 

17 

16.9 

01.7 

77 

76.6 

07.5 

137 

136. 

13.4 

197 

196.1 

19.3 

257 

255.8 

25.2 

18 

17.9 

01.8 

78 

77.6 

07.6 

138 

137. 

13.5 

198 

197.0 

19.4 

258 

256.  b 

25.3 

19 

18.9 

01.9 

79 

78.6 

07.7 

188 

138. 

13.  G 

199 

198.0 

19.5 

259 

257.8 

25.4 

20 

19.9 

02  0 

80 

79.6 

07.8 

140 

139. 

13.7 

200 

199.0 

19.6 

260 

258  7 

25.5 

21 

20.9 

02.1 

81 

80.6 

07.9 

1411  140. 

13.8 

201 

200.  G 

19.7 

*261 

259. 

25.6 

22 

21  6 

02.2 

82 

81.6 

08.0 

142   141. 

13.9 

202 

201.0 

19.8 

262 

260. 

25.7 

23 

22.9 

02.3 

83 

82.6 

08.1 

143 

142. 

14.  G 

203 

202.0 

19.9 

263 

261. 

25.8 

24 

23.9 

02.4 

84 

83.6 

08.2 

144 

143. 

14.1 

204 

2G3.0 

20.  G 

264 

262. 

25.9 

25 

24.9 

02.4 

85 

84.6 

08.3 

145 

144. 

14.2 

205 

204.  G 

20.1 

265 

263. 

26.0 

26 

25.9 

02  5 

86 

85.6 

08.4 

146 

145. 

14.3 

206 

205.0 

20.2 

266 

264. 

26.1 

27 

26.9 

02.6 

87 

86.6 

08.5 

147 

146. 

14.4 

207 

206.  G 

20.3 

267 

265. 

26.2 

28 

27.9 

02.7 

8b 

87.6 

08.6 

148 

147. 

14.5 

208 

207.0 

20.4 

268 

266. 

26.3 

29 

28.9 

02.8 

89 

88.608.7 

149 

148. 

14.6 

209 

208.0 

20.5 

269 

267 

26.4 

30 

29.9 

02.9 

90 

89.6,08.8 

150 

149. 

14.7 

210 

209.0 

20.6 

270 

268. 

26.5 

31 

30.9 

03.0 

91 

90.608.9 

151 

150. 

14.  b 

211 

210.0 

20.7 

271 

209. 

26.6 

32 

31.8 

03.1 

92 

91.609.0 

152 

151. 

14.9 

212 

211.0 

20.8 

272 

270. 

26.7 

33 

32.8 

03.2 

93 

92  609.1 

153 

152. 

15.  G 

213 

212.0 

20.9 

273 

271. 

26.8 

34 

33.8 

03.3 

94 

93  509.2 

154 

153. 

15.1 

214 

213.0 

21.0 

274 

272. 

26.9 

35 

34.8 

03.4 

95 

94  509.3 

155 

154. 

15.2 

215 

214.0 

21.1 

275 

273. 

27.0 

36  35.8 

03.5 

96 

95.509.4 

156 

155. 

15.3 

216 

215.0 

21.2 

276 

274. 

27.1 

37  136.8 

03.6 

97 

96.509.5 

157 

156.2 

15.4 

217 

216.0 

21.3 

277 

275.7 

27.2 

38 

37.8 

03.7 

98 

97.509.6 

158 

157.2 

15.5 

218 

216.9 

21.4 

278 

276.7 

27.3 

39 

38.8 

03.8 

99 

98.5 

09.7 

159 

158.2 

15.6 

219 

217.9 

21.5 

279 

277.7 

27.3 

40 

39.8 

03.9 

100 

99.5 

09.8 

160 

159.2 

15.7 

220 

218.9 

21.6 

280 

278.7 

27.4 

41 

40.  b 

04.  G 

101 

1G0.5 

09.9 

161 

160.2 

15.8 

221 

219.9 

21.7    281 

279.  G 

27  5 

42 

41.8 

04.1 

102 

101.5 

10.0 

162 

161.2 

15.9 

222 

220.9 

21.8 

282 

280.6 

27.6 

43 

42.8 

04.2 

103 

102.5 

10.1 

163 

162.2 

16.0 

223 

221.9 

21.9 

283 

281.6 

27.7 

44 

43.8 

04.3 

104 

103.5 

10.2 

164 

163.2 

16.1 

224 

222.9 

22.0 

284 

282.6 

27.8 

45 

44.8 

04.4 

105 

104.510.3 

165 

164.2 

16.2 

225 

223.9 

22.1 

285 

283.6 

27.9 

46 

45.8 

04.5 

106 

105.510.4 

166 

165.2 

16.3 

226 

224.9 

22  2 

286 

284.6 

28.0 

47 

46.8 

04.6 

107 

106.5110.5 

167 

166.2 

16.4 

227 

225.9 

22~2 

287 

285.6 

28.1 

48 

47.8 

04.7 

108 

107.5 

10.6 

168 

167.2 

16.5 

228 

226.9 

22.3 

288 

286.6 

28.2 

49 

48.8 

04.8 

109 

108.5 

10.7 

169 

168.2 

16.6 

229 

227.9 

22.4 

289 

287.6 

28.3 

50 

49.8 

04.9 

110 

109.5 

10.8 

170 

169.2 

16.7 

230 

228.9 

22.5 

290 

288.6 

28.4 

51  150.8 

05.0 

111 

110.5 

10.9 

171 

170.2 

16.8 

231 

229.9 

22.6' 

291 

289.6 

28.5 

52 

51.7 

05.1 

112 

111.5 

11.0 

172 

171.2 

16.9 

232 

230.9 

22.7 

292 

290.6 

28.6 

53 

52.7 

05.2 

113 

112.5 

11.1 

173 

172.2 

17.0 

233 

231.9 

22.8 

293 

291.6 

28.7 

54 

53.7 

05.3 

114 

113.5 

11.2 

174 

173.2 

17.1 

234 

232.9 

22.  9: 

294 

292.6 

28.8 

55 

54.7 

05.4 

115 

114.4 

11.3 

175 

174.2 

17.2 

235 

233.9 

23.0 

295 

293.6 

28.9 

56 

55.7 

05.5 

116 

115.4 

11.4 

176 

175.2 

17.3 

236 

234.9 

23.1 

296 

294.6 

29.0 

57 

56.7 

05.6 

117 

116.4 

11.5 

177 

176.1 

17.4 

237 

235.9 

23.2 

297 

295.6 

29.1 

58 

57.7 

05.7 

118 

117.4 

11.6 

178 

177.1 

17.4 

238 

236.9 

23.  31 

298 

296.6 

29.2 

59 

58.7 

05.8 

119 

118.4 

11.7 

179 

178.1 

17.5 

239 

237.8 

23.4 

299 

297.6 

29.3 

60 

59.7 

05.9 

120 

119.4 

11.8 

180 

179.1 

17.6 

240 

238.8 

23.5 

300 

298.6 

29.4 

Dist.  Dep 

Lat. 

Dist. 

Dcp. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dcp. 

Lat. 

Dist. 

Dcp. 

Lat, 

For  7£  Points. 

190                                         TABLE  III. 

DIFFERENCE   OF   LATITUDE   AND   DEPARTURE   FOR   J   POINT. 

Dist, 

Lat. 

Dep 

Dist, 

Lat. 

Dep 

Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

Jl.G 

00.1 

61 

60.3 

09.0 

121 

119.7 

17.8 

181 

179.0 

26.6 

241 

238.4 

35.4 

2 

02.0 

00.3 

62 

61.3 

09.1 

122 

120.7 

17.9 

182 

180.0 

26.7 

242 

239.4 

35.5 

3 

03.0 

00.4 

63 

62.3 

09.2 

123 

121.7 

18.1 

183 

181.0 

26.9 

243 

240.4 

35.7 

4 

04'.  I 

00.6 

64 

63.3 

08.4 

124 

122.7 

18.2 

184 

182.0 

27.0 

244 

241.4 

35.8 

5 

04.9 

00.7 

65 

64.3 

09.5 

125 

123.7 

18.3 

185 

183.0 

27.2 

245 

242.4 

36.0 

6 

05.8 

00.9 

66 

65.3 

09.7 

126 

124.6 

18.5 

186 

184.0 

27.3 

246 

243.3 

36.1 

7 

06.9 

Jl.O 

67 

66.3 

09.8 

127 

125.6 

18.6 

187 

185.0 

27.4 

247 

244.3 

36.2 

8 

07.9 

01.2 

68 

67.3 

10.0 

128 

126.6 

18.8 

188 

186.0 

27.6 

248 

245.3 

36.4 

9 

J8.9 

01.3 

69 

68.3 

10.1 

129 

127.  C 

18.9 

189 

187.0 

27.7 

249 

246.3 

36.5 

10 

09.9 

J1.5 

70 

69.2 

10.3 

131 

128.  C 

19.1 

19ii 

187.9 

27.9 

250 

247.3 

36.7 

11 

10.9 

Ol.b 

71 

70.* 

10.4 

131 

129.6 

19.  '2 

19  1 

188.9 

28.0 

251 

148.3 

36.8 

12 

11.9 

01.8 

72 

71.2 

10.6 

132 

130.6 

19.4 

192 

189.9 

28.2 

252 

249.3 

37.0 

13 

12.9 

01.9 

73 

72.2 

10.7 

133 

131.6 

19.5 

193 

190.9 

28.3 

253 

250.3 

37.1 

14 

13.9 

02  1 

74 

73.2 

10.9 

134 

132.6 

19.7 

194 

191.9 

28.  £ 

254 

251.3 

37.3 

15 

14.  8 

02.2 

75 

74.2 

11.0 

135 

133.5 

19.8 

195 

192.9 

28.6 

255 

252.2 

37.4 

16 

15.8 

02.3 

76 

75.2 

11.2 

136 

134.5 

20.0 

196 

193.9 

28.8 

256 

253.2 

37.6 

17 

16.8 

02.5 

77 

76.2 

11.3 

137 

135.5 

20.1 

197 

194.9 

28.9 

257 

254.2 

37.7 

18 

17.8 

02.6 

78 

77.2 

11.4 

138 

136.5 

20.3 

198 

195.9 

29.1 

258 

255.2 

37.9 

19 

18.8 

02.8 

79 

78.1 

11.6 

139 

137.5 

20.4 

199 

196.8 

29.2 

259 

256.2 

38.0 

'20 

19.8 

02.9 

80 

79.1 

11.7 

140 

138.5 

20.5 

200 

197.8 

29.4 

260 

257.2 

38.2 

21 

20.8 

J3.1 

81 

80.1 

11.9 

141 

139.5 

20.7 

201 

198.8 

29.5 

261 

*58  .  2 

38.3 

22 

21> 

03.2 

82 

81.1 

12.0 

142 

140  5 

20.8 

202 

199.8 

29.6 

262 

259  .'2 

38.4 

23 

22.8 

03.4 

83 

82.1 

12.2 

143 

141.5 

21.0 

203 

200.8 

29.8 

263 

260.2 

38.6 

24 

23.7 

03.5 

84 

83.1 

12.3 

144 

142.4 

21.1 

204 

201.8 

29.9 

264 

261.1 

38.7 

25 

24.7 

03.7 

85 

84.1 

12.5 

145 

143.4 

21.3 

205 

202.8 

30.1 

265 

262.1 

38.9 

26 

25.7 

03.8 

86 

85.1 

12.6 

146 

144.421.4 

206 

203.8 

30.2 

266 

263.1 

39.0 

27 

26.7 

04.0 

87 

86.1 

12.8 

147 

145.4 

21.6 

207 

204.8 

30.4 

267 

264.1 

39  2 

28 

27.7 

04.1 

88 

87.1 

12.9 

148 

146.4 

21.7 

208 

205.8 

30.5 

268 

265.1 

39.3 

29 

28.7 

04.3 

89 

88.0 

13.1 

149 

147.4 

21.9 

209 

206.7 

30.7 

269 

266.1 

39.5 

30 

29.7 

04.4 

90 

89.0 

13.2 

150 

148.4 

22.0 

210 

207.7 

30.8 

270 

267.1 

39.6 

31 

30.7 

04.6 

91 

90.013.4 

151 

1±9.4 

22.  '2 

211 

208.7 

31.0 

271 

268.1 

39.8 

32 

31.7 

04.7 

92 

91.013.5 

152 

150.4 

22.3 

212 

209.7 

31.1 

272 

269.1 

39.9 

33 

32.604.8 

93 

92.013.7 

153 

151.3 

22.5 

213 

210.7 

31.3 

273 

270.0 

40.1 

34 

33.6 

05.0 

94 

93.013.8 

154 

152.3 

22.6 

214 

211.7 

31.4 

274 

271.0 

40.2 

35 

34.6 

05.1 

95 

94.0!13.9 

155 

153.3 

22.7 

215 

212.7 

31.6 

275 

272.0 

40.4 

36 

35.6 

05.3 

96 

95.014.1 

156 

154.3 

22.9 

216 

213.7 

31.7 

276 

273.0 

40.5 

37 

36.6 

()5.4 

97 

96.014.2 

157 

155.3 

23.0 

217 

214.7 

31.8 

277 

274.0 

40.6 

38 

37.6 

05.6 

98 

96.914.4 

158 

156.3 

23.2 

218 

215.6 

32.0 

278 

275.0 

40.8 

I  39 

38.6 

05.7 

99 

97.914.5 

159 

157.3 

23.3 

219 

216.6 

32.1 

279 

276.0 

40.9 

40 

39.6 

05.9 

100 

98.914.7 

160 

158.3 

23.5 

220 

217.6 

32.3 

280 

277.0 

41.1 

41 

40.6 

06.0 

101 

99.9114.  8 

161 

159.3 

23.6 

221 

218.6 

32.4 

281 

278.0 

41.2 

42 

41.6 

06.2 

102 

100.915.0 

162 

160.3 

23.8 

222 

219.6 

32.6 

282 

279.0 

41.4 

43 

42.5 

06.3 

103 

101.915.1 

163 

161.2 

23.9 

223 

220.6 

32.7 

283 

279.9 

41.5 

44 

43.5 

06.5 

104 

102.915.3 

164 

162.2 

24.1 

224 

221.6 

32.9 

284 

280.9 

41.7 

45 

44.5 

06.6 

105 

103.9 

15.4 

165 

163.2 

24.2 

225 

222.6 

33.0 

285 

281.9 

41.8 

46 

45.5 

06.8 

106 

104.9 

15.6 

166 

164.2 

24.4 

226 

223.6 

33.2 

286 

282.9 

42.0 

47 

46.5 

06.9 

107 

105.8 

15.7 

167 

165.2 

24.5 

227 

224.5 

33.3 

287 

283.9 

42.1 

48 

47.5 

07.0 

108 

106.815.9 

168 

166.2 

24.7 

228 

225.5 

33.5 

288 

284.9 

42.3 

49 

48.5 

07.2 

109 

107.816.0 

169 

167.2 

24.8 

229 

226.5 

33.6 

289 

285.9 

42.4 

50 

49.5 

07.3 

110 

108.816.1 

170 

168.2 

24.9 

230 

227.5 

33.8 

290 

286.9 

42.6 

51 

50.5 

07.5 

111 

109.8 

16.3 

171 

169.2 

25.1 

231 

228.5 

33.9 

291 

287.9 

42.7 

52 

51.4 

07.6 

112 

110.8 

16.4 

172 

170.1 

25.3 

232 

229.5 

34.0 

292 

288.8 

42.9 

53 

52.4 

07.8 

113 

111.8 

16.6 

173 

171.1 

25.4 

233 

230.5 

34.2 

293 

289.8 

43.0 

54 

53.4 

07.9 

114 

112.8 

16.7 

174 

172.1 

25.5 

234 

231.5 

34.3 

294 

290.8 

43.1 

55 

54.4 

08.1 

115 

113.8 

16.9 

175 

173.1 

25.7 

235 

232.5 

34.5 

295 

291.8 

43.3 

56 

55.4 

08.2 

116 

114.7 

17.0 

176 

174.1 

25.8 

236 

233.4 

34.6 

296 

292.8 

43.4 

57 

56.4 

08.4 

117 

115.7 

17.2 

177 

175.1 

26.0 

237 

234.4 

34.8 

297 

293.8 

43.  fc 

58 

57.4 

08.5 

118 

116  7 

17.3 

178 

176.1 

26.1 

238 

235.4 

34.9 

298 

294.8 

43.7 

59 

58.4 

08.7 

119 

117.7 

17.5 

179 

177.1 

26.3 

239 

236.4 

35.1 

299 

295.8 

43.0 

60 

59.4 

08.8 

120 

118.7 

17.6 

180 

178.1 

26.4 

240 

237.4 

35.2 

300 

296.8 

44.  ( 

Dist.  Dep 

Lat. 

Dist, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

L^t. 

For  7£  Points.    , 

TABLE  III.                                          191 

DIFFERENCE   OF   LATITUDE   AND   DEPARTURE   FOR   1    POINT. 

Dep 

Lat. 

Dist. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist, 

Lat. 

Dep. 

1 

01.0 

00.2 

61 

59.8 

11.9 

121 

118.7 

23.6 

181 

177.5 

35.3 

241 

236.4 

47.0 

2 

02.0 

00.4 

62 

60.8 

12.1 

122 

119.7 

23.8 

182 

178.5 

35.5 

242 

237.4 

47.2 

3 

02.9 

00.6 

63 

61.8 

12.3 

123 

120.6 

24.0 

183 

179.5 

35.7 

243 

238.3 

47.4 

4 

03.9 

00.8 

64 

62.8 

12.5 

124 

121.6 

24.2 

184 

180.5 

35.9 

244 

239.3 

47.6 

5 

04.9 

01.0 

65 

63.8 

12.7 

125 

122.6 

24.4 

185 

181.5 

36.1 

245 

240.3 

47.8 

6 

05.9 

01.2 

66 

64.7 

12.9 

'126 

123.6 

24.6 

186 

182.4 

36.3 

246 

241.3 

48.0 

7 

06.9 

01.4 

67 

65.7 

13.1 

127 

124.6 

24.8 

187 

183.4 

36.5 

247 

242.3 

48.2 

8 

07.8 

01.6 

68 

66.7 

13.3 

128 

125.5 

25.0 

188 

184.4 

36.7 

248 

243.2 

48.4 

9 

08.8 

01.8 

69 

67.7 

13.5 

129 

126.5 

25.2 

189 

185.4 

36.9 

249 

244.2 

48.6 

10 

09.8 

02.0 

70 

68.7 

13.7 

130 

127.5 

25.4 

190 

186.4 

37.1 

250 

245.2 

48.8 

11 

10.8 

U2.2 

71 

69.6 

13.9 

131 

128.5 

25.0 

19  1 

187.3 

37.3 

251 

246.2 

49.0 

12 

11.8 

02.3 

72 

70.6 

14.0 

132 

129  5 

25.8 

192 

188.3 

37.5 

252 

247.2 

49.2 

13 

12.8 

02.  L 

73 

71.6 

14.2 

133 

130.5 

26.0 

19J 

189.3 

37.7 

253 

248.1 

49.4 

14 

13.7 

02.7 

74 

72.  C 

14.4 

134 

131.4 

26.1 

194 

190.3 

37.8 

254 

249.1 

49.6 

15 

14.7 

02.9 

75 

73.  C 

14.6 

135 

132.4 

26.3 

195 

191.3 

38.0 

255 

250.1 

49.7' 

16 

15.7 

03.1 

76 

74.5 

14.8 

136 

133.4 

26.5 

196 

192.2 

38.2 

256 

251.  1 

49.9 

17 

16.7 

03.3 

77 

75.5 

15.0 

137 

134.4 

26.7 

197 

193.2 

38.4 

257 

252.1 

50.1 

18 

17.7 

03.5 

78 

76.5 

15.2 

138 

135.4 

26.9 

198 

194.2 

38.6 

258 

253.0 

50.3 

19 

18.6 

03.7 

79 

77.5 

15.4 

139 

136.3 

27.1 

199 

195.2 

38.8 

259 

254.0 

50.5 

20 

19.6 

03.9 

80 

78.5 

15.6 

140 

137  3 

27.3 

200 

196.2 

39.0 

260 

255.0 

50.7 

21 

20.6 

04.1 

81 

79.4 

15.  b 

141 

138.3 

27.5 

201 

197.1 

39.2 

261 

256.0 

50.9 

22 

21.6 

04.3 

82 

80.4 

16.0 

142 

139.3 

27.7 

20'2 

198.1 

39.4 

262 

257.0 

51.1 

23 

22.  C 

04.5 

83 

81.4 

16.2 

143 

140.3 

27.9 

203 

199.1 

39.6 

263 

258.0 

51.3 

24 

23.5 

04.7 

84 

82.4 

16.4 

144 

141.2 

28.1 

204 

200.1 

39.8 

264 

258.9 

51.5 

25 

24.  & 

04.9 

85 

83.4 

16.6 

145 

142.2 

28.3 

205 

201.1 

40.0 

265 

259.9 

51.7 

26 

25.5 

05.1 

86 

84.4 

16.8 

146 

143.2 

28.5 

206 

202.0 

40.2 

266 

260.9 

51.9 

27 

26.5 

05.3 

87 

85.3 

17.0 

147 

144.2 

28.7 

207 

203.0 

40.4 

267 

261.9 

52.1 

28 

27.5 

05.  C 

88 

86.3 

17.2 

148 

145.2 

28.9 

208 

204.0 

40.6 

268 

262.9 

52.3 

29 

28.4 

05.7 

89 

87.3 

17.4 

149 

146.1 

29.1 

209 

205.0 

40.8 

269 

263.8 

52.5 

30 

29.4 

05.0 

90 

88.3 

17.6 

150 

147.1 

29.3 

210 

206.0 

41.0 

270 

264.8 

52.7 

31 

30.4 

06.0 

91 

89.3 

17.8 

151 

148.1 

29.5 

211 

207.0 

41.2 

271 

265.8 

52.9 

32 

31.-  i 

06.2 

92 

90.2 

18.0 

152 

149.1 

29.7 

212 

207.9 

41.4 

272 

266.8 

53.1 

33 

32.4 

06.4 

93 

91.2 

18.1 

153 

150.1 

29.9 

213 

208.9 

41.  6  1  273 

267.8 

53.3 

34 

33.4 

06.6 

94 

92.  * 

18.3 

154 

151.0 

30.0 

214 

209.9 

41.8 

274 

268.7 

53.5 

35 

34.3 

^6.8 

95 

93.2 

18.5 

155 

152.0 

30.2 

215 

210.9 

41.9 

275 

269.7 

53.6 

36 

35.3 

07.0 

96 

94.2 

18.7 

156 

153.0 

30.4 

216 

211.9 

42.1 

276 

270.7 

53.8 

37 

36.3 

07.2 

97 

95.1 

18.9 

157 

154.0 

30.6 

217 

212.8 

42.3 

277 

271.7 

54.0 

38 

37.3 

07.4 

98 

96.1 

19.1 

158 

155.0 

30.8 

218 

213.8 

42.5 

278 

272.7 

54.2 

39 

38.3 

07.6 

99 

97.1 

19.3 

159 

156.0 

31.0 

219 

214.8 

42.7 

279 

273.6 

54.4 

40 

39.2 

07.8 

100 

98.1 

19.5 

160 

156.9 

31.2 

220 

215.8 

42.9 

280 

274.6 

54.6 

41 

40.2 

08.0 

101 

99.1 

19.7 

161 

157.9 

31.4 

221 

216.8 

43.1 

281 

275.6 

54.8 

42 

41.2 

08.2 

102 

100.0 

19.  9 

162 

158.9 

31.6 

222 

217.7 

43.3 

282 

276.6 

55.0 

43 

42.2 

08.4 

103 

101.0 

20.1 

163 

159.9 

31.  & 

223 

218.7 

43.5 

283 

277.6 

55.2 

44 

43.2 

08.6 

104 

102.020.3 

164 

160.9 

32.0 

224 

219.7 

43.7 

284 

278.5 

55.4 

45 

44.1 

08.8 

105 

103.020.5 

165 

161.8 

32.2 

225 

220.7 

43.9 

285 

279.5 

55.6 

46 

45.1 

09.0 

106 

104.020.7 

166 

162.8 

32.4 

226 

221.7 

44.1 

286 

280.5 

55.8 

47 

46.1 

09.2 

107 

104.920.9 

167 

163.8 

32  6 

227 

222.6 

44.3 

287 

281.5 

56.0 

48 

47.1 

09.4 

108 

105.921.1 

168 

164.8 

32.8 

228 

223.6 

44.5 

288 

282.5 

56.2 

49 

48.1 

09.6 

109 

106.921.3 

169 

165.8 

33.0 

229 

224.6 

44.7 

289 

283.5 

56.4 

50 

49.0 

09.8 

110 

107.921.5 

170 

166.7 

S3.  2 

230 

225.6 

44.9 

290 

284.4 

56.6 

51 

50.0 

10.0 

111 

108.9:21.7 

171 

167.7 

33.4 

231 

226.6 

45.1 

291 

285.4 

56.  b 

52 

51.0 

10.1 

112 

109  921.9 

172 

168.7 

33.6 

232 

227.5 

45.3 

292 

286.4 

57.0 

53 

52.0 

10.3 

113 

110.822.0 

173 

169.7 

33.8 

233 

228.5 

45.5 

293 

287.4 

57.2 

54 

53.0 

10.5 

114 

111.822.2 

174 

170.7 

34.0 

234 

229.5 

45.7 

294 

288.4 

57.4 

55 

53.9 

10.7 

115 

112.822.4 

175 

171.6 

34.1 

235 

230.5 

45.9 

295 

289.3 

57.6 

56 

54.9 

10.9 

116 

113.  822.  C 

176 

172.6 

34.3 

236 

231.5 

46.0 

296 

290.3 

57.7 

57 

55.9 

11.1 

117 

114.822.8 

)77 

173.  C 

34.5 

237 

232.5 

46.2 

297 

291.3 

67.9 

58 

56.9 

11.3 

118 

115.7 

23.0 

178 

174.6 

34.7 

238 

233.4 

46.4 

298 

292.3 

58.1 

59 

57.9 

11.5 

119 

116.7 

23.2 

179 

175.6 

34.9 

239 

234.4 

46.6 

299 

293.3 

58.3 

60 

58.8 

11.7 

120 

117.7 

23.4 

180 

176.5 

35.1 

240 

235.4 

46.8 

300 

294.2 

58.5 

Dist, 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat.    Dist. 

Dep. 

Lat. 

For  7  Points. 

192                                         TABLE  III. 

DIFFERENCE   OF    LATITUDE    AND    DEPARTURE   FOR   1J   POINT. 

Dist. 

Lat. 

Dep  Dist. 

Lat. 

Dep 

'Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

01.000.2 

61 

59.2 

14.8 

121 

117.4 

29.4 

181 

175.6 

44.0 

241 

233.8 

58.6 

2 

01.900.5 

62 

60.1 

15.1 

122 

118.4129.6 

182 

176.5 

44.2 

242 

234.8 

58.8 

3 

02.900.7 

63 

61.1 

15.3 

123 

119.329.9 

183 

177.5 

44.5 

243 

235.7 

59.0 

4 

03.9 

01.0 

64 

62.1 

15.6 

124 

120.330.1 

184 

178.5 

44.7 

244 

236.7 

59.3 

5 

04.9 

01.2 

65 

63.1 

15.8 

125 

121.330.4 

185 

179.5 

45.0 

245 

237.7 

59.5 

6 

05.8 

01.5 

66 

64.0 

16.0 

126 

122.2 

30.6 

186 

180.4 

45.2 

246 

238.6 

59.8 

7 

06.8 

01.7 

67 

65.0 

16  3 

127 

123.2 

30.9 

187 

181.4 

45.4 

247 

239.6 

60.0 

8 

07.8 

01.9 

68 

66.0 

16.5 

128 

124.231.1 

188 

182.4 

45.7 

248 

240.6 

60.3 

9 

08.7 

02.2 

69 

66.9 

16.8 

129 

125.1 

31.3 

189 

183.3 

45.9 

249 

241.6 

60.5 

10 

09.7 

02.4 

70 

67.9 

17.0 

130 

126.1J31  6 

190 

184.3 

46.2 

250 

242.5 

60.8 

11 

10.7 

02.7 

71 

6a.y 

17.3 

131 

127.1 

31.8 

191 

185.3 

46.4 

251 

243.5 

61.0 

12 

11.6 

02.9 

72 

69.9 

17.5 

132 

128.1 

32.1 

192 

186.2 

46.7 

252 

244.5 

61.2 

13 

12.6 

03.2 

73 

70.8 

17.7 

133 

129.  Oi  32.  3 

193 

187.2 

46.9 

253 

245.4 

61.5 

14 

13.6 

03.4 

74 

71.8 

18.0 

134 

130.032.6 

194 

188.2 

47.1 

254 

256.4 

61.7 

15 

14.6 

03.6 

75 

72.8 

18.2 

135 

131.032.8 

195 

189.2 

47.4 

255 

247.4 

62.0 

16 

15.5 

03.9 

76 

73.7 

18.5 

136 

131.933.1 

196 

190.1 

47.6 

256 

248.3 

62.2 

17 

16.5 

04.1 

77 

74.7 

18.7 

137 

132.933.3 

197 

191.1 

47.9 

257 

249.3 

62.5 

18 

17.5 

04.4 

78 

75.7 

19.0 

138 

133.933.5 

198 

192.1 

48.1 

258 

250.3 

62.7 

19 

18.4 

04.6 

79 

76.6 

19.2 

139 

134  833.8 

199 

193.0 

48.4 

259 

251.3 

62.9 

20 

19.4 

04.9 

80 

77.6 

19.4 

140 

135.834.0 

200 

194.0 

48.6 

260 

252.2 

63.2 

21 

20.4 

05.1 

81 

78.6 

19.7 

141 

136.834.3 

201 

195.0 

48.8 

261 

253.2 

63.4 

22 

21.3 

05  4 

82 

79.6 

19.9 

142 

137.834.5 

202 

196.0 

49.1 

262 

254.2 

63.7 

23 

22.3 

05.6 

83 

80.5 

20.2 

143 

138.7 

34.8 

203 

196.9 

49.3 

263 

255.1 

63.9 

24 

23.3 

05.8 

84 

81.5 

20.4 

144 

139.735.0 

204 

197.9 

49.6 

264 

256.1 

64.2 

25 

24.3 

06.1 

85 

82.5 

20.7 

145 

140.7 

35.2 

205 

198.9 

49.8 

265 

257.1 

64.4 

26 

25.2 

06.3 

86 

83.4 

20.9 

146 

141.6 

35.5 

206 

199.8 

50.1 

266 

258.0 

64.6 

27 

26.2 

06  6 

87 

84.4 

21.1 

147 

142.6 

35.7 

207 

200.8 

50.3 

267 

259.0 

64.9 

28 

27.2 

06.8 

88 

85.4 

21.4 

148 

143.6 

36.0 

208  201.8 

50.5 

268 

260.0 

65.1 

29 

28.1 

07.1 

89 

86.3 

21.6 

149 

144.5 

36.2 

209  202.7 

50.8 

269 

261.0 

65.4 

30 

29.1 

07.3 

90 

87.321.9 

150 

145.5 

36.5 

210 

203.7 

51.0 

270 

261.9     65.  6^ 

31 

30.1 

07.5 

91 

88.322.1 

151 

146.536.7 

211 

204.7 

51.3 

271 

262.9 

65.9 

32 

31.0 

07.8 

92 

89.3 

22.4 

152 

147.4 

36.9 

212  205.7 

51.5 

272 

263.9 

66.1 

33 

32.0 

08.0 

93 

90.222.6 

153 

148.4 

37.2 

213  206.6 

51.8 

273 

264.8 

66.3 

34 

33.0 

08.3 

94 

91.222.8 

154 

149.4!37.4 

214  207.6 

52.0 

274 

265.8 

66.6 

35 

34.0 

08.5 

95 

92.223.1 

155 

150.437.7 

215 

208.6 

52.2 

275 

266.8 

66.8 

36 

34.9 

08.8 

96 

93.1 

23.3 

156 

151.337.9 

216 

209.5 

52.5 

276 

267.7 

67.1 

37 

35.9 

09.0 

97 

94.1 

23.6 

157 

152.338.2 

217 

210.5 

52.7 

277 

268.7 

67.3 

38 

36.9 

09.2 

98 

95.1 

23.8 

158 

153.3J38.4 

218 

211.5 

53.0 

278 

269.7 

67.6 

39 

37.8 

09.5 

99 

96.0 

24.1 

159 

154.2 

38.6 

219 

212.5 

53.2 

279 

270.7 

67.8 

40 

38.8 

00.7 

100 

97.0 

24.3 

160 

155.  2|  38.  9 

220 

213.4 

53.5 

280 

271.6 

68.0 

41 

39.8 

10.0 

101 

9S.O 

24.5 

161 

156.239.1 

221 

214.4 

53.7 

281 

272.6 

68.3 

42 

40.7 

10.2 

102 

99.0 

24.8 

162 

157.2 

39.4 

222 

215.4 

53.9 

282 

273.6 

68.5 

43 

41.7 

10.5 

103 

99.9 

25.0 

163 

158.1 

39.6 

223 

216.3 

54.2 

283 

274.5 

68.8 

44 

42.7 

10.7 

104 

100.9 

25.3 

164 

159.1 

39.9 

224 

217.3 

54.4 

284 

275.5 

69.0 

45 

43.7 

10.9 

105 

101.9 

25.5 

165 

160.1 

40.1 

225 

218.3 

54  7 

285 

276.5 

69.3 

46 

44.6 

11.2 

106 

102.8 

25.8 

166 

161.0 

40.3 

226 

219.2 

54.9 

286 

277.4 

69.5 

47 

45.6 

11.4 

107 

103.8 

26.0 

167 

162  0 

40.6 

227 

220.2 

55.2 

287 

278.4 

69.7 

48 

46.6 

11.7 

108 

104.8 

26.2 

168 

163.0 

40.8 

228 

221.2 

55.4 

288 

279.4 

70.0 

49 

47.5 

11.9 

109 

105.7 

26.5 

169 

163.9 

41.1 

229 

222  2 

55  6 

289 

280.4 

70.2 

50 

48  512.2 

110 

106.7 

26.7 

170 

164.9 

41.3 

230 

223.1 

55.9 

290 

281.3 

70.5 

51 

49.512.4 

111 

107.7 

27.0 

171 

165.9 

41.6 

231 

224.1 

56.1 

291 

282.3 

70.7 

52 

50.412.6 

112 

108.7 

27.2 

172 

166.9 

41.8 

232 

225.1 

56.4 

292 

283.3 

71.0 

53 

51.412.9 

113 

109.6 

27.5 

173 

167.842.0 

233 

226.0 

56.6 

293 

284.2 

71.2 

54 

52.413.1 

114 

110.6 

27.7 

174 

168.842.3 

234 

227.0 

56.9 

294 

285.2 

71  4 

55 

53.413.4 

115 

111.6 

27.9 

175 

169.8 

42.5 

235 

228.0 

57.1 

295 

286.2 

71.7 

56 

54.313.6 

116 

112.5 

28.2 

176 

170.7 

42.8 

236 

228.9 

57.3 

296 

287.1 

71.9 

57 

55.313.9 

117 

113.5 

28.4 

177 

171.7 

43.0 

237 

229.9 

57.6 

297 

288.1 

72.2 

58 

56.314.1 

118 

114.5 

28.7 

178 

172.7 

43.3 

238 

230.9 

57.8 

298 

289.1 

72.4 

59 

57.214.3 

119 

115.4 

28.9 

179 

173.6 

43.5 

239 

231.8 

58.1 

299 

290.1 

72.7 

60 

58.2 

14.6 

120 

116.4 

29.2 

180 

174.6 

43.7 

240 

232.8 

58.3 

300 

291.0 

72.9 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  6| 

Points. 

TABLE  HI.                                          193 

DIFFERENCE    OF    LATITUDE   AND   DEPARTURE   FOR    1^   POINT. 

Dist. 

Lat. 

Dep1  Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

01.0'00.3 

61 

58.4 

17.7 

121 

115.8 

35.1 

181 

173.2 

52.5 

241 

230.6 

70.0 

2 

H.900.6 

62 

59  3 

18  0| 

122 

116.8 

35.4 

182 

174.2 

52.8 

242 

231.6 

70.3 

3 

02.900.9 

63 

60.3 

18.3 

123 

117.7 

35.7 

183 

175.1 

53.1 

243 

232.5 

70.5 

4 

03.801.2 

64 

61.2 

18.6 

124 

118.7 

36.0 

184 

176.1 

53.4 

244 

233.5 

70.8 

5 

04.801.5 

65 

62.2 

18.9 

125 

119.6 

36.3 

185 

177.0 

53.7 

245 

234.5 

71.1 

6 

05.701.7 

66 

63.2 

19.2 

126 

120.  G 

36.6 

186 

178.0 

54.0 

246 

235.4 

71.4 

7 

06.702.0 

67 

64.1 

19  5 

127 

121  5 

36.9 

187 

179.0 

54.3 

247 

236.4 

71.7 

8 

07.702.3 

68 

65.1 

19.7 

128 

122.5 

37.2 

188 

179.9 

54.6 

248 

237  3 

72.0 

9 

08.602.6 

69 

66  0 

20.0 

129 

123.5 

37.5 

189 

180.9 

54.9 

249 

238.3 

72.3 

10 

09.602.9 

70 

67.0 

20.3 

130 

124.4 

37.7 

190 

181.8 

55.2 

250 

239.2 

72.6 

11 

10.503.2 

71 

67.9 

20.6 

131 

125.4 

38.0 

191 

182.S 

55.4 

'2ul 

240.2 

72.9 

12 

11.503.5 

72 

68.9 

20.9 

132 

126.3 

38.3 

192 

183.7 

55.7 

252 

241.2 

73.2 

13 

12.403.8 

73 

69.9 

•21.2 

133 

127.3 

38.6 

193 

184.7 

56.0 

253 

242  .  1 

73.4 

14 

13.404.1 

74 

70.8 

21.5 

134 

128.2 

38.9 

194 

185.7 

56.3 

254 

243.1 

73.7 

15 

14.4,04.4 

75 

71.8 

21.8 

135 

129.2 

39.2 

195 

186.6 

56.6 

255 

244.0 

74.0 

16 

15.304.6 

76 

72.7 

22.1 

136 

130.1 

39.5 

196 

187.6 

56.9 

256 

245.0 

74.3 

17 

16.304.9 

77 

73.7 

22.4 

137 

131.1 

39.8 

197 

188.5 

57.  '2 

257 

245.9 

74.6 

18 

17.2'05.2 

78 

74  6 

22.6 

138 

132.1 

40.1 

198 

189.5 

57.5 

258 

246.9 

74.9 

19 

18.205.5 

79 

75.6 

22.9 

139 

133.0 

40.4 

199 

190.4 

57.8 

259 

247.9 

75.2 

20 

19.1|05  8 

80 

76.  G 

•23.2 

140 

134.0 

40.6 

200 

191.4 

58.1 

260 

248.8 

75.5 

21 

20.106.1 

81 

77.5 

23.5 

141 

134.  y 

40.9 

201 

192.3 

58.4 

'261 

249.8 

75.8 

22 

21.106.4 

82 

78.5 

23.8 

142 

135.9 

41  2 

202 

193.3 

58.  G 

262 

250.7 

76.1 

23 

22.006.7 

83 

79.4 

24.1 

143 

136.8 

41.5 

203 

194.3 

58.9 

263 

251.7 

76.3 

24 

23.0 

07.0 

84 

80.4 

24.4 

144 

137.8 

41.8 

204 

195.2 

59  2 

264 

252.6 

76.6 

25 

23.9 

07.3 

85 

81.3 

24.7 

145 

138.8 

42.1 

205 

196.2 

59.5 

265 

253.6 

76.9 

26 

24.9 

07  6 

86 

82  3 

25.0 

146 

139.7 

42.4 

206 

197.1 

59.8 

266 

254.6 

77.2 

27 

25.8 

07.8 

87 

83.3 

25.3 

147 

140.7 

42.7 

207 

198.1 

60.1 

267 

255.5 

77.5 

28 

26.8 

08.1 

86 

84.2 

25.5 

148 

141.6 

43.0 

208 

199.0 

60.4 

268 

256.5 

77.8 

29 

27.8 

08.4 

89 

85.2 

25.8 

149 

142.6 

43.3 

209 

200.0 

60.7 

269 

257.4 

78.1 

30 

28.7 

08.7 

90 

86.1 

26.1 

150 

143.5 

43.5 

210 

201.0 

61.0 

270 

258.4 

78.4 

31 

29.7 

09.0 

91 

87.1 

26.4 

151 

144.5 

43.8 

'211 

201.9 

61.3 

271 

259.3 

78.7 

32 

30.6 

09.3 

92 

88.0 

26.7 

152 

145.5 

44.1 

212 

202.9 

61.5 

272 

260  3 

79.0 

33 

31.6 

09.6 

95 

89.0 

27  0 

153 

146.4 

44.4 

213 

203.8 

61.  & 

273 

261.2 

79.3 

34 

32.5 

09.9 

94 

90  0 

27  3 

154 

147.4 

44.7 

214 

204.8 

62.1 

274 

262.2 

79.5 

35 

33.5 

10.2 

95 

90.9 

27.6 

155 

148.3 

45.0 

215 

205.7 

62.4 

275 

283.2 

79.8 

36 

34.5 

10.5 

96 

91.9 

27.9 

156 

149.3 

45.3 

216 

206.7 

62.7 

276 

264.1 

80.1 

37 

35.4 

10  7 

97 

92.8 

28.2 

157 

150.2 

45.6 

217 

207.7 

63  0 

277 

2G5.1 

80.4 

38 

3G.4 

11.0 

98 

93.8 

28.5 

158 

151.2 

45.9 

218 

208.6 

63.3 

278 

266.0 

80.7 

39 

37.  1 

11.8 

99 

94.7 

28.7 

159 

152.2 

46.2 

219 

209.  G 

63.6 

279 

267.0 

81.0 

40 

33.3 

11.  G 

100 

95.7 

29.0 

160 

153.1 

46.4 

220 

210.5 

63.9 

280 

2G7.9 

81.3 

41 

39.  ^ 

11.9 

101 

96.7 

29.3 

161 

154.1 

46.7 

2'21 

211.5 

64.2 

281 

268.9 

81.6 

42 

40.2 

12.2 

102 

97.6 

29.  G 

162 

155.0 

47.0 

222 

212.4 

64.4 

282 

269.9 

81.9 

43 

41.2 

12.5 

103 

98.6 

29.9 

163 

156.0 

47.3 

223 

213.4 

64.7 

283 

270.8 

82.2 

44 

42.1 

12.  b 

104 

99.5 

30.2 

164 

156.9 

47.  C 

224 

214.4 

65.0 

284 

271.8 

82.4 

45 

43.1 

13.1 

105 

100.5 

30.5 

165 

157.9 

47.9 

225 

215.3 

65.3 

285 

272.7 

82.7 

46 

14.0 

13.4 

106 

101.4 

30.8 

166 

158.9 

48.2 

226 

216.3 

65.6 

286 

273.7 

83.0 

47 

45.013.6 

107 

102.4 

31.1 

167 

159.8 

48.5 

227 

217.2 

65.9 

287 

274.6 

83.3 

48 

415.913.9 

108 

103.4 

31.4 

168 

160.8 

48.8 

228 

218.2 

66.2 

288 

275.6 

83.6 

49 

46.9 

14.2 

109 

104.3 

31.6 

169 

161.7 

49.1 

229 

219.1 

66.5 

289 

276.6 

83.9 

50 

17.914.5 

110 

105.3 

31.9 

170 

162.7 

49.4 

230 

220.1 

66.8 

290 

277.5 

84.2 

51 

48.814.8 

111 

106.2 

32.2 

171 

163.6 

49.6 

231 

221.1 

67.1 

291 

278.5 

84.5 

52 

49.815.1 

112 

107.2 

32.5 

172 

164.6 

49.9 

232 

222.0 

67.3 

292 

279.4 

84.8 

53 

50.715.4 

113 

108.1 

32.8 

173 

165.6 

50.2 

233 

223.0 

67.  G 

293 

280.4 

85.0 

54 

51.715.7 

114 

109.1 

33.1 

174 

166.5 

50.5 

234 

223.9 

67.9 

294 

281.3 

85.3 

55 

52.616.0 

115 

110.1 

33.4 

175 

167.5 

50.8 

235 

224.9 

68.2 

295 

282.3 

85.6 

56 

53.616.3 

116 

111.0 

33.7 

176 

168.4 

51.1 

236 

225.8 

68.5 

296 

283.3 

85.9 

57 

54.616.6 

117 

112.0 

34.0 

177 

169.4 

51.4 

237 

226.8 

68.8 

297 

284.2 

86.2 

58 

55.516.8 

118 

112.9 

34.3 

178 

170.3 

51.7 

238 

227.8 

69.1 

298 

285.2 

86.5 

59 

36.517.1 

119 

113.9 

34.5 

179 

171.3 

52.0 

239 

228.7 

69.4 

299 

£86.1 

86.8 

60 

57.4 

17.4 

120 

114.8 

34.8 

180 

172.3 

52.3 

240 

229.7 

69.7 

300 

287.1 

87.1 

Dist. 

Dep  Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.  i'Dist. 

Dep. 

Lat. 

For  6£  Points. 

194 

TABLE  III. 

DIFFERENCE    OF   LATITUDE    AND    DEPARTURE   FOR    If   POINT. 

[list. 

Lat. 

DcpDist. 

Lat. 

Dep;.Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.3 

61 

,  57.420.6    121 

113.940.8 

181 

170.4 

61.0    241 

226.9 

81.2 

2 

01.9 

00.7 

62 

58.420.9 

122 

114.9 

41.1 

182 

171.4 

61.3 

242 

227.9 

81.5 

3 

02.8 

01.0 

63 

59.321.2 

123 

115.8 

41.4 

183 

172.3 

61.7 

243 

228.8 

81.9 

4 

03.8 

01.4 

64 

60.321.6 

124 

116.8 

41.8 

184 

173.2 

62.0 

244 

229.7 

82.2 

5 

04.7 

01.7 

65 

61.221.9 

125 

117.7 

42.1 

185 

174.2 

62.3 

245 

230.7 

82.5 

6 

05.7 

02.0 

66 

62.1J22.2 

126 

118.6 

42.5 

186 

175.1 

62.7 

246 

231.6 

82.9 

7 

06.6 

02.4 

67 

63.122.6 

127 

119.6 

42.8 

187 

176.1 

63.0 

247 

232.6 

83.2 

8 

07.5 

02.7 

68 

64.022.9 

128 

120.5 

43.1 

188 

177.0 

63.3 

248 

233.5 

83.6 

9 

08.5 

03  0 

69 

65.023.3 

129 

121.5 

43.5 

189 

177.9 

63.7 

249 

234.4 

83.9 

10 

09.4 

03.4 

70 

65.923.6 

130 

122.4 

43.8 

190 

178.9 

64.0 

250 

235.4 

84.2 

11 

10.4 

03.  7 

71 

66.923.9 

131 

123.3 

44.1 

191 

179.8 

64.4 

251 

*36.3 

84.6 

12 

11.3 

04.0 

72 

67.824.3 

132 

124.3 

44.5 

192 

180.8 

64.7 

252 

237.3 

84.9 

13 

12.2 

04.4 

73 

68.724.6 

133 

125.2 

44.8 

193 

181.7 

65.0 

253 

238.2 

85.2 

14 

13.2 

04.7 

74 

69.7r24.9 

134 

126.2 

45.1 

194 

182  7 

65.4 

254 

239.1 

85.6 

15 

14.1 

05.1 

75 

70.625.3 

135 

127.1 

45.5 

195 

183.6 

65.7 

255 

240.1 

85.9 

16 

15.1 

05.4 

76 

71.6 

25.6 

136 

128.1 

45.8 

196 

184.5 

66.0 

256 

241.0 

86.2 

17 

16.0 

05.7 

77 

72.525.9 

137 

129.0 

46.2 

197 

185.5 

66.4 

257 

242.0 

86.6 

18 

17.0 

06.1 

78 

73.426.3 

138 

129.9 

46.5 

198 

186.4 

66.7 

258 

242.9 

86.9 

19 

17.9 

06.4 

79 

74  426.6 

139 

130.9 

46.8 

199 

187.4 

67.0 

259 

243.9 

87.3 

20 

18.8 

06.7 

80 

75.327  0 

140 

131.8 

47.2 

200 

188.3 

67.4 

260 

244.8 

87.6 

21 

19.8 

07.1 

81 

76.3 

27.3 

141 

132.8 

47.5 

201 

189.3 

67.7 

261 

245.7 

87.9 

22 

20.7 

07.4 

82 

77.2 

27.6 

142 

133.7 

47.8 

202 

190.2 

68.1 

262 

246.7 

88.3 

23 

21.7 

07.8 

83 

78.2128.0 

143 

134.6 

48.2 

203 

191.1 

68.4 

263 

247.6 

88.6 

21 

22.6 

08.1 

84 

79.128.3 

144 

135.6 

48.5 

204 

192.1 

68.7 

264 

248.6 

88.9 

25 

23.5 

08.4 

85 

80.028.6 

145 

136.5 

48.9 

205 

193.0 

69.1 

265 

249.5 

89.3 

26 

24.5 

08.8 

86 

81.029.0 

146 

137.5 

49.2 

206 

194.0 

69.4 

266 

250.5 

89.6 

27 

25.4 

09.1 

87 

81.929.3 

147 

138.4 

49.5 

207 

194.9 

69.7 

267 

251.4 

90.0 

28 

26.4 

09.4 

88 

82.929.7 

148 

139.4 

49.9 

208 

195.8 

70.1 

268 

252.3 

90.3 

29 

27.3 

09.8 

89 

83.830.0 

149 

140.3 

50.2 

209 

196.8 

70.4 

269 

253.3 

90.6 

30 

28.3 

10.1 

90 

84.7 

30.3 

150 

141.2 

50.5 

210 

197.7 

70.8 

270 

254.2 

91.0 

31 

29.2 

10.4 

91 

85.730.7 

151 

142.2 

50.9 

211 

198.7 

71.1 

271 

255.2 

91.3 

32 

30.1 

10.8 

92 

86.631.0 

152 

143.1 

51.2 

212 

199.6 

71.4 

2T2 

256.1 

91.6 

33 

31.1 

11.1 

93 

87.6 

31.3 

153 

144.1 

51.5 

213 

200.6 

71.8 

273 

257.0 

92.0 

34 

32.0 

11.5 

94 

88.5 

31.7 

154 

145.0 

51.9 

214 

201.5 

72.1 

274 

258.0 

92.3 

35 

33.0 

11.8 

95 

89.532.0 

155 

145.9 

52.2 

215 

202.4 

72.4 

275 

258.9 

92.6 

36 

33.9 

12.1 

90 

90.432.3 

156 

146.9 

52.6 

216 

203.4 

72.8 

276 

259.9 

93.0 

37 

34.8 

12.5 

97 

91.332.7 

157 

147.8 

52.9 

217 

204.3 

73.1 

277 

260.8 

93.3 

38 

35.8 

12.8 

98 

92.333.0 

158 

148.8 

53.2 

218 

205.3 

73.4 

278 

261.8 

93.7 

39 

36.7 

13.1 

99 

93.233.4 

159 

149.7 

53.6 

219 

206.2 

73.8 

279 

262.7 

94.0 

40 

37.7 

13.5 

100 

94.233.7 

160 

150.7 

53.9 

220 

207.1 

74.1 

280 

263.6 

94.3 

41 

38.6 

13.8 

101 

95.134.0 

161 

151.6 

54.2 

221 

208.1 

74.5 

281 

264.6 

94.7 

42 

39.5 

14.2 

102 

96.034.4 

162 

152.5 

54.6 

222 

209.0 

74.8 

282 

265.5 

95.0 

43 

10.5 

14.5 

103 

97.034.7 

163 

153.5 

54.9 

223 

210.0 

75.1 

283 

266.5 

95.3 

44 

41.4 

14.8 

104 

97.935.0 

164 

154  4 

55.3 

224 

210.9 

75.5 

284 

267.4 

95.7 

45 

42.4 

15.2 

105 

98.935.4 

165 

155.4 

55.6 

225 

211.9 

75.8 

285 

268.3 

96.0 

46 

43.3 

15.5 

106 

99.835.7 

166 

156  3 

55.9 

226 

212.8 

76.1 

286 

269.3 

96.4 

47 

44.3 

15.8 

107 

100.736.1 

167 

157.2 

56.3 

227 

213.7 

76.5 

287 

270.2 

96.7 

48 

45.2 

16.2 

108 

101.736.4 

168 

158.2 

56.6 

228 

214.7 

76.8 

288 

271.2 

97.0 

49 

46.1 

16.5 

109 

102.636.7 

169 

159.1 

56.9 

229 

215.6 

77.2 

289 

272.1 

97.4 

50 

47.1 

16.8 

110 

103.637.1 

170 

160.1 

57.3 

230 

216.6 

77.5 

290 

273.0 

97.7 

51 

48.0 

17.2 

111 

104.537.4 

171 

161.0 

57.6 

231 

217.5 

77.8 

291 

274.0 

98.0 

52 

49.0 

17.5 

112 

105.537.7 

172 

161.9 

58.0 

232 

218.4 

78.2 

292 

274  9 

98.4 

53 

49.9 

17.9 

113 

106.438.1 

173 

162.9 

58.3 

233 

219.4 

78.5 

293 

275.9 

98.7 

54 

50.8 

18.2 

114 

1Q7.338.4 

174 

163.8 

58.6 

234 

220.3 

78.8 

294 

276.8 

99.0 

55 

51.8 

18.5 

115 

108.338.7 

175 

164.8 

59.0 

235 

221.3 

79.2 

295 

277.8 

99.4 

56 

52.7 

18.9 

116 

109.239.1 

176 

165.7 

59.3 

236 

222.2 

79.5 

296 

278  7 

99.7 

57 

53.7 

19.2 

117 

110.239.4 

177 

166.7 

59.6 

237 

223.1 

79.8 

297 

279.6 

100  1 

58 

54.6 

19.5 

118 

111.139.8 

178 

167.6 

60.0 

238 

224.1 

80.2 

298 

280.6 

100  4 

59 

55.6 

19.9 

119 

112.040.1 

179 

168.5 

60.3 

239 

2'25.0 

80.5 

299 

281.5 

100.7 

60 

56.5 

20.2 

120 

113.0 

40.4 

180 

169.5 

60.6 

240 

226.0 

80.9 

300 

282.5 

101.1 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  6|  Points. 

TABLE  III.                                          195 

DIFFERENCE   OF    LATITUDE   AND    DEPARTURE   FOR    2    POINTS. 

Dist,  LatJDep  Dist. 

Lat.    ] 

Dep 

Dist. 

Lat 

Dep 

Dist. 

Lat. 

Dep. 

ist. 

Lat, 

Dep. 

1 

KK900.4 

61 

56.423.3 

121 

111.8 

i6.3 

181 

167.2 

69.3 

241 

222.7 

92.2 

2 

J1.9U0.8 

62 

57.323.7 

122 

112.7 

46.7 

182 

168.2 

69.7 

242 

223.6 

92.6 

3 

J2.8;01.2 

63 

58.224.1 

123 

113.647.1 

183 

169.1 

70.0 

243 

224.5 

93.0 

4 

J3.701.5 

64 

59.124.5 

124 

114.647.5 

184 

170.0 

70.4 

244 

225.4 

93.4 

5 

34.601.9 

65 

60.124.9 

125 

115.547> 

185 

170.9 

70.8 

245 

226.4 

93  8 

6 

J5.502.3 

66 

61.025.3 

126 

116.448.2 

186 

171  8 

71.2 

246 

227.3 

94.1 

7 

36.502.7 

67 

61.925.6 

127 

117.3 

48.6 

187 

172.8 

71.6 

247 

228.2 

94.5 

8 

1)7.403.1 

68 

62.826.0 

128 

118.3 

49.0 

188 

173.7 

71.9 

248 

229.1 

94.9 

9 

08.  303.  4 

69 

63.826.4 

129 

119.249.4 

189 

174.6 

72.3 

249 

230.1 

95.3 

10 

09.203.8 

70 

64.7126.8 

130 

120.149.8 

190 

175  5 

72.7 

250 

231.0 

95.6 

11 

10.204.2 

7J 

65.6 

27.2 

131 

121  050.1 

191 

176  5 

73.1 

251 

231.9 

96.1 

12 

11.104.6 

72 

66.5 

27.6 

132 

122.050.5 

192 

177.4 

73  5 

252 

232.8 

96.4 

13 

12.0 

[)5.0 

73 

67.4 

27.9 

133 

122.950.9 

193 

178.3 

73  9: 

253 

233.7 

96.8 

14 

12.9 

J5.4 

74 

68.4 

28.3 

134 

123.8 

51  3 

194 

179.2 

74.  2! 

254 

234.7 

97.2 

15 

13.9 

05.7 

75 

69.3 

28.7 

135 

124.7 

51.7 

195 

180.2 

74.6, 

255 

235.6 

97  6 

16 

14.8 

06.1 

70 

70.2 

29.1 

136 

125.7 

52.0 

196 

181.1 

75.0 

256 

236.5 

98.0 

17 

15.7 

06.5 

77 

71.1 

29.5 

137 

126.6 

52.4 

197 

182.0 

75.4 

257 

237.4 

98.4 

18 

16.6 

J6.9 

78 

72.1 

29.9 

138 

127.5 

52.8! 

198 

182.9 

75.  81 

258 

238.4 

98.7 

19 

17.6 

07.3 

79 

73  0 

30.2 

139 

128.4 

53.2 

199 

183.9 

76.  2! 

259 

239.3 

99.1 

20 

18.5 

07.7 

80 

73.9 

30.6 

140 

129.3 

53.6 

200 

184.8 

76.  6| 

260 

240  2 

99.5 

ill 

19.4 

08.0 

81 

74.8 

31.0 

141 

130.3 

54.0 

201 

185.7 

76.9) 

261 

241.1 

99.9 

22 

20  3 

08  4 

82 

75.8 

31.4 

142 

131.2 

54.3 

202 

186.6 

77.3 

262 

242.1 

100.3 

23 

21.3 

08.8 

83 

76.7 

31.8 

143 

132.154.7: 

203 

187.6 

77.7' 

263 

243.0 

100.6 

24 

22.2 

09.2 

84 

77.6 

32.2 

144 

133.055.1 

204 

188.5 

78.1 

264 

243.9 

101.0 

25 

23.1 

09.6 

85 

78.5 

32.5 

145 

134.055.5 

205 

189.4 

78.5, 

265 

244.8 

101.4 

26 

24.0 

10.0 

86 

79.5 

32.9 

146 

134.955.9 

206 

190.3 

78.8 

266 

245.8 

101.8 

27 

24.9 

10.3 

87 

80.4 

33.3 

147 

135.856.3 

207 

191.2 

79.2 

267 

246.7 

102.2 

28 

25.9 

10.7 

88 

81.3 

33.7 

148 

136.7 

56.6 

208 

192.2 

79.6 

268 

247.6 

102.6 

29 

26.8 

11.1 

89 

82.2 

34.1 

149 

137.7 

57.0 

209 

193.1 

80.  0| 

269 

248.5 

102.9 

30 

•27.7 

11.5 

90 

83.2 

34.4 

150 

138.6 

57.4 

210 

194.0 

80.4 

270 

249.5 

103.3 

31 

•Ji.G 

11.9 

91 

84.1 

34.8 

151 

139.5 

57.8, 

211 

194.9 

80.8 

271 

250.4 

103.7 

32 

29.6 

12.3 

92 

85.0 

35.2 

152 

140.4 

58.2 

212 

195.9 

81.1 

272 

251.3 

104.1 

33 

30.5 

12.6 

93 

85.935.6 

153 

141.458.6 

213 

196.8 

81.5 

273 

252.2 

104.5 

34 

31.4 

13.0 

94 

86.9 

36.0 

154 

142.358.9 

214 

197.7 

81  9 

274 

253.1 

104.9 

35 

32.3 

13.4 

95 

87.8 

36.4 

155 

143.259.3 

215 

198.6 

82.3 

275 

254.1 

105.2 

3G 

33.3 

13.8 

96 

88.7 

36.7 

156 

H4.159.7 

216 

199.6 

82.7 

27G 

255.0 

105  6 

37 

34.2 

14.2 

9" 

89.6 

37.1 

157 

145  160.1 

217 

200.5 

83.0 

277 

255.9 

106.0 

38 

35.1 

14.5 

98 

90.5 

37.5 

158 

146.060.5 

218 

201.4 

83.4 

278 

256.8 

106.4 

39 

36.0 

14.9 

99 

91.5 

37.9 

159 

146.9 

60.9 

219 

202.3 

83.8 

279 

257.8 

106.8 

40 

37.  G 

15.3 

100 

92.4 

38.3 

160 

147.8 

61.2 

220 

203  3 

84  2 

280 

258.7 

107.2 

•a 

37.9 

lo.7 

101 

93.3 

38.7 

161 

148.7 

01.6 

221 

204.2 

84.6 

281   259.6 

107.5 

42 

38.8 

16.1 

102 

94.2 

39.0 

162 

149.7 

62.0 

222 

205.1 

85.0 

282 

260.5 

107.9 

43 

39.7 

16  5 

103 

95.2 

39.4 

163 

150.6 

62.4 

223 

206.0 

85.3 

283 

261.5 

108.3 

44 

40.7 

16.8 

104 

96.1 

39.8 

164 

151.5 

62.8 

224 

207.0 

85.7 

284 

262.4 

108.7 

45 

41.6 

17.2 

lOo 

97.0 

40.2 

165 

152  4 

63.1 

225 

207.9 

86.1 

285 

263.3 

109.1 

46 

42.5 

17.6 

106 

97.9 

40.6 

166 

153  4 

63.5 

226 

208  8 

86.5 

286 

264.2 

109.5 

47 

43.4 

ia.o 

107 

98.8 

41.0 

167 

154.3 

63  9 

227 

209.7 

86  9 

287 

265.2 

109.8 

48 

44.4 

18.4 

108 

99.8 

41.3 

168 

155.2 

64.3 

228 

210.6 

87.3 

288 

266.1 

110.2 

49 

45.3 

18.8 

10 

100.7 

41.7 

169 

156.1 

64.7 

229 

211.6 

87.6 

289 

267.0 

110.6 

50 

46.2 

19.1 

11C 

101.6 

42.1 

170 

157.1 

65.1 

230 

212.5 

88.0 

290 

267.9 

111.0 

51 

47.1 

19.5 

11 

102.6 

42.5 

171 

158.065.4 

231 

213.4 

88.4 

291 

268.9 

111.4 

52 

48.019.9 

11 

103.542  9 

172 

158.965.8 

232 

214.3 

88.8 

292 

269.8 

111.7 

53 

49.020.3 

11 

104.4 

43.2 

173 

159.866.2 

233 

215.3 

89.2 

293 

270.7 

112.1 

54 

49.9 

20.7 

11 

105.3 

43.6 

174 

160.866.6 

234 

216.2 

89.6 

294 

271.6 

112.5 

55 

50.8 

21.1 

11 

106.3 

44.0 

175 

161.767.0 

235 

217.1 

89.9 

295 

272.5 

112.9 

56 

51.7 

21.4 

11 

107.2 

44.4 

176 

162.  £ 

67.4 

236 

218.  C 

90.3 

296 

273.5 

113.3 

57 

52.7 

21.8 

11 

108.1 

44.8 

17r 

163.  £ 

67.7 

237 

219.  C 

90.7 

297 

274.4 

113.7 

58 

53.6 

22.2 

11 

109.  C 

45.2 

17 

164.568.1 

238 

219.8 

91.1 

298 

275.3 

114.0 

59 

54.5 

22.6 

11 

109.8 

45.5 

17 

165.468.5 

238 

220.  fc 

91.5 

299 

276.2 

114.4 

CO 

55.4 

23.0 

12 

110.  £ 

45.9 

18C 

166.  J 

168.9 

24C 

221.7 

91.8 

300 

277.2 

114.8 

DistJDep 

Lat. 

His* 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

For  6  Points. 

196                                         TABLE  III. 

DIFFERENCE   OF    LATITUDE   AND   DEPARTURE   FOR    2J   POINT. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

J0.4J 

61 

55.1 

26.1 

121 

109.4 

51.7 

181 

163.6 

77.4 

241 

217.9 

103.  C 

2 

01.8 

30.9 

62 

56.0 

26.5 

122 

110.3 

52.2 

182 

164.5 

77.8 

242 

218.  h 

103.5 

3 

02.7 

01.3 

63 

57.0 

26.9 

123 

111.2 

52.6 

183 

165.4 

78.3 

243 

219.7 

103.9 

4 

03.6 

01.7 

64 

57.9 

27.4 

124 

112.1 

53.0 

184 

166.3 

78.7 

244 

220.6 

104.3 

5 

04.5 

02.1 

65 

58.8 

27,8 

125 

113.0 

53.5 

185 

167.2 

79.1 

245 

221.5 

104.8 

6 

05.4 

02.6 

66 

59.7 

28.2 

126 

113.9 

53.9 

186 

168.1 

79.5 

246 

222.4 

105.2 

7 

06.3 

03.0 

67 

60.6 

28.7 

127 

114.8 

54.3 

187 

169.0 

80.0 

247 

223.3 

105.6 

8 

07.2 

J3.4 

68 

61.5 

29.1 

128 

115.7 

54.7 

388 

169.9 

80.4 

248 

224.2 

106.1 

9 

u8.1 

03.8 

69 

62.4 

29.5 

129 

116.6 

55.2 

189 

170.9 

80.8 

249 

225.1 

106.5 

10 

09.0 

04.3 

70 

63.3 

29.9 

130 

117.5 

55.6 

190 

171.8 

81.3 

250 

226.0 

106.9 

11 

U9.9 

04.7 

71 

ti4.2 

30.4 

131 

118.4 

66.0 

191 

172.7 

81.7 

251 

2*6.9 

107.3 

12 

10.8 

05.  1 

72 

65.1 

30.8 

132 

119.3 

56.5 

192 

173.6 

82.1 

252 

227.8 

107.8 

13 

11.8 

05.6 

73 

66.0 

31.2 

133 

120.2 

56.9 

193 

174.5 

82.5 

253 

228.7 

108.2 

14 

12.7 

06.0 

74 

66.9 

31.6 

134 

121.1 

57.3 

194 

175.4 

83.0 

254 

229.6 

108.6 

15 

13.6 

06.4 

75 

67.8 

32.1 

135 

122.0 

57.7 

195 

176.3 

83.4 

255 

230.5 

109.0 

16 

14.5 

06.8 

70 

68.7 

32.5 

136 

122.9 

58.2 

196 

177.2 

83.8 

25C 

231.4 

109.5 

17 

15.4 

07.3 

77 

69.6 

32.9 

137 

123.8 

58.6 

197 

178.1 

84.2 

257 

232.3 

109.9 

18 

16.3 

07.7 

78 

70.5 

33.4 

138 

124.7 

59.0 

198 

179.0 

84.7 

258 

233.2 

110.3 

19 

17.2 

08.1 

79 

71.4 

33.8 

139 

125.7 

59.4 

199 

179.9 

85.1 

259 

234.1 

110.8 

20 

18.1 

08.6 

80 

72.3 

34.2 

140 

126.6 

59.9 

200 

180.8 

85.5 

260 

235.0 

111.2 

21 

19.0 

09.0 

81 

73.2 

34.6 

141 

127.5 

OU.3 

201 

181.7 

85.9 

261 

235.9 

111.6 

22 

19.9 

09.4 

82 

74.1 

35.1 

142 

128.4 

60  7 

202 

182.  C 

86.4 

26; 

236.8 

112.0 

23 

20.8 

09.8 

83 

75.0 

35.5 

143 

129.3 

61.2 

203 

183..: 

86.8 

263 

237.7 

112.5 

24 

21.7 

10.3 

84 

75.9 

35.9 

144 

130.2 

61.6 

204 

184.4 

87.2 

264 

238.7 

112.9 

25 

22.6 

10.7 

85 

76.8 

36.3 

145 

131.1 

62.0 

205 

185.3 

87.7 

265 

239.6 

113.3 

26 

23.5 

11.1 

86 

77.7 

36.8 

146 

132.0 

62.4 

206 

186.2 

88.1 

266 

240.5 

113.7 

27 

24.4 

11.5 

87 

78.7 

37.2 

147 

132.9 

62.9 

207 

187.1 

88.5 

267 

241.4 

114  2 

28 

25.3 

12.0 

88 

79.6 

37.6 

148 

133.8 

63.3 

^08 

188.0 

88.9 

268 

242.3 

114.6 

29 

26.2 

12.4 

89 

80.5 

38.1 

149 

134.7 

63.7 

209 

188.9 

89.4 

269 

243.2 

115.0 

30 

27.1 

12.8 

90 

81.4 

38.5 

150 

135.6 

64.1 

210 

189.8 

89.8 

270 

244.1 

115.5 

31 

28.0 

13.3 

91 

82.3 

38.9 

151 

136.5 

eTe 

211 

190.7 

90.2 

27  J 

245.0 

lib.  9 

32 

28.9 

13.7 

92 

83.2 

39.3 

152 

137.4 

65.0 

212 

191.6 

90.7 

272 

245.9 

116.3 

33 

29.8 

14.1 

93 

84.1 

39.8 

153 

138.8 

65.4 

213 

192.6 

91.1 

273 

246.8 

116.7 

34 

30.7 

14.5 

94 

85.0 

40.2 

154 

139.2 

65.9 

214 

193.5 

91.5 

274 

247.7 

117.2 

35 

31.6 

15.0 

95 

85.9 

40.6 

155 

140.1 

66.3 

215 

194.4 

91.9 

275 

248.6 

117.6 

36 

32.5 

15.4 

96 

86.8 

41.1 

156 

141.0 

66.7 

216 

195.3 

92.4 

276 

249.5 

118.0 

37 

33.4 

15.8 

97 

87.7 

41.5 

157 

141.9 

67.1 

217 

196.2 

92.8 

277 

250.4 

118.5 

38 

34.4 

16.3 

98 

88.6 

41.9 

158 

142.8 

67.6 

218 

197.1 

93.2 

278 

251.3 

118.9 

39 

35.3 

16.7 

99 

89.5 

42.3 

159 

143.7 

68-0 

219 

198.0 

93.7 

279 

252  2 

119.3 

40 

36.2 

17.1 

100 

90.4 

42.8 

160 

144.6 

68.4 

220 

198.9 

94.1 

280 

253.1 

119.7 

41 

37.1 

17.5 

101 

91.3 

43.2 

161 

145.5 

68.8 

221 

199.8 

94.5 

28] 

254.0 

TiO.2 

42 

38.0 

18.0 

102 

92.2 

43.6 

162 

146.4 

69.3 

222 

200.7 

94.9 

282 

254.9 

120.6 

43 

38.9 

18.4 

103 

93.1 

44.1 

163 

147.3 

69.7 

223 

201.6 

95.4 

283 

255.8 

121.0 

44 

39.8 

18.8 

104 

94.0 

44.5 

164 

148.3 

70.1 

224 

202.5 

95.8 

284 

256.7 

121.5 

45 

40.7 

19.2 

105 

94.9 

44.9 

165 

149.2 

70.6 

225 

203.4 

96.2 

285 

257.6 

121.9 

46 

41.6 

19.7 

106 

95.8 

45.3 

166 

150.1 

71.0 

226 

204.3 

96.6 

286 

258.5 

122.3 

47 

42.5 

20.1 

107 

96.7 

45.8 

167 

151.0 

71.4 

227 

205.2 

97.1 

287 

259.4 

122.7 

48 

43.4 

20.5 

108 

97.6 

46.2 

168 

151.9 

71.8 

228 

206.1 

97.5 

288 

260.3 

123.2 

49 

44.3 

21.0 

109 

98.5 

46.6 

169 

152.8 

72.3 

229 

207.0 

97.9 

289 

261.3 

123.6 

50 

45.2 

21.4 

110 

99.4 

47.0 

170 

153.7 

72.7 

230 

207.9 

98.4 

290 

262.2 

124.0 

51 

46.1 

21.8 

111 

100.3 

47.5 

171 

154.6 

73.1 

231 

208.8 

98.8 

291 

263.1 

124.4 

52 

47.0 

22.2 

112 

101.2 

47.9 

172 

155.5 

73.6 

232 

209.7 

99.2 

292 

264.0 

124.9 

53 

47.9 

22.7 

113 

102.2 

48.3 

173 

156.4 

74.0 

233 

210.6 

99.6 

293 

264.9 

125.3 

54 

48.8 

23.1 

114 

103.1 

48.7 

174 

157.3 

74.4 

234 

211.5 

100.1 

294 

265.8 

125.7 

55 

49.7 

23.5 

115 

104.0 

49.2 

175 

158.2 

74.8 

235 

212.4 

100.5 

295 

266.7 

126.2 

56 

50.6 

23.9 

116 

104.9 

49.6 

176 

159.1 

75.3 

236 

213.3 

100.9 

296 

267.6 

126.6 

57 

51.5 

24.4 

117 

105.8 

50.0 

177 

160.0 

75.7 

237 

214.2 

101.4 

297 

268.5 

127.0 

58 

52.4 

24.8 

118 

106.7 

50  5 

178 

160.9 

76.1 

238 

215.1 

101.8 

298 

269.4 

127.4 

5'J 

53.3 

25.2 

119 

107.6 

50.9 

179 

161.8 

76.5 

239 

216.1 

102.2 

299 

270.3 

127.9 

60 

54.2 

25.7 

120 

108.5 

51.3 

180 

162.7 

77.0 

240 

217.0 

102.6 

300 

271.2 

128.3 

Dist.  Den 

Lat. 

Dist, 

Dcp. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  5£  Points. 

TABLE  III.                                          197 

DIFFERENCE  OP   LATITUDE   AND    DEPARTURE   FOR    2J   POINT. 

Dist. 

Lat. 

Dep 

list. 

Lat. 

Dep 

list. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.5 

61 

53.828.8 

121 

106.7 

57.0 

181 

159.6 

85.3 

241 

212.5 

113.6 

a 

01.8 

00.9 

6-2 

54.729.2 

122 

107.6 

57.5 

182 

160.5 

85.8 

242 

213.4 

114.1 

3 

02.6 

01.4 

63 

55.629.7 

123 

108.5 

58.0 

183 

161.4 

86.3 

243 

214.3 

114.6 

4 

03.501.9 

64 

56.430.2 

124 

109.4 

58.4 

184 

162.3 

86.7 

244 

215.2 

115.0 

5 

04.402.4 

65 

57.3 

30.6 

125 

110.2 

58.9 

185 

163.2 

87.2 

245 

216.1 

115.5 

G 

05.3 

02.8 

66 

58.2 

31.1 

126 

111.1 

59.4 

186 

164.0 

87.7 

246 

217.0 

116.0 

7 

06.2 

03.3 

67 

59.131.6 

127 

112.0 

59.9 

187 

164.9 

88.1 

247 

217.8 

116.4 

8 

07.1 

03.8 

68 

60.032.1 

128 

112.9 

60.3 

188 

165.8 

88.6 

248 

218.7 

116.9 

9 

07.9 

04.2 

69 

60.932.5 

129 

113.8 

60.8 

189 

166.7 

89.1 

249 

219.6 

117.4 

10 

08.8 

04.7 

70 

61.733.0 

130 

114.7 

61.3 

190 

167.6 

89.6 

250 

220.5 

117.8 

11 

09.7 

05.2 

71 

62.633.5 

131 

115.5 

61.71 

191 

168.5 

90.0 

251 

221.4 

118.3 

12 

10.6 

05.7 

72 

63.533.9 

132 

116.4 

62  2 

192 

169.3 

90.5 

252 

222.2 

118.8 

13 

11.5 

06.1 

73 

64.434.4 

133 

117.3 

62.7 

193 

170.2 

91.0 

253 

223.1 

119.3 

14 

12.3 

06.6 

74 

65.334.9 

134 

118.2 

63.2 

194 

171.1 

91.4 

254 

224.0 

119.7 

15 

13.2 

07.1 

75 

66.1 

35.4 

135 

119.1 

63.6 

195 

172.0 

91.9 

255 

224.9 

120.2 

16 

14.1 

07.5 

76 

67.0 

35.8 

136 

119.9 

G4.1 

196 

172.9 

92.4 

256 

225.8 

120.7 

17 

15.0 

08.0 

77 

67.9 

36.3 

137 

120.8 

64.6 

197 

173.7 

92.9 

257 

226.7 

121.1 

18 

15.9 

08.5 

78 

68.8 

36.8 

138 

121.7 

05.  0 

198 

174.6 

93.3 

258 

227.5 

121.6 

19 

16.8 

09.0 

79 

69.7 

37.2 

139 

122.6 

65.5 

199 

175.5 

93.8 

259 

228.4 

122.1 

20 

17.  C 

09.4 

80 

70.6 

37.7 

140 

123.5 

66.0 

200 

176.4 

94.3 

260 

229.3 

122.6 

21 

18.5 

09.9 

81 

71.4 

38-.*2 

141 

124.4 

66.5 

201 

177.3 

94.7 

261 

230.2 

123.0 

22 

19.4 

10.4 

82 

72.3 

38.6 

142 

125.2 

66.9 

202 

178.2 

95.2 

262 

231.1 

123.5 

23 

iO;3 

10.8 

83 

73.2 

39.1 

143 

126.1 

67.4 

203 

179.0 

95.7 

263 

231.9 

124.0 

24 

21.2 

11.3 

84 

74.1 

39.6 

144 

127.0 

67.9 

204 

179.9 

96.2 

264 

232.8 

124.4 

25 

22.1 

11.8 

85 

75.0 

40.1 

145 

127.9 

68.3 

205 

180.8 

96.6 

265 

233.7 

124.9 

26 

22.9 

J2.3 

86 

75.9 

40.5 

146 

128.8 

68.8 

206 

181.7 

97.1 

266 

234.6 

125.4 

27 

23.8 

12.7 

87 

76.7 

41.0 

147 

129.6 

69.3 

207 

182.6 

97.6 

267 

235.5 

125.9 

28 

24.7 

13.2 

88 

77.6 

41.5 

148 

130.5 

69.8 

208 

183.4 

98.0 

268 

236.4 

126.3 

29 

25.  C 

13.7 

89 

78.5 

41.9 

149 

131.4 

70.2 

209 

184.3 

98.5 

269 

237.2 

-126.8 

30 

26.5 

14.1 

90 

79.4 

42.4 

150 

132.3 

70.7 

210 

185.2 

99.0 

270 

238.1 

127.  3 

31 

i7.b 

14.6 

91 

80.3 

42.9 

•151 

133.2 

71.2 

211 

186.1 

99.5 

271 

239  0 

127.7 

32 

28.2 

15.1 

92 

81.1 

43.4 

152 

134.1 

71.6 

212 

187.0 

99.9 

272 

239.9 

128.2 

33 

29.1 

15.6 

93 

82.0 

43.8 

153 

134.9 

72.1 

213 

187.8 

100.4 

273 

240.8 

128.7 

34 

30.0 

16.0 

94 

82.9 

44.3 

154 

135.8 

72.6 

214 

188.7 

100.9 

274 

241.7 

129.2 

35 

30.9 

16.5 

95 

83.8 

44.8 

155 

136.7 

73.1 

215 

189.6 

101.3 

275 

242.5 

129.6 

36 

31.8 

17.0 

96 

84.7 

45.2 

156 

137.6 

73.5 

216 

190.5 

101.8 

276 

243.4 

130.1 

37 

32.6 

17.4 

97 

85.6 

45.7 

157 

138.5 

74.0 

217 

191.4 

102.3 

277 

244.3 

130.  C 

38 

33.5 

17.9 

98 

86.4 

46.2 

158 

139.3 

74.5 

218 

192.3 

102.8 

278 

245.2 

131.0 

39 

34.4 

18.4 

99 

87.3 

46.7 

159 

140.2 

74.9 

219 

193.1 

103.2 

279 

246.1 

131.5 

40 

35.  c 

18.9 

100 

88.2 

47.1 

160 

141.1 

75.4 

220 

194.0 

103.7 

280 

246.9 

132.0 

41 

36.2119.3 

101 

89.1 

47.6 

161 

142.0 

75.9 

221 

194.9 

104.2 

281 

247.8 

132.5 

42 

37.019.8 

102 

90.0 

48.1 

162 

142.9 

76.4 

222 

195.8 

104.6 

282 

248.7 

132.9 

43 

37.9 

20.3 

103 

90.8 

48.5 

163 

143.8 

76.8 

223 

196.7 

105.1 

283 

249.6 

133.4 

44 

38.8 

20.7 

104 

91.7 

49.0 

164 

144.6 

77.3 

224 

197.6 

105.6 

284 

250.5 

133.9 

45 

39.7 

21.2 

105 

92.6 

49.5 

165 

145.5 

77.8 

225 

198.4 

106.1 

285 

251.4 

134.3 

46 

40.  621.  7 

106 

93.550.0 

166 

146.4 

78.2 

226 

199.3 

106.5 

286 

252.2 

134.8 

47 

41.522.2 

107 

94.450.4 

167 

147.3 

78.7 

227 

200.2 

107.0 

287 

253.1 

135.3 

48 

42.322.6 

108 

9o.350.iJ 

168 

148.2 

79.2 

228 

201.1 

107.5 

288 

254.0 

135.8 

49 

43.223.1 

109 

96.151.4 

169 

149.0 

79.7 

229 

202.0 

107.9 

289 

254.9 

136.2 

50 

44.123.6 

110 

97.051.8 

170 

149.980.1 

230 

202.8 

108.4 

290 

255.8 

136.7 

51 

45.0 

24.0 

111 

97.952.3 

171 

150.880.6 

231 

203.7 

108.9 

291 

256.6 

137.2 

52 

45.9 

24.5 

112 

98.852.8 

172 

151.781.1 

232 

204.6 

109.4 

292 

257.5 

137.6 

53 

46.7 

25.0 

113 

99.753.3 

173 

152.681.5 

233 

205.5 

109.8 

293 

258.4 

138.1 

54 

47.  C 

25.5 

114 

100.553.7 

174 

153.582.0 

234 

206.4 

110.3 

294 

259.3 

138.6 

55 

48.  G 

25.9 

115 

101.454.2 

175 

154.382.5 

235 

207.3 

110.8 

295 

260.2 

139.1 

56 

49.4 

26.4 

116 

102.354.7 

176 

155.2 

83.0 

236 

208.1 

111.2 

296 

261.1 

139.5 

57 

so.  a 

26.9 

117 

103.2 

55.1 

177 

156.1 

83.4 

237 

209.0 

111.7 

297 

261.9 

140.0 

58 

51.2 

27.3 

118 

104.1 

55.6 

178 

157.  C 

83.9 

238 

209.9 

112.2 

298 

262.8 

140.5 

59 

52.  C 

27.8 

119 

105.056.1 

179 

157.984.4 

239 

210.8 

112.7 

299 

263.7 

140.9 

CO 

52.  £ 

28. 

12C 

105.856.6 

180 

158.8 

84.8 

240 

211.7 

113.1 

300 

264.6 

141.4 

Dint. 

Dep 

Lat 

Dist 

Dep. 

Lnt 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  5£  Points. 

198                                         TABLE  III. 

DIFFERENCE   OF   LATITUDE   AND    DEPARTURE    FOR    2f   POINT. 

[list. 

Lat. 

Dep 

»ist. 

Lat. 

Dep  Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.5 

61 

52.3 

31.  41 

121 

103.8 

62.2 

181 

155.3 

93.0 

241 

206.7 

123.9 

2 

01.7 

01.0 

62 

53  2131.9' 

122 

104.6 

62.7 

182 

156.1 

93.6' 

242 

207  6 

124.4 

3 

02.6 

01.5 

63 

54.0 

32.4 

123 

105.5 

63.2 

183 

157.0 

94.1; 

243 

208.4 

124.9 

4 

03.4 

02  1 

64 

54.9 

32.9! 

124 

106.4 

63.7 

184 

157.8 

94.6 

244 

209.3 

125.4 

5 

04.3 

02.6 

65 

55.8 

J3.4 

125 

107.2 

64.3 

185 

158.7 

95.1 

245 

210.1 

125.9 

6 

05.1 

03.1 

66 

56.6 

33.9 

126 

108.1 

64.8 

186 

159.5 

95.  61 

246 

211.0 

126  5 

7 

06  0 

03  6 

67 

57.5 

34.4 

127 

108  9 

65.3 

187 

160.4 

96.  li 

247 

211.9 

127.0 

8 

06.9 

04.1 

68 

58.335.0 

128 

109.865.8 

188 

161.2 

96.6 

248 

212.7 

127.5 

9 

07.7 

04.6 

69 

59.235.5 

129 

110.6 

66.3 

189 

162.1 

97.2 

249 

213.6 

128.0 

10 

08.6 

05.1 

70 

60.036.0 

130 

111.5 

66.8!  190 

163.0 

97.7 

250 

214.4 

128.5 

11 

09.4 

05.7 

71 

60.936.5 

131 

112.4 

67.31   191 

163.8 

98.2 

251 

215.3 

1-29.0 

12 

10.3 

06.2 

72 

61.837.0 

132 

113.2167.9 

192 

164.7 

98.7 

252 

216.1 

129.5 

13 

11.2 

06.7 

73 

62.637.5 

133 

114.1 

68.4 

193 

165.5 

99.2 

253 

217.0 

130.1 

14 

12.0 

07.2 

74 

63.538.0 

134 

114.9 

68.9 

194 

166.4 

99.7 

254 

217.9 

130.6 

15 

12.9 

07.7 

75 

64.338.6 

135 

115.8 

69.4 

195 

167.3 

100.2 

255 

218.7 

131.1 

16 

13.7 

08.2 

76 

65.239.1 

136 

116.6 

69.9 

196 

168.1 

100.8 

256 

219.6 

131.6 

17 

14.6 

08.7 

77 

66.039.6 

137 

117.5 

70.4 

197 

169.0 

101.3 

257 

220.4 

132.1 

18 

15.4 

09.3 

78 

66  940.1 

138 

118.4 

70.9    198 

169.8 

101.8 

258 

221.3 

132.6 

19 

16.3 

09.8 

79 

67.840.6 

139 

119.2 

71.5    199 

170.7 

102.3 

259 

222.2 

133.1 

20 

17.2 

10.3 

80 

68.641.1 

140 

120.1 

72.0   200 

171.5 

102.8 

260 

223.0 

133.7 

21 

18.0 

10.8 

81 

69.541.6 

141 

120.9 

72.5 

201 

172.4 

103.3 

261 

223.9 

134.2 

22 

18.9 

11.3 

82 

70.3 

42.1 

142 

121.8 

73  0 

202 

173.3 

103.8 

262 

224.7 

134.7 

23 

19.7 

11.8 

83 

71.2 

42.7 

143 

122.7 

73.5 

203 

174.1 

104.4 

263 

225.6 

135.2 

24 

•20.6 

12.3 

84 

72.0 

43.2 

144 

123.5 

74.0 

204 

175.0 

104  9 

264 

226.4 

135.7 

25 

21.4 

12.9 

85 

72.943.7 

145 

124.4 

74.5 

205 

175.8 

105.4 

265 

227.3 

136.2 

26 

22.3 

13  4 

86 

73.844.2 

146 

125.2 

75.1 

206 

176.7 

105.9 

266 

228.2 

136.7 

27 

23.2 

13.9 

87 

74.644.7 

147 

126.1 

75.6 

207 

177.5 

106.4 

267 

229.0 

137.3 

28 

24.0 

14.4 

88 

75.545.2 

148 

126  9 

76.1 

208 

178.4 

106.9 

268 

229.9 

137.8 

29 

24.9 

14.9 

89 

76.345.7 

149 

127.8 

76.6 

209 

179.3 

107.4 

269 

230  7 

138.3 

30 

25.7 

15.4 

90 

77.2 

46.3 

150 

128.7 

77.1 

210 

180.1 

108.0 

270 

231.  t 

138.8 

31 

•26.6 

15.  i/ 

91 

78.1 

46.8 

151 

129.5 

77.6 

kill 

181.0 

108.5 

271 

232.4 

139.3 

32 

27.4 

16.5 

92 

78.947.3 

152 

130.4 

78.1 

212 

181.8 

109.0 

272 

233.3 

139.8 

33 

•28.3 

17.0 

93 

79.8 

47.8 

153 

131.2 

78.7 

213 

182.7 

109.5 

273 

234.2 

140.3 

34 

29.2 

17.5 

94 

80.6 

48  3 

154 

132.1 

79.2 

214 

183.5 

110.0 

274 

235.0 

140.9 

35 

30.0 

18.0 

95 

81.5 

48.8 

155 

132.979.7 

215 

184.4 

110.5 

275 

235.9 

141.4 

3o 

30.9 

18.5 

96 

82.3 

49.3 

156 

133.8|80.2 

216 

185.3 

111.0 

276 

236.7 

141.9 

37 

31.7 

19.0 

97 

83.2 

49.9 

157 

134.7 

80.7 

217 

186.1 

111  6 

277 

237.6 

142.4 

38 

32.6 

19.5 

98 

84.1 

50.4 

158 

135.5 

81.2 

218 

187.0 

112.1 

278 

238.4 

142.9 

39 

33.5 

20.1 

99 

84.9 

50.9 

159 

136.4 

81.7 

219 

187.8 

112.6 

279 

239.3 

143.4 

40 

34.3 

20.6 

100 

85.8 

51.4 

160 

137.2 

82.3 

220 

188.7 

113.1 

280 

240.2 

143.9 

41 

35.2 

21.1 

101 

86.6'51.9 

161 

138.1 

82.8 

221 

189.6 

113.6 

281 

241.0 

144.5 

42 

36.0 

21.6 

102 

87.5 

52.4 

162 

138.9  83.3 

222 

190.4 

114.1 

282 

241.9 

145.0 

43 

36.9 

22.1 

103 

88.3 

52.9 

163 

139.8 

83.8 

223 

191.3 

114.6 

283 

242.7 

145.5 

44 

37.7 

22.6 

104 

89.2 

53.5 

164 

140.7 

84.3 

224 

192.1 

115.2 

284 

243.6 

146.0 

45 

38.6 

23.1 

105 

90.1 

54.0 

165 

141.5 

84.8 

225 

193.0 

115.7 

285 

244.4 

146.5 

46 

39.5 

23.6 

106 

90.9 

54.5 

166 

142.4 

85.3 

228 

193.8 

116.2 

286 

245.3 

147.0 

47 

40.3 

24.2 

107 

91.8 

55.0 

167 

143  2 

85.8 

227 

194.7 

116.7 

287 

246.2 

147.5 

48 

41.2 

24.7 

108 

92.6 

55.5 

168 

144.1 

86.4 

228 

195.6 

117.2 

288 

247.0 

148.1 

49 

42.0 

25.2 

109 

93.5 

56.0 

169 

145.0 

86.9 

229 

196.4 

117  7 

289 

247.9 

148.6 

50 

42  9 

25.7 

110 

94.3 

56.5 

170 

145.8 

87.4 

230 

197.3 

118.2 

290 

248.7 

149.1 

51 

43.7 

•26.2 

111 

95.2 

57.1 

171 

146.7 

87.9 

231 

198  1 

118.8 

291 

249.6 

149.6 

52 

44.6 

26.7 

112 

96.1 

57.6 

172 

147.5 

88.4 

232 

199.0 

119  3 

292 

250  5 

150.1 

53 

45.5 

27.2 

113 

96.9 

58.1 

173 

148.4 

88.9 

233 

199.8 

119.8 

293 

251.3 

150.6 

54 

46.3 

27.8 

114 

97.8 

58.6 

174 

149.2 

89.4 

234 

200.7 

120.3 

294 

252.2 

151.1 

55 

47  2 

28.3 

115 

98.6 

59.1 

175 

150.1 

90.0 

235 

201.6 

120.8 

295 

253.0 

151.7 

56 

48.0 

28.8 

116 

99.5 

59.6 

176 

151.0 

90.5 

236 

202.4 

121.3 

296 

253.9 

152.2 

57 

48.9 

29  3 

117 

100.4 

60.1 

177 

151.8 

91.0 

237 

203.3 

121.8 

297 

254.7 

152.7 

58 

49.7 

29.8 

118 

101.2 

60.7 

178 

152.7 

91.5 

238 

204.1 

122.4 

298 

255.6 

153.2 

59 

50.6 

30.3 

119 

102.1 

61.2 

179 

153.5 

92.0 

239 

205.0 

122.9 

299 

256.5 

153.7 

60 

51.5 

30.8 

120 

102.9 

61.7 

180 

154.4 

92.5 

240 

205.9 

123.4 

300 

257.3 

154.2 

[list. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  5J  Points. 

TABLE  III.                                          199 

DIFFERENCE   OF    LATITUDE    AND   DEPAETUKE   FOR   3    POINTS. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

l 

00.8 

00.6 

61 

50.7 

33.9 

121 

100.6 

67.2 

181 

150.5 

100.6 

241 

200.4 

133.9 

2 

01.7 

01.1 

62 

51.5 

34.4 

122 

101.4 

67.8 

182 

151.3 

101.1 

242 

201.2 

134.4 

3 

02.5 

01.7 

63 

52.4 

35.0 

123 

102.3 

68.3 

183 

152.2 

101.7 

243 

202.0 

135.0 

4 

03.3 

02.2 

64 

53.2 

35.6 

124 

103.1 

68.9 

184 

153.0 

102.2 

244 

202.9 

135.6 

5 

04.2 

02.8 

65 

54.0 

36.1 

125 

103.9 

69.4 

185 

153.8 

102.8 

245 

203.7 

136.1 

6 

05.0 

03.3 

66 

54.9 

36.7 

126 

104.8 

70.0 

186 

154.6 

103.3 

246 

204.5 

136.7 

7 

05.8 

03.9 

67 

55.7 

37  2 

127 

105.6 

70.6 

187 

155.5 

103.9 

247 

205.4 

137.2 

8 

06.7 

04.4 

68 

56.5 

37.8 

128 

106.4 

71.1 

188 

156.3 

104  4 

248 

206.2 

137.8 

9 

07.5 

05.0 

69 

57.4 

38.3 

129 

107.3 

71.7 

189 

157.1 

105.0 

249 

207.0 

138.3 

10 

08.3 

05.6 

70 

58.2 

38.9 

130 

108  1 

72.2 

190 

158.0 

105.6 

250 

207.9 

138  9 

11 

09.1 

06.1 

71 

59.0 

39.4 

131 

108.9 

72.8 

191 

158.8 

106.1 

251 

2U8.7 

139.4 

12 

10.0 

06.7 

72 

59.9 

40.0 

132 

109.7 

73.3 

192 

159.6 

106.7 

25* 

209.5 

140.0 

13 

10.8 

07.2 

73 

60.7 

40.6 

133 

110.6 

73.9 

193 

160.5 

107.2 

253 

210.4 

140.6 

14 

11.6 

07.8 

74 

61.5 

41.1 

134 

111.4 

74.4 

194 

161.3 

107.8 

254 

211.2 

141.1 

15 

12.5 

08.3 

75 

62.4 

41.7 

135 

112.2 

75.0 

195 

162.1 

108.3 

255 

212.0 

141.7 

16 

13.3 

08.9 

76 

63.2 

42.2 

136 

113.1 

75.6 

196 

163.0 

108.9 

256 

212.9 

142.2 

17 

14.1 

09  4 

77 

64.0 

42.8 

137 

113.9 

76.1 

197 

163.8 

109.4 

257 

213.7 

142.8 

18 

15.0 

10.0 

78 

64.8 

43.3 

138 

114  7 

76.7 

198 

164.6 

110.0 

258 

214.5 

143.3 

19 

15  8 

10.6 

79 

65.7 

43.9 

139 

115.6 

77  2 

199 

165.5 

110.  61 

259 

215.3 

143.9 

20 

16.6 

11.1 

80 

66.5 

44.4 

140 

116.4 

77.8 

200 

166.3 

111.1 

260 

216.2 

144.4 

21 

17.5 

11.7 

81 

67.3 

45.0 

141 

117.2 

78.3 

201 

ib7.1 

111.7 

261 

217.0 

145.0 

22 

18.3 

12  2 

82 

68.2 

45.6 

142 

118.1 

78.9 

202 

168.0 

112.2 

262 

217.8 

145.6 

23 

19.1 

12.8 

83 

69.0 

46.1 

143 

118  9 

79.4 

203 

168.8 

112.8 

263 

218.7 

146.1 

24 

20.0 

13.3 

84 

69.8 

46.7 

144 

119.7 

80.0 

204 

169.6 

113.3 

264 

219.5 

146.7 

25 

20.8 

13.9 

85 

70.7 

47.2 

145 

120.6 

80.6 

205 

170.4 

113.9 

265 

220.3 

147.2 

26 

21.6 

14.4 

86 

71.5 

47.8 

146 

121.4 

81.1 

206 

171.3 

114.4 

266 

221.2 

147.8 

27 

22.4 

15.0 

87 

72.3 

48.3 

147 

122.2 

81.7 

207 

172.1 

115.0 

267 

222.0 

148.3 

28 

23.3 

15.6 

88 

73.2 

48.9 

148 

123.1 

82.2 

208 

172.9 

115.6 

268 

222.8 

148  9 

29 

24.1 

16.1 

89 

74.0 

49.4 

149 

123  9 

82.8 

209 

173.8 

116.1 

269 

223.7 

149.4 

30 

24.9 

16.7 

90 

74.8 

50.0 

150 

124.7 

83.3 

210 

174.6 

116.7 

270 

224.5 

150.0 

31 

2o.8 

17.2 

91 

75.7 

50.6 

151 

125.5 

83.9 

211 

175.4 

117.2 

271 

225.3 

160.6 

32 

26.6 

17.8 

92 

76.5 

51.1 

152 

126.4 

84.4 

212 

176.3 

117.8 

27i 

226.2 

151.1 

33 

27.4 

18.3 

93 

77.3 

51.7 

153 

127.2 

85.0 

213 

177.1 

118.3 

273 

227.0 

151.7 

34 

28.3 

18.9 

94 

78.2 

52.2 

154 

128.0 

85.6 

214 

177.9 

118.9 

274 

227.8 

152.2 

35 

29.1 

19.4 

95 

79.0 

52.8 

155 

128.9 

86.1 

215 

178.8 

119.4 

275 

228.6 

152.8 

36 

29.9 

20.0 

96 

79.8 

53.3 

156 

129.7 

86.7 

216 

179.6 

120.0 

276 

229.5 

153.3 

37 

30.8 

20.6 

97 

80.6 

53.9 

157 

130.5 

87.2 

217 

180.4 

120.6 

277 

230.3 

153.9 

38 

31.6 

21.1 

98 

81.5 

54.4 

158 

131.4 

87.8 

218 

181.3 

121.1 

278 

231.1 

l-r)4.4 

39 

32.4 

21  7 

99 

82.3 

55.0 

159 

132.2 

88.3 

219 

182.1 

121.7 

279 

232.0 

155.0 

40 

33.3 

22.2 

100 

83.1 

55.6 

160 

133.0 

88.9 

220 

182.9 

122.2 

280 

232.8 

155.6 

41 

34.1 

22.8 

101 

84.0 

56.1 

1U1 

133.9 

89.4 

221 

183.7 

122.8 

281 

233.6 

156.1 

42 

34.9 

23.3 

102 

84.8 

56.7 

162 

134.7 

90.0 

222 

184.6 

123.3 

282 

234.5 

156.7 

43 

35.8 

23.9 

103 

85.6 

57.2 

163 

135.5 

90.6 

223 

185.4 

123.9 

283 

235.3 

157.2 

44 

36.6 

24.4 

104 

86.5 

57.8 

164 

136.4 

91.1 

224 

186.2 

124.4 

284 

236.1 

157.8 

45 

37.4 

25.0 

105 

87.3 

58.3 

165 

137.2 

91.7 

225 

187.1 

125  0 

285 

237.0 

158.3 

46 

38.2 

25.6 

106 

88.1 

58.9 

166 

138.0 

92.2 

226 

187.9 

125.6 

286 

237.  fe 

158.9 

47 

39.1 

26.1 

107 

89.0 

59.4 

167 

138  9 

92.8 

227 

188.7 

126.1 

287 

238.6 

159.4 

48 

39.9 

26.7 

108 

89.8 

60.0 

168 

139.7 

93.3 

228 

189.6 

126.7 

288 

239.5 

160.0 

49 

40.7 

27.2 

109 

90.6 

60.6 

169 

140.5 

93.9 

229 

190.4 

127.2 

289 

240.3 

160.6 

50 

41.6 

27.8 

110 

91.5 

61.1 

170 

141.3 

94.4 

230 

191.2 

127.8 

290 

241.1 

161.1 

51 

42  4 

28.3 

111 

92.3 

61.7 

171 

142.2 

95.0 

231 

192.1 

128.3 

291 

242.0 

161.7 

52 

43.2 

28.9 

112 

93.1 

62.2 

172 

143.0 

95.6 

232 

192.9 

128.9 

292 

242  8 

162.2 

53 

44.1 

29.4 

113 

94.0 

62.8 

173 

143.8 

96.1 

233 

193.7 

129.4 

293 

243.6 

162.8 

54 

44.9 

30.0 

114 

94.8 

63.3 

174 

144.7 

96.7 

234 

194.6 

130.0 

294 

244.4 

163.3 

55 

45.7 

30.6 

115 

95.6 

63.9 

175 

145.5 

97.2 

235 

195.4 

130.6 

295 

245.3 

163.9 

56 

46.6 

31.1 

116 

96.4 

64.4 

176 

146.3 

97.8 

236 

196.2 

131.1 

296 

246  1 

164.4 

57 

47.4 

31.7 

117 

97.3 

65.0 

177 

147.2 

98.3 

237 

197.1 

131.7 

297 

246.9 

165.0 

58 

48.2 

32.2 

118 

98.1 

65  6 

178 

148.0 

98.9 

238 

197.9 

132.2 

298 

247.8 

165.6 

59 

49.1 

32.8 

119 

98  9 

66.1 

179 

148.8 

S9.4 

239 

198.7 

132.8 

299 

248.6 

166.1 

60 

49  9 

33.3 

120 

99.8 

66.7 

180 

149.7 

100.0 

240 

199.5 

133.3 

300 

249.4 

166.7 

Dist. 

Dep 

Lat. 

Dist. 

Dep 

Lat. 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  5  Points. 

—  •  1 

200                                         TABLE  III. 

DIFFERENCE    OF    LATITUDE    AND    DEPARTURE   FOR   3J   POINT. 

Hist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.8 

00.6 

61 

49.0 

36  3 

121 

97.2 

72.1 

181 

145.4 

107.8 

241 

193.6 

143.6 

2 

01.6 

01.2 

62 

49.836.9 

122 

98.0 

72.7 

182 

146.2 

108.4 

242 

194.4 

144.2 

3 

02.4 

01.8 

63 

50.637.5 

123 

98.8 

73.3 

183 

147.0 

109.0 

243 

195.2 

144.8 

4 

03.2 

02.4 

64 

51.438J 

124 

99.6 

73.9 

184 

147.8 

109.6 

244 

196.0 

145.4 

5 

04.0 

03  0 

65 

52.238.7 

125 

100.4 

74.5 

185 

14*.  6 

110.2 

245 

196.8 

146  0 

6 

04.8 

03.6 

66 

53.039  3 

126 

101.2 

75.1 

186 

149  4 

110.8 

24.6 

197.6 

146.5 

7 

05.6 

04.2 

67 

53.839.9 

127 

102.0 

75.7 

187 

150.2 

111.4 

247 

198  4 

147.1 

8 

06.4 

04.8 

68 

54.640.5 

128 

102.8 

76.3 

188 

151.0 

112.0 

248 

199  2 

147.7i 

9 

07.2 

05.4 

69 

55.441.1 

129 

103.6 

76.9 

189 

151.8 

112.6 

249 

200.0 

148.3 

10 

08.0 

06  0 

70 

56.241.7 

130 

104.4 

77.4 

190 

152.6 

113.2 

250 

200.8 

148.9 

11 

08.8 

06.6 

71 

57.042.3 

131 

105.2 

78  0 

191 

153.4 

113.8 

251 

201.6 

149.0 

12 

09.6 

07.1 

72 

57.842.9 

132 

106.0 

78.6 

192 

154.2 

114.4 

252 

202.4 

150.1 

13 

10.4 

07.7 

73 

58.6*43.5 

133 

106.8 

79.2 

193 

155.0 

115.0 

253 

203.2 

150.7 

14 

11.2 

08.3 

74 

59.444.1 

134 

107  6 

79.8 

194 

155.8 

115.6 

254 

204.0 

151.3 

15 

12.0 

u8.9 

75 

60.244.7 

135 

108.4 

80.4 

195 

156.6 

116.2 

255 

204.8 

151  9 

16 

12.9 

09.5 

76 

61.045.3 

136 

109.2 

81.0 

196 

157.4 

116.8 

256 

205  6 

152.5 

17 

13.7 

10.1 

77 

01.845.9 

137 

110.0 

81.6 

197 

158.2 

117.4 

257 

206.4 

153.1 

18 

14.5 

10.7 

78 

62.646.5 

138 

110.8 

82.2 

198 

159.0 

118.0 

258 

207.2 

153.7 

19 

15.3 

11.3 

79 

63.447.1 

139 

111.6 

82.8 

199 

159.8 

118.5 

259 

208  0 

154.3 

20 

16.1 

11.9 

80 

64.347.7 

140 

112.4 

83.4 

200 

160.6 

119.1 

260 

208  8 

154.9 

21 

16.9 

12.5 

81 

65.148.3 

141 

113.2 

84.0 

201 

161.4 

119.7 

261 

209.6 

155.5 

22 

17.7 

13  1 

82 

65.948.9 

142 

114.0 

84.6 

202 

162.2 

120.3 

262 

210.4 

156.1 

23 

18.5 

13.7 

83 

66.749.4 

143 

114.9 

85.2 

203 

163.0 

120.9 

263 

211.2 

156.7 

24 

19.3 

14  3 

84 

67.550  0 

144 

115.7 

85.8 

204 

163.9 

121.5 

264 

212.0 

157.3 

25 

20.1 

14.9 

85 

68.350.6 

145 

116.5 

86.4 

205 

164.7 

122.1 

265 

212.8 

157.9 

26 

20.9 

15.5 

86 

69.151.2 

146 

117.3 

87.0 

206 

165.5 

122.7 

266 

213.6 

158.5 

27 

21.7 

16.1 

87 

69.9151.8 

147 

118.1 

87.6 

207 

166.3 

123.3 

267 

214.5 

159.1 

28 

22.5 

16.7 

88 

70.752.4 

148 

118.9 

88.2 

208 

167.1 

123.9 

268 

215.3 

159  6 

29 

23.3 

17.3 

89 

71.5 

53.0 

149 

119.7 

88.7 

209 

167.9 

124.5 

269 

216.1 

160.2 

30 

24.1 

17.9 

90 

72.3 

53.6 

150 

120.5 

89.4 

210 

168.7 

125.1 

270 

216.9 

160.8J 

31 

24.9 

18^ 

91 

73.1 

54.2 

151 

121.3 

90.0 

211 

109.5 

125.7 

271 

217.7 

161.4 

32 

25.7 

19.1 

92 

73.9 

54.8 

152 

122.1 

90.5 

212 

170.3 

126.3 

272 

218.5 

162.0 

33 

26.5 

19.7 

93 

74.7 

55.4 

153 

122.9 

91.1 

213 

171.1 

126.9 

273 

219  3 

162.6 

34 

27.3 

20.3 

94 

75.5 

56.0 

154 

123.7 

91.7 

214 

171.9 

127.5 

274 

220.1 

163.2 

35 

28.1 

20.9 

95 

76.3 

56.6 

155 

124.5 

92.3 

215 

172.7 

128.1 

275 

220.9 

163.8 

36 

28.9 

21.4 

96 

77.1 

57.2 

156 

125.3 

92.9 

216 

173.5 

128.7 

276 

221.7 

164.4 

37 

29.7 

22.0 

97 

77.9 

57.8 

157 

126.1 

93  5 

217 

174.3 

129.3 

277 

222.5 

165.0 

38 

30.5 

22.6 

98 

78.7 

58.4 

158 

126.9 

94.1 

218 

175.1 

129.9 

278 

223.3 

165.6 

39 

31.3 

23.2 

99 

79.5 

59.0 

159 

127.7 

94.7 

219 

175.9 

130.5 

279 

224.1 

166.2 

40 

32.1 

23.8 

100 

80.3 

59.6 

160 

128.5 

95.3 

220 

176.7 

131.1 

280 

224.9 

168.8 

41 

32.9 

24.4 

101 

81.1 

60.2 

161 

129.3 

95.9 

221 

177.5 

131.7 

281 

225.7 

167.4 

42 

33.7 

25.0 

102 

81.9 

60.8 

162 

130.1 

96.5 

222 

178.3 

132.2 

282 

226-5 

168.0 

43 

34  L 

25.6 

103 

82.7 

61.4 

163 

130.9 

97.1 

223 

179.1 

132.8 

283 

227.3 

168.6 

44 

35.3 

26.2 

104 

83.5 

62.0 

164 

131.7 

97.7 

224 

179.9 

133.4 

284 

228J 

169.2 

45 

36.1 

26  8 

105 

84.3 

62.6 

165 

132.5 

98.3 

225 

180.7 

134.0 

285 

228.9 

169.8 

46 

36.9 

27.4 

106 

85.1 

63.1 

166 

133.3 

98  9 

226 

181.5 

134.6 

286 

229.7 

170.4 

47 

37.7 

28.0 

107 

85.9 

63.7 

167 

134  1 

99.5 

227 

182.3 

135.2 

287 

230.5 

171.0 

48 

38.6 

28.6 

108 

86.7 

64.3 

168 

134.9 

100.1 

228 

183.1 

135.8 

288 

231.3 

171.6 

49 

39.4 

29.2 

109 

87.5 

64.9 

169 

135.7 

100.7 

229 

183.9 

136.4 

289 

232.1 

172.2 

50 

40.2 

29.8 

110 

88.4 

65.5 

170 

136.5 

101.3 

230 

184.7 

137.0 

290 

232.9 

172.8 

51 

41.0 

30.4 

111 

89.2 

66.1 

171 

137.3 

101.9 

231 

185.5 

137.6 

291 

233.7 

173.3 

52 

41.8 

31.0 

112 

90.0 

66.7 

172 

138.1 

102.5 

232 

186.3 

138.2 

292 

234.5 

173.9 

53 

42.6 

31.6 

113 

90.8 

67.3 

173 

138.9 

103.1 

233 

187.1 

138.8 

293 

235.3 

174.5 

54 

43.4 

32.2 

114 

91.6 

67.9 

174 

139.8 

103.7 

234 

187.9 

139.4 

294 

236.1 

175.1 

55 

44.2 

32.8 

115 

92.4 

68.5 

175 

140.6 

104.2 

235 

188.8 

140.0 

295 

236.9 

175.7 

56 

45.0 

33.4 

116 

93.2 

69.1 

176 

141.4 

104.8 

236 

189.6 

140.6 

296 

237.7 

176.3 

57 

45.8 

34.0 

117 

94.0 

69.7 

177 

142.2 

105.4 

237 

190.4 

141.2 

297 

238.5 

176.9 

58 

46.6 

34.6 

118 

94.8 

70.3 

178 

143.0 

106.0 

238 

191.2 

141.8 

298 

239.4 

177.5 

59 

47.4 

35.1 

119 

95.6 

70.9 

179 

143.8 

106.6 

239 

192.0 

142.4 

299 

240.2 

178.1 

60 

48.2 

35.7 

120 

96.4 

71.5 

180 

144.6 

107.2 

240 

192.8 

143.0 

300 

241.0 

178.7 

Dist. 

Dep 

Lat. 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  4f  Points. 

TABLE  III.                                          201 

DIFFERENCE   OF    LATITUDE   AND   DEPARTURE  FOR  3^  POINTS. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat, 

Dep. 

l 

00.8 

00.6 

61 

47.138.7 

121 

93.5 

76.8 

181 

139.9 

114.8 

241 

186.3 

152.9 

2 

01.5 

01.  b 

62 

47.9 

39.3 

122 

94.3 

77.4 

182 

140.7 

115.5 

242 

187.1 

153.5 

3 

02.3 

01.9 

63 

48.7 

40  0 

123 

95.1 

78.0 

183 

141.5 

116.1 

243 

187.8 

154.2 

4 

03.1 

02.5 

64 

49.5 

40.6 

124 

95.8 

78.7 

184 

142.2 

116.7 

244 

188.6 

154  8 

5 

03.9 

03.2 

65 

50.2 

41.2 

125 

96.6 

79.3 

185 

143.0 

117.4 

245 

189.4 

155.4 

6 

04.6 

03.8 

66 

51.0 

41.9 

126 

97.4 

79.9 

186 

143.8 

118.0 

246 

190.2 

156.1 

7 

05.4 

04.4 

67 

51.8 

42.5 

127 

98.2 

80.6 

187 

144.5 

118.6 

247 

190.9 

156.7 

8 

06.  2 

05.1 

68 

52.6 

43.1 

128 

98.9 

81.2 

188 

145.3 

119.3 

248 

191.7 

157.3 

9 

07.0 

05.7 

69 

53.3 

43.8 

129 

99.7 

81.8 

189 

146.1 

119.9 

249 

192.5 

158.0 

10 

07.7 

06.3 

70 

54.1 

44.4 

130 

100.5 

82.5 

190 

146.9 

120.5 

250 

193.2 

158.6 

il- 

08.5 

07.0 

71 

54.9 

45.0 

131 

101.3 

83.1 

191 

147.6 

121.2 

251 

194.  U 

159.  ii 

ia 

09.3 

07.6 

72 

55.7 

45.7 

132 

102.0 

83.7 

192 

148.4 

121.8 

25'2 

194.8 

159.9 

13 

10.0 

08  2 

73 

56.4 

46.3 

133 

102.8 

84.4 

193 

149.2 

122.4 

253 

195.6 

160.5 

14 

10.8 

08.9 

74 

57.2 

46.9 

134 

103.6 

85.0 

194 

150  0 

123.1 

254 

196.3 

161.1 

15 

11.6 

09.5 

75 

58.0 

47.6 

135 

104.4 

85.6 

195 

150.7 

123.7 

255 

197.1 

161.8 

16 

12.4 

10.1 

76 

58.7 

48.2 

136 

105.1 

86.3 

196 

151.5 

124.3 

256 

197.9 

162.4 

17 

13.1 

10.8 

77 

59.5 

48.8 

137 

105.9 

86.9 

197 

152.3 

125.0 

257 

198.7 

163.0 

18 

13.9 

11.4 

78 

60.3 

49.5 

138 

106.7 

87.5 

198 

153.1 

125.6 

258 

199.4 

163.7 

19 

14.7 

12.0 

79 

61.1 

50  1 

139 

107.4 

88.2 

199 

153.8 

126.2 

259 

200.2 

164.3 

20 

15.5 

12.7 

80 

61.8 

50.7 

140 

108.2 

88.8 

200 

154.6 

126.9 

260 

201.0 

164.9 

21 

16.2 

13.  b 

81 

62.6 

51.4 

141 

109.0 

89.4 

201 

155.4 

127.5 

261 

201.8 

165.6 

22 

17.0 

14.0 

82 

63.4 

52.0 

142 

109.8 

90.1 

202 

156.1 

128.1 

262 

202.5 

166.2 

23 

17.8 

14.6 

83 

64.2 

52.7 

143 

110.5 

90.7 

203 

156.9 

128.8 

263 

203.3 

166.8 

24 

18.  C 

15.2 

84 

64.9 

53.3 

144 

111.3 

91.3 

204 

157.7 

129.4 

264 

204.1 

167.5 

25 

19.3 

15.9 

8565.7 

53.9 

145 

112.1 

92.0 

205 

158.5 

130.0 

265 

204.8 

168.1 

26 

20.1 

16.5 

86 

36.5 

54.6 

146 

112.9 

92.6 

206 

159.2 

130.7 

266 

205.6 

168.7 

27 

20.9 

17.1 

87 

67.2 

55.2 

147 

113.6 

93.3 

207 

160.0 

131.3 

267 

206.4 

169.4 

28 

21.6 

17.8 

88 

38.0 

55.8 

148 

114.4 

93.9 

208 

160.8 

132.0 

268 

207.2 

170.0 

29 

22.4 

18.4 

89 

68.8 

56.5 

149 

115.2 

94.5 

209 

161.6 

132.6 

269 

207.9 

170.6 

30 

23.2 

19.0 

90 

69.6 

57.1 

150 

115.9 

95.2 

210 

162.3 

133.2 

270 

208.7 

171.3 

31 

24.0 

19,7 

91 

70.3 

57.7 

151 

116.7 

95.8 

211 

163.1 

133.9 

271 

209.5 

171.9 

32 

24.7 

20.3 

92 

71.1 

58.4 

152 

117.5 

96.4 

212 

163.9 

134.5 

272 

*210.3 

172.6 

33 

25.5 

20.9 

93 

71.9 

59.0 

153 

118.3 

•   97.1 

213 

164.6 

135.1 

273 

211.0 

173.2 

34 

26.3 

21.6 

94 

72.7 

59.6 

154 

119.0 

97.7 

214 

165.4 

135.8 

274 

211.8 

173.8 

35 

27.1 

22.2 

95 

73.4 

60.3 

155 

119.8 

98.3 

215 

166.2 

136.4 

275 

212.6 

174.5 

36 

27.8 

22.8 

96 

74.2 

60.9 

156 

120.6 

99.0 

216 

167.0 

137.0 

276 

213.3 

175.1 

37 

28.6 

23.5 

97 

75.0 

61.5 

157 

121.4 

99.6 

217 

167.7 

137.7 

277 

214.1 

175.7 

38 

29.4 

24.1 

98 

75.7 

62.2 

158 

122.1 

100.2 

218 

168.5 

138.3 

278 

214.9 

176.4 

39 

30.1 

24.7 

99 

76.5 

62.8 

159 

122.9 

100.9 

219 

169.3 

138.9 

279 

215.7 

177.0 

40 

30.9 

25.4 

100 

77.3 

63.4 

160 

123.7 

101.5 

220 

170.1 

139.6 

280 

216.4 

177.6 

41 

31.7 

26.0 

101 

78.1 

64.1 

161 

124.4 

102.1 

221 

170.8 

140.2 

281 

217.2 

178.3 

42 

32.5 

26.6 

102 

78.8 

64.7 

162 

125.2 

102.8 

222 

171.6 

140.8 

282 

218.0 

178.9 

43 

33.2 

27.3 

103 

79.6 

65.3 

163 

126.0 

103.4 

223 

172.4 

141.5 

283 

218.8 

179.5 

44 

34.0 

27.9 

104 

80.4 

66.0 

164 

126.8 

104  0 

224 

173.1 

142.1 

284 

219.5 

180.2 

45 

34.8 

28.5 

10o|81.2 

66.6 

165 

127.5 

104.7 

225 

173.9 

142.7 

285 

220.3 

180.8 

46 

35.6 

29.2 

106 

81.9 

67.2 

166 

128.3 

105  3 

226 

174.7 

143.4 

286 

221.1 

181.4 

47 

36.3 

29.8 

107 

82.7 

67.9 

167 

129.1 

105.9 

227 

175.5 

144.0 

287 

221.8 

182.1 

48 

37.1 

30.4 

108 

83.5 

68.5 

168 

129.  a 

106.6 

228 

176.2 

144.6 

288 

222.6 

182.7 

49 

37.9 

31.1 

109 

84.3 

69.1 

169 

130.6 

107.2 

229 

177.0 

145.3 

289 

223.4 

183.3 

50 

38.6 

31.7 

110 

85.0 

69.8 

170 

131.4 

107.8 

230 

177.8 

145.9 

290 

224.2 

184.0 

51 

39.4 

32.3 

111 

85.8 

70.4 

171 

132.2 

108.5 

231 

178.6 

146.5 

291 

224.9 

184.6 

52 

40.2 

33.0 

112 

86.6 

71.0 

172 

133.0 

109.1 

232 

179.3 

147.2 

292 

225.7 

185.2 

53 

41.0 

33.6 

113 

87.3 

71.7 

173 

133.7 

109.7 

233 

180.1 

147.8 

293 

226.5 

185.9 

54 

41.7 

34.3 

114 

88.1 

72.3 

174 

134.5 

110.4 

234 

180.9 

148.4 

294 

227.3 

186.5 

55 

42.5 

33.9 

115 

88.9 

73.0 

175 

135.3 

111.0 

235 

181.7 

149.1 

295 

228.0 

187.1 

56 

43.3 

35.5 

116 

89.7 

73.6 

176 

136.0 

111.6 

236 

182.4 

149.7 

296 

228.8 

187.8 

57 

44.1 

36.2 

117 

90.4 

74.2 

177 

136.8 

112.3 

237 

183.2 

150.3 

297 

229.6 

188.4 

58 

44.8 

36.8 

118 

91.2 

74.9 

178 

137.6 

112.9 

238" 

184.0 

151.0 

298 

230.4 

189.0 

59 

45.6 

37.4 

119 

92.0 

75.5 

179 

138.4 

113.6 

239 

184.7 

151.6 

299 

231.1 

189.7 

60 

46.4 

38.1 

120 

92.8 

76.1 

180 

139.1 

114.2 

240 

185.5 

152.3 

300 

231.9 

190.3 

Dist. 

Dep 

Lat. 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

For  4£  Points. 

202 

TABLE  III. 

DIFFERENCE 

OF    LATITUDE    AND    DEPARTURE    FOR    3f    POINT. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep  Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

l 

00.7 

00.7 

61 

45.2 

41.1 

121 

80.6 

81.3 

181 

134.1 

121.5 

241 

178.6 

161.8 

2 

01.5 

01.3 

6i 

45.9 

41.6 

122 

90.4 

81.9 

182 

134.8 

122.2 

242 

179.3 

162.5 

3 

02.2 

02.0 

63 

46.7 

42.3 

123 

91.1 

82.6 

183 

135.6 

122.9 

243 

180.0 

163.2 

4 

03.0 

02.7 

64 

47.4 

43.0 

124 

91.9 

83.3 

184 

136.3 

123.6 

244 

180.8 

163.8 

5 

03.7 

03.4 

6548.2 

43.6 

125 

92.6 

83.9 

185 

137.1 

124.2 

245 

181.5 

164.5 

6 

04.4 

04.0 

6648.9 

44.3 

126 

93.4 

84.6 

186 

137.8 

124.9 

246 

182.3 

165.2 

7 

05.2 

04.7 

6749.6 

45.0 

127 

94.1 

85.3 

187 

138.6 

125.6 

247 

183.0 

165.9 

8 

05.9 

05.4 

6850.4 

45.7 

128 

94.8 

86.0 

188 

139.3 

126.2 

248 

183.8 

166.5 

9 

06.7 

06.0 

6951.1 

46.3 

129 

95.6 

86.6 

189 

140.0 

126.9 

249 

184.4 

167.2 

10 

U7.4 

06.7 

7051.947.0 

130 

96.3 

87.3 

190 

140.8 

127.6 

250 

185.2 

167.9 

11 

08.2 

07.4 

71j52.647.7 

131 

97.1 

88.0 

191 

141.5 

128.3 

251 

186.0 

108.5 

12 

08.9 

08.1 

7253.348.3 

132 

97.8 

88.6 

192 

142.3 

128.9 

252 

186.7 

169.2 

13 

09.6 

08.7 

7354.149.0 

133 

98.5 

89.3 

193 

143.0 

129.6 

253 

187.5 

169.9 

14 

10.4 

09.4 

7454.  849.  7i 

134 

99.3 

90.0 

194 

143.7 

130.3 

254 

188.2 

170.6 

15 

11.1 

10.1 

7555.650.4 

135 

100.0 

90.7 

195 

144.5 

130.9 

255 

188.9 

171.2 

16 

11.9 

10.7 

7656.351.0 

136 

100.8 

91.3 

196 

145.2 

131.6 

256 

189.7 

171.9 

17 

12.6 

11.4 

7757.051.7 

137 

101.5 

92.0 

197 

146.0 

132.3 

257 

190.4 

172.6 

18 

13.3 

12.1 

78,77.852.4 

138 

102.2 

92.7 

198 

146.7 

133.0 

258 

191.2 

173.2 

19 

14.1 

12.8 

7958.553.0 

139 

103.0 

93.3 

199 

147.4 

133.6 

259 

191.9 

173.9 

20 

14.8 

13.4 

8059.353.7 

140 

103.7 

94.0 

200 

148.2 

134.3 

260 

192.6 

174.6 

21 

15.6 

14.1 

8160.054.4 

141 

104.5 

94.7 

201 

148.9 

135.0 

261 

193.4 

175.3 

22 

16.3 

14.8 

8260.8,55.1; 

142 

105  2 

95.4 

202 

149.7 

135.6 

262 

194.1 

175.9 

23 

17.0 

15.4 

8b61.5:55.7j 

143 

106.0 

96.0 

203 

150.4 

136.3 

263 

194.8 

176.6 

24 

17.8 

16.1 

8462.256.4 

144 

106.7 

96.7 

204 

151.1 

137.0 

264 

195.6 

177.3 

25 

18.5 

16.8 

8563.057.1 

145 

107.4 

97.4 

205 

151.9 

137.7 

265 

196.3 

178.0 

26 

19.3 

17.5 

8663.757.7 

146 

108.2 

98.0 

206 

152.6 

138.3 

266 

197.1 

178.6 

27 

20.0 

18.1 

8764.558.4 

147 

108.9 

98.7 

207 

153.4 

139.0 

267 

197.8 

179  3 

28 

20.7 

18.8 

8865.259.1 

148 

109.7 

99.4 

208 

154.1 

139.7 

268 

198.6 

180.0 

29 

21.5 

19.5 

8965.959.8 

149 

110.4 

100.1 

209 

154.9 

140.3 

269 

199.3 

180.6 

30 

•22.2 

20.1 

9066.760.4 

150 

111.1 

100.7 

210 

155.6 

141.0 

270 

200.1 

181.3 

31 

•23.0 

20.8 

91  67.  4)61.1 

151 

111.9 

101.4 

211 

156.3 

141.7 

271 

200.8 

182.0 

3-2 

23.7 

21.5 

9268.261.8 

152 

112.6 

102.1 

21'2 

157.1 

142.4 

272 

201.5 

182.7 

33 

24.4 

22.2 

93 

68.962.4 

153 

113.4 

102.7 

213 

157.8 

143.0 

273 

202.3 

183.3 

34 

25.2 

22.8 

94 

69.663.1 

154 

114.1 

103.4 

214 

158.6 

143.7 

274 

203.0 

184.0 

35 

25.9 

23.5 

95'(70.463.8    155 

114.8 

104.1 

215 

159.3 

144.4 

275 

203.8 

184.7 

36 

26.7 

24.2 

9671.164.51  156 

115.6 

104.8 

216 

160.0 

145.0 

276 

204.5 

185.3 

37 

27.4 

24.8 

9771.9 

65.1 

157 

116.3 

105.4 

217 

160.8 

145.7 

277 

205.2 

186.0 

38 

28.2 

25.o 

9872.6 

65.8 

158 

117.1 

106.1 

218 

161.5 

146.4 

278 

206.0 

186.7 

39 

28  9 

26.2 

9973.3 

66.5 

159 

117.8 

106.8 

219 

162.3 

147.1 

279 

206.7 

187.4 

40 

29.6 

26.9 

10074.  167A 

160 

118.5 

107.4 

220 

163.0 

147.7 

280 

207.5 

188.0 

41 

30.4 

27.5 

101 

74.867.8 

161 

119.3 

1U8.1 

221 

103.7 

148.4 

281 

i;08.2 

168.7 

42 

31.1 

28.2 

102 

75.668.5 

162 

120.0 

108.8 

222 

164.5 

149.1 

282 

208.9 

189.4 

43 

31.9 

28.9 

103 

76.  369.  L 

163 

120.8 

109.5 

223 

165.2 

149.7 

283 

209.7 

190.0 

44 

32.6 

29.5 

10477.169.8 

164 

121.5 

110.1 

224 

166.0 

150.4 

284 

210.4 

190.7 

45 

33.3 

30.2 

10577.870.5 

165 

122.3 

110.8 

225 

166.7 

151.1 

285 

211.2 

191.4 

46 

34.1 

30.  J 

10678.571.2 

166 

123.0 

111.5 

226 

167.4 

151.8 

286 

211.9 

192.1 

47 

34.8 

31.6 

10779.371.8 

167 

123.7 

112.1 

227 

168.2 

152.4 

287 

212.6 

192.7 

48 

35.6 

32.2 

10880.072.5 

168 

124.5 

112.8 

228 

168.9 

153.1 

288 

213.4 

193.4 

49 

36.3 

32.9 

10980.873.2 

169 

125.2 

113.5 

229 

169.7 

153.8 

289 

214.1 

194.1 

50 

37.0 

33.6 

11081.573.9 

170 

126.0 

114.2 

'230 

170.4 

154.5 

290 

214.9 

194.7 

51 

37.8 

34.2 

11182.274.5 

171 

126.7 

114.8 

231 

171.2 

155.1 

291 

215.0 

195.4 

52 

38.5 

34.9 

11283.075.2 

172 

127.4 

115.5 

232 

171.9 

155.8 

292 

216.4 

196.1 

53 

39.3 

35.6 

11383.775.9 

173 

128.2 

116.2 

233 

172.6 

156.5 

293 

217.1 

196.8 

54 

40.0 

36.3 

11484.576.5 

174 

128.9 

116.8 

234 

173.4 

157.1 

294 

217.8 

197.4 

55 

40.7 

36.9 

115 

85.277.2 

175 

129.7 

117.5 

235 

174.1 

157.8 

295 

218.6 

198.1 

56 

41.5 

37.6 

116 

85.977.9 

176 

130.4 

118.2 

236 

174.9 

158.5 

296 

219.3 

198.8 

57 

42.2 

38.3 

11786.778.6 

177 

131.1 

118.9 

237 

175.6 

159.1 

2S7 

220.1 

199.4 

58 

43.0 

38.9 

11887  479.2 

178 

131.9 

119.5 

238 

176.3 

159.8 

298 

220.8 

200.1 

59 

43.7 

39.6 

11988.279.9 

179 

132.6 

120.2 

239 

177.1 

160.5 

299 

221.5 

200.8 

60 

44.5 

40.  J 

12088.9 

80.6 

180 

133.4 

120.9 

240 

177.8 

161.2 

300 

222.3 

201.5 

Dist. 

Dep 

Lat. 

Dist.  Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat, 

For  4J  Points. 

TABLE  III.                                          203 

DIFFERENCE  OF   LATITUDE   AND    DEPARTURE   FOR   4    POINTS. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

l 

00.7 

00.7 

61 

43.1 

43.1 

121 

85.  C 

85.6 

181 

128.0 

128.0 

241 

170.4 

170.4 

2 

01.4 

01.4 

62 

43.843.8 

122 

86.3 

86.3 

182 

128.7 

128.7 

242 

171.1 

171.1 

3 

02.1 

02.1 

63 

44.5 

44.5 

123 

87.0 

86.0 

183 

129.4 

129.4 

243 

171.  8 

171.8 

4 

02.8 

02.8 

64 

45.3 

45.3 

124 

87.7 

87.7 

184 

130.1 

130.1 

244 

172.5 

172.5 

5 

03.5 

03.5 

/if; 

46.0 

46.0 

125 

88.4 

88.4 

185 

130.8 

130.8 

245 

173.2 

173.2 

6 

04.2 

04.2 

66 

46.7 

46.7 

126 

89.1 

89.1 

186 

131.5 

131.5 

246 

173.9 

173.9 

7 

04.9 

04.9 

67 

47.4 

47.4 

127 

89.8 

89.8 

187 

132.2 

132.2 

247 

174.7 

174.7 

8 

05.7 

05.7 

68 

48.1 

48.1 

128 

90.5 

90. 

188 

132.9 

132.9 

248 

175.4 

175.4 

9 

06.4 

06.4 

69 

48.8 

48.8 

129 

91.2 

91. 

189 

133.6 

133.6 

240 

176.1 

176.1 

10 

07.1 

07.1 

70 

49.5 

49.5 

130 

91.9 

91. 

190 

134.3 

134.3 

250 

176.8 

176.  b 

11 

o7.b 

07.8 

71 

50.2 

50.2 

131 

92.  b 

92. 

191 

135.1 

135.1 

251 

177.5 

177.5 

12 

08.5 

08.5 

72 

50.9 

50.9 

132 

93.3 

93. 

192 

135.8 

135.8 

252 

178.2 

178.2 

13 

09.2 

09.2 

73 

51.6 

51.6 

133 

94.0 

94. 

193 

136.5 

136.5 

253 

178.9 

178.9 

14 

09.9 

09.9 

74 

52.3 

52.3 

134 

94.8 

94. 

194 

137.2 

137.2 

254 

179.6 

179.6 

15 

10.6 

10.6 

75 

53.0 

53.0 

135 

95.5 

95. 

195 

137.9 

137.9 

255 

180.3 

180.3 

16 

11.3 

11.3 

76 

53.7 

53.7 

136 

96.2 

96. 

196 

138.6 

138.6 

256 

181.0 

181.0 

17 

12.0 

12.0 

77 

54.4 

54.4 

137 

96.9 

96. 

197 

139.3 

139.3 

257 

181.7 

181.7 

18 

12.7 

12.7 

78 

55.2 

55.2 

138 

97.6 

97. 

198 

140.0 

140.0 

258 

182.4 

182.4 

19 

13.4 

13.4 

7£ 

55.9 

55.9 

139 

98.3 

98. 

199 

140.7 

140.7 

259 

183.1 

183.1 

20 

14.1 

14.1 

80 

56.6 

56.6 

140 

99.0 

99.0 

200 

141.4 

141.4 

260 

183.8 

183.8 

21 

14.8 

14.8 

81 

57.3 

57.3 

141 

yy.7 

99.7 

201 

142.1 

142.1 

261 

184.  b 

184.6 

22 

15.6 

15.6 

82 

58.0 

58.0 

142 

100.4 

100.4 

202 

142.8 

142.8 

262 

185.3 

185.3 

23 

16.3 

16.3 

83 

58.7 

58.7 

143 

101.1 

101.1 

203 

143.5 

143.5 

263 

186.0 

186.0 

24 

17.0 

17.0 

84 

59.4 

59.4 

144 

101.8 

101.8 

204 

144.2 

144.2 

264 

186.7 

186.7 

25 

17.7 

17.7 

85 

60.1 

60.1 

145 

102.5 

102.5 

205 

145.0 

145.0 

265 

187.4 

187.4 

26 

18.4 

18.4 

86 

60.8 

60.8 

146 

103.2 

103.2 

206 

145.7 

145.7 

266 

188.1 

188.1 

27 

19.1 

19.1 

87 

61.5 

61.5 

147 

103.9 

103.9 

207 

146.4 

146.4 

267 

188.8 

188.8 

28 

19.8 

19.8 

88 

62.2 

62.2 

148 

104.7 

104.7 

208 

147.1 

147.1 

268 

189.5 

189.5 

29 

20.5 

20.5 

89 

62.9 

62.9 

149 

105.4 

105.4 

209 

147.8 

147.8 

269 

190.2 

190.2 

30 

21.2 

21.2 

90 

63.6 

63.6 

150 

106.1 

106.1 

210 

148.5 

148.5 

270 

190.9 

190.9 

31 

21.9 

21.9 

91 

64.3 

64.3 

151 

106.8 

106.8 

211 

149.2 

149.2 

271 

191.6 

191.6 

32 

22.6 

22.6 

92 

65.1 

65.1 

152 

107.5 

107.5 

212 

149.9 

149.9 

272 

192.3 

192.3 

33 

23.3 

23.3 

93 

65.8 

65.8 

153 

108.2 

108.2 

213 

150.6 

150.6 

273 

193.0 

193.0 

31 

24.0 

24.0 

94 

66.5 

66.5 

154 

108.9 

108.9 

214 

151.3 

151.3 

274 

193.7 

193.7 

35 

24.7 

24.7 

95 

67.2 

67.2 

155 

109.  6 

109.6 

215 

152.0 

152.0 

275 

194.5 

194.5 

36 

25.5 

25.5 

9C 

67.9 

67.9 

156 

110.3 

110.3 

216 

152.7 

152.7 

276 

195.2 

195.2 

37 

26.2 

26.2 

97 

68.6 

68.6 

157 

111.0 

111.0 

217 

153.4 

153.4 

277 

195.9 

195.9 

38 

26.9 

26.9 

98 

69.3 

69.3 

158 

111.7 

111.7 

218 

154.1 

154.1 

278 

196.6 

196.6 

39 

27.6 

27.6 

99 

70.0 

70.0 

159 

112.4 

112.4 

219 

154.9 

154.9 

279 

197.3 

197.3 

40 

28.3 

28.3 

100 

70.7 

70.7 

160 

113.1 

113.1 

220 

155.6 

155.6 

280 

198.0 

198.0 

41 

29.0 

29.0 

101 

71.4 

71.4 

161 

113.8 

113.8 

221 

156.3 

156.3 

281 

198.7 

198.7 

42 

29.7 

29.7 

102 

72.1 

72.1 

162 

114.5 

114.5 

222 

157.0 

157.0 

282 

199.4 

199.4 

43 

30.4 

30.4 

103 

72.8 

72.8 

163 

115.3 

115.3 

223 

157.7 

157.7 

283 

200.1 

200.1 

44 

31.1 

31.1 

104 

73.5 

73.5 

164 

116.0 

116.0 

224 

158.4 

158.4 

284 

200.8 

200.8 

45 

3L.8 

31.8 

105 

74.2 

74.2 

165 

116.7 

116.7 

225 

159.1 

159.1 

285 

201.5 

201.5 

46 

32.5 

32.5 

106 

75.0 

75.0 

166 

117.4 

117.4 

226 

159.8 

159.8 

286 

202.2 

202.2 

47 

33.2 

33.2 

107 

75.7 

75.7 

167 

118.1 

118.1 

227 

160.5 

160.5 

287 

202.9 

202.9 

48 

33.9 

33.9 

108 

76  4 

76.4 

168 

118.8 

118.8 

228 

161.2 

161.2 

288 

203.6 

203.6 

49 

34.6 

34.6 

109 

77.1 

77.1 

169 

119.5 

119.5 

229 

161.9 

161.9 

289 

204.3 

204.3 

50 

35.4 

35  4 

110 

77.8 

77.8 

170 

120.2 

120.2 

230 

162.6 

162.6 

290 

205.1 

205.1 

51 

3J.1 

36.1 

111 

78.5 

78.5 

17J 

120.9 

120.9 

231 

163.3 

163.3 

291 

205.8 

205.8 

52 

36.8 

36.8 

112 

79.2 

79.2 

172 

121.6 

121.6 

232 

164.0 

164.0 

292 

206.5 

206.5 

53 

37.5 

37.5 

113 

79.9 

79.9 

173 

122.3 

122.3 

233 

164.8 

164.  & 

293 

207.2 

207.2 

54 

38.2 

38.2 

114 

80.6 

80.6 

174 

123.0 

123.0 

234 

165.5 

165.5 

294 

207.9 

207.9 

55 

38.9 

38.9 

115 

81.3 

81.3 

175 

123.7 

123.7 

235 

166.2 

166.2 

295 

208.6 

208.6 

56 

39.6 

39.6 

116 

82.0 

82.0 

176 

124.4 

124.4 

236 

166.9 

166.9 

296 

209.3 

209.3 

57 

40  3 

40.3 

117 

82.7 

82.7 

177 

125.2 

125.2 

237 

167.6 

167.6 

297 

210.0 

210.0 

58 

41.0 

41  0 

118 

83.4 

83.4 

178 

125.9 

125.9 

238 

168.3 

168.3 

298 

210.7 

210.7 

59 

41.7 

41.7 

119 

84.1 

84.1 

179 

126.6 

126.6 

239 

169.0 

169.0 

299 

211.4 

211.4 

60 

42.4 

42.4 

120 

84.8 

84.8 

180 

127.3 

127.3 

240 

169.7 

169.7 

300 

212.1 

212.1 

5ist. 

Dep 

Lat. 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  4  Points. 

204                                         TABLE  IV. 

DIFFERENCE  OF   LATITUDE    AND   DEPARTURE   FOR   1    DEGREE. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

!Dist, 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

01.0 

00.0 

61 

61.0 

01.1 

121 

121.0 

02.1 

181 

181.0 

03.2 

241 

241.0 

04.2 

2 

02.0 

00.0 

62 

62.0 

01.1 

122 

122  0 

02.1 

182 

182.0 

03.2 

242 

242.0 

04.2 

3 

03.0 

00.1 

63 

63.0 

01.1 

123 

123.0 

02.1 

183 

183.0 

03.2 

243 

243.0 

04.2 

4 

04.0 

00.1 

64 

64.0 

01.1 

124 

124.0 

02.2 

184 

184.0 

03.2 

244 

244.0 

04.3 

5 

05.0 

00.1 

65 

65.0 

01.1 

125 

125.0 

02.2 

185 

185.0 

03.2 

245 

245.0 

04.3 

6 

06.0 

00.1 

66 

66.0 

01.2 

126 

126.002.2 

186 

186.0 

03.2 

246 

246.0 

04.3 

7 

07.0 

00.1 

67 

67.0 

01.2 

127 

127.0 

02.2 

187 

187.0 

03.3 

247 

247.0 

04.3 

8 

08.0 

00.1 

68 

68.0 

01.2 

128 

128.0 

02.2 

188 

188.0 

03.3 

248 

248.0 

04.3 

9 

09.0 

00.2 

69 

69.0 

01.2 

129 

129.0 

02.2 

189 

189.0 

03.3 

249 

249.0 

04.3 

10 

10.0 

00.2 

70 

70.0 

01.2 

130 

130.0 

02.3 

190 

190.0 

03.3 

250 

250.0 

04.4 

11 

11.0 

00.2 

71 

71.0 

01.2 

131 

131.  (i 

02.3 

191 

191.0 

03.3 

251 

251.0,     04.4 

12 

12.0 

00.2 

72 

72.0 

01.3 

132 

132.0 

02.3 

192 

192.0 

03.4 

25-2 

252.0     04.4 

13 

13.0 

00.2 

73 

73.0 

01.3 

133 

133.0 

02.3 

193 

193.0 

03.4 

253 

253.0 

04.4 

14 

14.0 

00.2 

74 

74.0 

01.3 

134 

134.0 

02.3 

194 

194.0 

03.4 

254 

254.0 

04.4 

15 

15.0 

00.3 

75 

75.0 

01.3 

135 

135.0 

02.4 

195 

195.0 

03.4 

255 

255.0 

04.4 

16 

16.0 

00.3 

76 

76.0 

01.3 

136 

136.0 

02.4 

196 

196.0 

03.4 

256 

256.0 

04.5 

17 

17.0 

00.3 

77 

77.0 

01.3 

137 

137.0 

02.4 

197 

197.0 

03.4 

257 

257.0 

04.5 

18 

18.0 

00.3 

78 

78.0 

01.4 

138 

138.0 

02.4 

198 

198.0 

03.5 

258 

258.0 

04.5 

19 

19.0 

00.3 

79 

79.0 

01.4 

139 

139.0 

02  4 

199 

199.0 

03.5 

259 

259.0 

04.5 

20 

20.0 

00.3 

80 

80.0 

01.4 

140 

140.0 

02.4 

200 

200.0 

03.5 

260 

260.0 

04.5 

21 

21.0 

00.4 

81 

81.0 

01.4 

14-1 

141.0 

U2.5 

201 

201.0 

03.5 

'/til 

261.01     04.5 

22 

22.0 

00.4 

82 

82.  C 

01.4 

142 

142.0 

02.5 

202 

202.0 

03.5 

262 

262.0 

04.6 

23 

23.  ( 

00.4 

83 

83.0 

01.4 

143 

143.0 

02.5 

203 

203.0 

03.5 

263 

263.0 

04.6 

24 

24.0 

00.4 

84 

84.001.5 

144 

144.0 

02.5 

204 

204.0 

03.6 

264 

264.0 

04.  G 

25 

25.0 

00.4 

85 

85.001.5 

145 

145.0 

02.5 

205 

205.0 

03.6 

265 

265.0 

04.6 

2G 

•26.0 

00.5 

86 

86.001.5 

146 

146.0 

02.5 

206 

206.0 

03.6 

266 

266.0 

04.6 

27 

27.0 

00.5 

87 

87.001.5 

147 

147.002.6 

207 

207.0 

03.6 

267 

267.0 

04.7 

28 

28.0 

00.5 

88 

88.001.5 

148 

148.0 

02.6 

208 

208.0 

03.6 

268 

268.0 

04  7 

29 

29.0 

00.5 

89 

89.001.6 

149 

149.0 

02.6 

209 

209.0 

03.7 

269 

269.0 

04.7 

30 

30.0 

00.5 

90 

90.0 

01.6 

150 

150.0 

02.6 

210 

210.0 

03.7 

270 

270.0 

04.7 

31 

31.0 

00.5 

91 

91.0 

01.6 

151 

151.0 

02.6 

211 

211.0 

03.7 

271 

271.0 

04.7 

32 

32.0 

30.6 

92 

92.0 

01.6 

15'2 

152  0 

02.7 

212 

212.0 

03.7 

272 

272.0 

04.7 

33 

33.0 

00.6 

93 

93.0 

01.6 

153 

153.0 

02.7 

213 

213.0 

03.7 

273 

273.0 

04.8 

34 

34.0 

00.6 

94 

94.0 

01.6 

154 

154.0 

02.7 

214 

214.0 

03.7 

274 

274.0 

04.8 

35 

35.0 

00.6 

95 

95.0 

01.7 

155 

155.  1 

02.7 

215 

215.0 

03.8 

'275 

275.0 

04.8 

3G 

36.000.6 

96 

96.0 

01.7 

156 

156.0 

02.7 

216 

216.0 

03.8 

276 

276.0 

04.8 

37 

37.000.6 

97 

97.0 

01.7 

157 

157.0 

02.7 

217 

217.0 

03.8 

277 

277.0 

04.8 

38 

38.000.7 

98 

98.0 

01.7 

158 

158.0 

02.8 

218 

218.0 

03.8 

278 

278.0 

04.9 

39 

39.000.7 

99 

99.0 

01.7 

159 

159.0 

02.8 

219 

219.0 

03.8 

279 

279.0 

04.9 

40 

40.0 

00.7 

100 

100.0 

01.7 

160 

160.0 

02.8 

220 

220.0 

03.8 

280 

280.0 

04.9 

41 

41.0 

00.7 

101 

101.0 

01.8 

161 

161.0 

02.8 

221 

221.0 

03.9 

281 

281.0 

04  9 

42 

42.000.7 

102 

102.0 

01.8 

162 

162.0 

02.8 

222 

222.0 

03.9 

282 

282.0 

04.9 

43 

43.000.8 

103 

103.0 

01.8 

163 

163.0 

02.8 

223 

223.0 

03.9 

283 

283.0 

04.9 

44 

44.000.8 

104 

104.0 

01.8 

164 

164.0 

02.9 

224 

224.0 

03.9 

284 

284.0 

05.0 

45 

45.000.8 

105 

105.0 

01.8 

165 

165.0 

02.9 

225 

225.0 

03  9 

285 

285.0 

05.0 

46 

46.000.8 

106 

106.0 

01.8 

166 

166.0 

02.9 

226 

226.0 

03.9 

286 

286.0 

05.0 

47 

47.000.8 

107 

107.0 

01.9 

167 

167.0 

02.9 

227 

227.0 

04.0 

287 

287.0 

05.0 

48 

48.000.8 

108 

108.0 

01.9 

168 

168.0 

02.9 

228 

228.0 

04.0 

288 

288.0 

05.0 

49 

49.0 

00.9 

109 

109.0 

01.9 

169 

169.0 

02.9 

229 

229.0 

04.0 

289 

289.0 

05.0 

50 

50.0 

00.9 

110 

110.0 

01.9 

170 

170.0 

03.0 

230 

230.0 

04.0 

290 

290.0 

05.1 

51 

51.000.9 

111 

111.0 

01.9 

171 

171.0 

03.0 

231 

231.0 

04.  0 

291 

'291.0 

05.1 

52 

52.000.9 

112 

112.0 

02.0 

172 

172.0 

03.0 

232 

232.0 

04.0 

292 

292  0 

05.1 

53 

53.000.9 

113 

113.0 

02.0 

173 

173.0 

03.0 

233 

233.0 

04.1 

293 

293.0 

05.1 

54 

54.000.9 

114 

114.0 

02.0 

174 

174.0 

03.0 

234 

234.0 

04.1 

294 

294.0 

05.1 

55 

55.0 

01.0 

115 

115.0 

02.0 

175 

175.0 

03.1 

235 

235.0 

04.1 

295 

295.0 

05.1 

56 

56.0 

01.0 

116 

116.0 

02.0 

176 

176.0 

03.1 

236 

236.0 

04.1 

296 

296  0 

05.2 

57 

57.0 

01.0 

117 

117.0 

02.0 

177 

177.0 

03.1 

237 

237.0 

04.1 

297 

297  0 

05.2 

58 

58.0 

01.0 

118 

118.0 

02.1 

178 

178.0 

03.1 

238 

238.0 

04.2 

298 

298.0 

05.2 

59 

59.0 

01.0 

119 

119.0 

02.1 

179 

179.0 

03.1 

239 

239.0 

04.2 

299 

299.0 

05.2 

60 

60.0 

01.0 

120 

120.0 

02.1 

180 

180.0 

03.1 

240 

240.0 

04.2 

300 

300.0 

05.2 

Dist. 

Dep 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat, 

For  89  Degrees. 

TABLE  IV.                                          205 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE  FOR    2    DEGREES. 

[list. 

Lat. 

Dep 

I'M. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

01.0 

00.0 

61 

61  002.1 

121 

120.  CJ 

04.2 

181 

180.9 

06.3 

241 

240.9 

08.4 

2 

02.0 

00.1 

62 

62.0:02  2 

122 

121.9 

04.3 

182 

181.9 

06.4 

242 

241.9 

08.4 

3 

03.0 

UO.l 

63 

63.002.2 

123 

122.9 

04.3 

183 

182.9 

06.4 

243 

242.9 

08.5 

4 

04.0 

00.1 

64 

64  002.2 

124 

123.9 

04.3 

184 

183.9 

06.4 

244 

243.9 

08.5 

5 

05.0 

00.2 

65 

65.0 

02.3 

125 

124.9 

04.4 

185 

184.9 

06.5 

245 

244.9 

08.6 

6 

06.0 

00.2 

66 

66.0 

02.3 

126 

125.9 

04.4 

186 

185.9 

06.5 

246 

245.8 

08.6 

7 

07.0 

00.2 

67 

67.0 

02.3 

127 

126.9 

04  4 

187 

186.9 

06.5 

247 

246.8 

08.6 

8 

OS.O 

00.3 

68 

68.0 

02.4 

128 

127.9 

04.5 

188 

187.9 

06.6 

248 

247.8 

08.7 

9 

>9.0 

00.3 

69 

69.0 

02  4 

129 

128.9 

04.5 

189 

188.  9 

06.6 

249 

248  8 

08.7 

10 

10.  0 

00.3 

70 

70.0 

02.4 

130 

129.9 

04.5 

190 

189.9 

00.6 

250 

249.8 

08.7 

11 

11  0 

00.4 

71 

71.0 

02.5 

131 

130.9 

04.6 

191 

190.9 

00.7 

251 

250.6 

OS.H 

12 

12.0 

)0.4 

72 

72.0 

02.5 

132 

131.9 

04.6 

192 

191.9 

06.7 

252 

251.8 

08.8 

13 

13.0 

00.5 

73 

73.0 

02.5 

133 

132.9 

04.6 

193 

192.9 

06.7 

253 

252.8 

08.8 

14 

14.0 

•0.5 

74 

74.0 

02.6 

134 

133.9 

04.7 

194 

193.9 

06.8 

254 

253.8 

08.9 

15 

15.0 

00.5 

75 

75.002.6 

135 

134.9 

04.7 

195 

194.9 

06.8 

255 

254.8 

08.9 

1C 

16.0 

00.6 

76 

76.002.7 

136 

135.9 

04.7 

196 

195.9 

06.8 

256 

255.8 

08.9 

17 

17.0 

00.  C 

77 

77.0 

02.7 

137 

136.9 

04.8 

197 

196.9 

06.9 

257 

256.8 

Oi)  0 

18 

18.0 

00.6 

78 

78.0 

02  7 

138 

137.9 

04.8 

198 

197.9 

06.9 

258 

257.8 

09.0 

19 

19.0 

00.7 

79 

79.0 

02.8 

139 

138.9 

04.9 

199 

198.9 

06.9 

259 

258.8 

09.0 

20 

20  0 

00.7 

80 

80.0 

02.8 

140 

139.9 

04.9 

200 

199.9 

07.0 

26d 

259  8 

09.1 

iii 

Ji.O 

00.7 

81 

81.0 

02.8 

141 

140.9 

04.9 

201 

200.9 

07:0 

261 

260.  8 

09.1 

22 

22.0 

00.8 

8i 

81.9 

02.9 

142 

141  9 

05  0 

202 

201.9 

07.0 

262 

261.8 

09.1 

23 

23.  ( 

00.8 

83 

82.902.9 

143 

142.9 

05.0 

203 

202.9 

07.1 

263 

262.8 

09.2 

24 

24.0 

00.8 

84 

83.902.9 

144 

143.9 

05.  0 

204 

203.9 

07  1 

264 

263.8 

09.2 

25 

25.0 

JO.  9 

85 

84  9 

03.0 

145 

144.9 

05.1 

205 

204.9 

07.2 

265 

264.8 

09.  i 

26 

26  0 

00.9 

86 

85.9 

03  0 

146 

145.9 

05.1 

206 

205.9 

07.2 

266 

265.8 

09.3 

27 

27.  (' 

00.9 

87 

86.9 

03.0 

147 

146.9 

05.1 

207 

206.9 

07.2 

267 

266.8 

09.3 

28 

28.0 

01.0 

8s 

87.9 

03.1 

148 

147  9 

05  2 

208 

207.9 

07.3 

268 

267.8 

09.41 

29 

29.0 

01.0 

89 

88.9 

03.1 

149 

148.9 

05.2 

209 

208.9 

07.3 

269 

268.8 

09  4 

30 

30.0 

01.0 

90 

89  9 

03.1 

150 

149.9 

05.2 

210 

209.9 

07.3 

270 

269.8 

09.4 

31 

Jl.O 

01.1 

91 

90.9 

03.2 

151 

150.9 

05.3 

211 

210.9 

07.4 

271 

H70.b 

09.5 

32 

32.  G 

01.1 

92 

91.9 

03.2 

152 

151.9 

05  3 

212 

211.9 

07.4 

272 

271.8 

09.5 

33 

33.0 

01.2 

93 

92.9 

03.2 

153 

152.9 

05.3 

213 

212.9 

07.4 

273 

272.8 

09.5 

34 

34.0 

01.2 

94 

93  9 

03.3 

154 

153.9 

05.4 

214 

213.9 

07.5 

274 

273.8 

09.6 

35 

55.  0 

01.2 

95 

94  9 

03.3 

155 

154.9 

05.4 

215 

214.9 

07.5 

275 

274.8 

09.6 

33 

33.0 

01.3 

96 

95.9 

03.4 

156 

155.9 

05.4 

216 

215.9 

07  5 

276 

275.8 

09.6 

37 

37.  G 

01.3 

97 

96.9 

03.4 

157 

156.9 

05.5 

217 

216.9 

07  C 

277 

276.8 

09.7 

38 

38.  G 

01.3 

98 

97.9 

03.4 

158 

157.9 

05.5 

218 

217.9 

07.6 

278 

277.8 

09.7 

39 

39.0 

01.4 

99 

98.9 

03.5 

159 

158.9 

05.5 

219 

218.9 

07.6 

279 

278.8 

09.7 

40 

to.o 

01.4 

100 

99.9 

03.5 

160 

159.9 

05.6 

220 

219.9 

07.7 

280 

279.8 

09.8 

41 

41  A 

01.4 

101 

100.9 

03.5 

161 

160.9 

05.6 

2-21 

220.9 

07.7 

"281 

280  b 

09.8 

42 

4-2.0 

01.5 

102 

101.903.6 

162 

161.9 

05.7 

222 

221.9 

07.7 

282 

281.8 

09.8 

43 

43.0 

01.5 

103 

102.9 

03.6 

163 

162.9 

05.7 

223 

222.9 

07.8 

283 

282.8 

09.9 

44 

44.0 

01.5 

104 

103.9 

03.6 

164 

163.9 

05.7 

224 

223.9 

07.8 

284 

283.8 

09.9 

45 

45.0 

01.6 

105 

104.903.7 

165 

164.9 

05.8 

225 

224.9 

07.9 

285 

284.8 

09.9 

40 

46.0 

01.6 

106 

105.903.7 

166 

165.9 

05.8 

226 

225.9 

07.9 

286 

285.8 

10.0 

47 

47.0 

01.6 

107 

106  903  7 

167 

166.9 

05  8 

227 

226.9 

07.9 

287 

286.8 

10.0 

48 

48  0 

01.7 

108 

107.903.8 

168 

167.9 

05.9 

228 

227.9 

08.0 

288 

287.8 

10.1 

49 

49.0 

01.7 

109 

108.903.8 

109 

168.9 

05.9 

229 

228.9 

08.0 

289 

288.8 

10.1 

50 

50  0 

01.7 

110 

109.903.8 

170 

169.9 

05.9 

230 

229.9 

08.0 

290 

289.8 

10.1 

51 

51.0 

01.8 

111 

110.903.9 

171 

170.9 

00.0 

231 

230.9 

08.1 

291 

290.8 

10.2 

52 

52.0 

01.8 

112 

111.903.9 

172 

171.9 

06.0 

232 

231.9 

08.1 

292 

291.8 

10.2 

53 

53.0 

01.8 

113 

112.903.9 

173 

172.9 

06.0 

233 

232.9 

08.1 

293 

292.8 

10.2 

54 

54.0 

01.9 

114 

113.904.0 

174 

173.9 

06.1 

234 

233.9 

08.2 

294 

293.8 

10.3 

55 

55.  C 

01.9 

115 

114.904.0 

175 

174.9 

06.1 

235 

234.9 

08.2 

295 

294.8 

10.3 

5G 

56.0 

02.0 

116 

115.904.0 

176 

175.9 

00.1 

236 

235.9 

08.2 

296 

295.8 

10.3 

57 

57.0 

02.0 

117 

116.904.1 

177 

176.9 

06.2 

237 

236.9 

08.3 

297 

296.8 

10.4 

58 

58.0 

02.0 

118 

117.904.1 

178 

177.9 

06.2 

238 

237.9 

08.3 

298 

297.8 

10.4 

59 

59.0 

02.1 

119 

118.904.2 

179 

178.9 

06.2 

239 

238.9 

08.3 

299 

298.8 

10.4 

60 

60  0 

02.1 

120 

119.9 

04.2 

180 

179.9 

06.3 

240 

239.9 

08.4 

300 

299.8 

10.5 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  88  Degrees. 

206 

TABLE  III. 

DIFFERENCE   OF   LATITUDE   AND  DEPABTUBE  FOB  3  DEGREES. 

Mst, 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Bist. 

Lat. 

Dep.  I 

Dist. 

Lat. 

Dep. 

1 

01.0 

00.1 

61 

60.9 

03.2 

121 

120.8 

06.3 

181 

180.8 

09.  5! 

241 

240.7 

12.6 

2 

02.0 

00  1 

62 

61.9,03.2 

122 

121.8 

06.4 

182 

181.8 

09.  5J 

242 

241.7 

12.7 

3  03.0 

00.2 

63 

62.903.3 

123 

122.8 

06.4 

183 

182.7 

09.6 

243 

242.7 

12.7 

4 

04.0 

00.2 

64 

63.903.3 

124 

123.8f06.5 

184 

183.7 

09.6 

244 

243  7 

12.8 

5 

05.0 

00.3 

65 

64.903.4 

125 

124.806.5 

185 

184.7 

09.7 

245 

244.7 

12.8 

6 

06.0 

00.3 

66 

65.903.5 

126 

125.8 

06.6 

186 

185.7 

09.7 

246 

245.7 

12.9 

7 

07.0 

00.4 

67 

66.903.5 

127 

126.8 

06.6 

187 

186.7 

09.8' 

247 

246.7 

12.9 

8 

08.0 

00.4 

68 

67.903.6 

128 

127.8 

06.7 

188 

187.7 

09.8 

248 

247.7 

13.0 

9  09.0 

00  5 

69 

68.903.6 

129 

128.8 

06.8 

189 

188.7 

09.9 

249 

248.7 

13.0 

10  |10.0 

00.5 

70 

69.903.7 

130 

129.8 

06.8 

190 

189.7     09.9 

250 

249.7 

13.1 

11 

11.0 

00.6 

71 

70.903.  7 

131 

130.8 

06.9 

191 

190.7 

10.  Oj 

251 

250.7 

13.1 

12 

12.0 

00.6 

72 

71.903.8 

132 

131.8 

06.  9 

192 

191.7 

10.0 

252 

251.7 

13.2 

13 

13  0 

00.7 

73 

72.903.8 

133 

132.8 

07.0 

193 

192.7 

10.1 

253 

252.7 

13.2 

14 

14.0 

00.7 

74 

73.903.9 

134 

133.8 

07.0 

194 

193.7 

10  2 

254 

253.7 

13.3 

15 

15.0 

00.8 

75 

74.903.9 

135 

134.8 

07.1 

195 

194.7 

10.2 

255 

254.7 

13.3 

16 

16.0 

00.  b 

76 

75.904.0 

136 

135.8 

07.1 

196 

195.7 

10.3 

256 

255.6 

13.4 

17 

17.0 

00.9 

77 

76.904.0 

137 

136.8 

07.2 

197 

196.7 

10.3 

257 

256.6 

13.5 

18 

18.0 

00.9 

78 

77.904.1 

138 

137.8 

07.2 

198 

197.7 

10.4 

258 

257.6 

13.5 

19 

19.0 

01.0 

79 

78  904.1 

139 

138.8 

07.3 

199 

198.7 

10.4 

259 

258.6 

13.6 

20 

20.0 

01.0 

80 

79  9104.2 

140 

139.8 

07.3 

200 

199.7 

10.5 

260 

259.6 

13.6 

21 

21.0 

01.1 

81 

80.904.2 

141 

140.8 

07.4 

'201 

200.7 

10.5 

261 

260.6 

13.7 

2-2 

22.0 

01.2 

82 

81.904.3 

142 

141.8 

07.4 

202 

201.7 

10.6 

262 

261.6 

13.7 

23 

23.0 

01.2 

83 

82.904.3 

143 

142.8 

07.5 

203 

202.7 

10.6 

263 

262.6 

13.8 

24 

24.0 

01.3 

84 

83.904.4 

144 

143.8 

07.5 

204 

203.7 

10.7 

264 

263.  C 

13.8 

25 

25.0 

01.3 

85 

84.904.4 

145 

144.8 

07.6 

205 

204.7 

10.7 

265 

264.6 

13.9 

26 

26.0 

01.4 

86 

85.904.5 

146 

145  8 

07.6 

206 

205.7 

10.8 

266 

265.6 

13.9 

27 

27.0 

01.4 

87 

86.904.6 

147 

146.8 

07.7 

207 

206.7 

10.8 

267 

266.6 

14.0 

28 

28.0 

01.5 

88 

87.904.6 

148 

147.8 

07.7 

208 

207.7 

10.9 

268 

267.6 

14.0 

29 

29.0 

01.5 

89 

88.904.7 

149 

148.8 

07.8 

209 

208.7 

10.9 

269 

268.6 

14  1 

30 

30.0 

01.6 

90 

89.904.7 

150 

149.8 

07.9 

210 

209.7 

11.0 

270 

269.6 

14.1 

31 

31.0 

01.6 

91 

90.904.8 

151 

150.8 

07.9 

211 

210.7 

11.0 

271 

270.6 

14.2 

32 

32.0 

01.7 

92 

91.904.8 

152 

151.8 

08.0 

212 

211.7 

11.1 

272 

271.6 

14.2 

33 

33.0 

01.7 

93 

92.9.04.9 

153 

152.8 

08.0 

213 

212.7 

11.1 

273 

272.6 

14.3 

34 

34.0 

01.8 

94 

93.904.9 

154 

153.8 

08.1 

214 

213.7 

11.2 

274 

273.6 

14.3 

35 

35.0 

01.8 

95 

94.905.0 

155 

154.8 

08.1 

215 

214.7 

11.3 

275 

274.6 

14.4 

36 

36.0 

01.9 

96 

95.905.0 

156 

155.8 

08.2 

216 

215.7 

11.3 

276 

275.6 

14.4 

37 

36.9 

01.9 

97 

96.905.1 

157 

156.8 

08.2 

217 

216.7 

11.4 

277 

276.  (i 

14.5 

38 

37.9 

02.0 

9h 

97.905.1 

158 

157.8 

08.3 

218 

217.7 

11  4 

278 

277.6 

14.5 

39 

38.9 

02.0 

99 

98.9;05.2 

159 

158.8 

08.3 

219 

218.7 

11.5 

279 

278.6 

14.6 

40 

39.9 

02.1 

100 

99.905.2 

160 

159.8 

08.4 

220 

219.7 

11.5 

.280 

279.6 

14.7 

41  |40.9 

02.1 

101 

100.  905.  3 

161 

160.8 

08.4 

221 

220.7 

11.6 

281 

2SO.O 

14.7 

42 

41.9 

02.2 

102 

101.905.3 

162 

161.8 

08.5 

222 

221.7 

11.6 

282 

281.6 

14.8 

43 

42.9 

02.3 

103 

102.905.4 

163 

162.8 

08.5 

223 

222.7 

11.7 

283 

282.6 

14.8 

44 

43.9 

02.3 

104 

103  905.4 

164 

163  8 

08.6 

224 

223.7 

11.7 

284 

283.6 

14.9 

45 

44.9 

02.4 

105 

104.9,05.5 

165 

164.8 

08.6 

225 

224.7 

11.8 

285 

284.6 

14.9 

46 

45.9 

02.4 

106 

105.905  5 

166 

165  8 

08.7 

226 

225.7 

11.8 

286 

285.6 

15.0 

47 

46.9 

02.5 

107 

106.905.6 

167 

166.8 

08.7 

227 

226.7 

11.9 

287 

286.  C 

15.0 

48 

47.9 

02.5 

108 

107.905.7 

168 

167.8 

08.8 

228 

227.7 

11.9 

288 

287.6 

15.1 

49 

48.9 

02.6 

109 

108.905.7 

169 

168.8 

08.8 

229 

228.7 

12.0 

289 

288.6 

15.1 

50 

49.9 

02.6 

110   109.805.8 

170 

169.8 

08.9 

230 

229.7 

12.0 

290 

289.6 

15.2 

51 

50.9 

02.7 

111 

110.805.8 

171 

170.8 

08.9 

231 

230.7 

12.1 

291 

290.6 

15.  '2 

52 

51.9 

02.7 

112 

111.805  9 

172 

171.8 

09.0 

232 

231.7 

12.1 

292 

2i>1.6 

15.3 

53 

52.9 

02.8 

113 

112.805.9 

173 

172.8 

09.1 

233 

232.7 

12.2 

293 

292.6 

15.3 

54 

53.9 

02.8 

114 

113.806.0 

174 

173.8 

09.1 

234 

233.7 

12.2 

294 

293.6 

15.4 

55 

54.9 

02.9 

115 

114.806.0 

175 

174.8 

09.2 

235 

234.7 

12.3 

295 

294.6 

15.4 

56 

55.9 

02.9 

116 

115.806.1 

176 

175.8 

09.2 

236 

235.7 

12.4 

296 

295.6 

15.5 

57 

56.9 

03.0 

117 

116.8'06.1 

177 

176.8 

09.3 

237 

236.7 

12.4 

297 

296.6 

15.5 

58 

57.9 

03.0 

118 

117.806.2 

178 

177.8 

09.3 

238 

237.7 

12.5 

298 

297.6 

15.6 

59 

58.9 

03.1 

119 

118.806.2 

179 

178.8 

09.4 

239 

238.7 

12.5 

299 

298.6 

15.6 

60 

59.9 

03.1 

120 

119.8 

06.3 

180 

179.8 

09.4 

240 

239.7 

12.6 

300 

299.6 

15.7 

Dist. 

Dep 

Lat. 

D~ist 

Dep. 

lLat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

For  87  Degrees. 

TABLE  IV.                                           207 

DIFFERENCE  OF 

LATITUDE    AND  DEPARTURE   FOR  4  DEGREES. 

)ist. 

..at. 

Dep 

Dist. 

Lat.  |Dep 

list. 

Lat. 

Dep 

ist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

)1.0 

30.1 

61 

60.90^.3 

121 

120.  708.  41 

181 

180.6 

12.6 

241 

240.4 

16.8 

2 

)2.0 

30.1 

62 

61.804.3 

122 

121.708.5 

182 

181.6 

12.7 

242 

241.4 

16.9 

3 

)3.0 

30.2 

63 

62.804.4 

123 

122.708.6 

183 

182.6 

12.8 

243 

242.4 

17.0 

4 

)4.0 

30.3 

64 

63.804.5 

124 

123.708.6 

184 

183.6 

12.8 

244 

243.4 

17.0 

5 

•5.0 

30.3 

65 

64.804.5 

125 

124.708.7 

185 

184.5 

12.9 

245 

244.4 

17.1 

6 

)6.0 

JO.  4 

66 

65.804.6 

126 

125.708.8 

186 

185.5 

13.0 

246 

245.4 

17.2 

7 

37.0 

(30.5 

67 

66.804.7 

127 

126.708.9 

187 

186.5 

13.0 

247 

246.4 

17.2 

8 

38.0 

00.6 

68 

67.804.7 

128 

127.708.9 

188 

187.5 

13.1 

248 

247.4 

17.3 

9 

J9.0 

JO.  6 

69 

68.804.8 

129 

128.709.0 

189 

188.5 

13.2 

249 

248.4 

17.4 

10 

10.0 

00.7 

70 

69.8:04  9 

130 

129.709.1 

190 

189.5 

13.3 

250 

249.4 

17.4 

11 

ii.O 

[JO.  8 

71 

70.805.0 

131 

130.709.1 

191 

190.5 

13.3 

251 

ii50.4 

17.5 

12 

12.0 

00.8 

72 

71.805.0 

132 

131.709.2 

192 

191.5 

13.4 

252 

251.4 

17.6 

13 

13.0 

00.9 

73 

72.805.1 

133 

132.709.3 

193 

192.5 

13.5 

253 

252.4 

17.6 

14 

14  0 

01.0 

74 

73.805.2 

134 

133.7U9.3 

194 

193.5 

13.5 

254 

253.4 

17.7 

15 

15.0 

01.0 

75 

74.805.2 

135 

134.709.4! 

195 

194.5 

13.6 

255 

254.4 

17.8 

16 

16.0 

01.1 

76 

75.805.3 

136 

135.7 

J9.5 

196 

195.5 

13.7 

256 

255.4 

.17.9 

17 

17.0 

01.2 

77 

76.805.4 

137 

136.709.6 

197 

196.5 

13.7 

257 

256.4 

17.9 

18 

18.0 

01.3 

78 

77.805.4 

138 

137.7|09.6 

198 

197.5 

13.8 

258 

257.4 

18.0 

19 

19.001.3 

79 

78.805.5 

139 

138.  7  09.7! 

199 

198.5 

13.9 

259 

258.4 

18.1 

20 

20.0|01.4 

80 

79.805.6 

140 

139.7 

09.8; 

200 

199.5 

14.0 

260 

259.4 

18.1 

21 

ZO.901.5 

81 

80.805.7 

141 

140.7 

09.  8, 

201 

•200.5 

14.0 

261 

260.4 

18.2 

22 

21.901.5 

82 

81.805.7 

142 

141.7 

09  9 

20'2 

201.5 

14.1 

262 

261.4 

18.3 

23 

22.901.6 

83 

82.805.8 

143 

142.7 

10.0 

203 

202.5 

14.2 

263 

262.4 

18.3 

24 

23.901.7 

84 

83.805.9 

144 

143.6 

10.0, 

204 

203.5 

14.2 

264 

263.4 

18.4 

25 

24.901.7 

85 

84.805.9 

145 

144.610.1 

205 

204.5 

14  3 

265 

264.4 

18.5 

26 

25.901.8 

86 

85.806.0 

146 

145.610.2! 

206 

205.5 

14.4 

266 

265.4 

18.6 

27 

26.901.9 

87 

86.806.1 

147 

146.6 

10.3 

207 

206.5 

14.4 

267 

266.3 

18.6 

28 

27.902.0 

88 

87.806.1 

148 

147.6 

10.3 

208 

207.5 

14.5 

268 

267.3 

18.7 

29 

28.902.0 

89 

88.806.2 

149 

148.6 

10.4 

209 

208.5 

14.6 

269 

268.3 

18.8 

30 

29.902.1 

90 

89.806.3 

150 

149.6 

10.5 

210 

209.5 

14.6 

270 

269.3 

18.8 

31 

30.902.2 

91 

90.806.3 

151 

150.  (i 

10.5 

211 

210.5 

14.7 

271 

270.3 

18.9 

32 

31.902.2 

92 

91.806.4 

152 

151.6 

10.6 

212 

211.5 

14.8 

272 

271.3 

19.0 

33 

32.902.3 

93 

92.806.5 

153 

152.6 

10.7 

213 

212.5 

14.9 

273 

272.3 

19.0 

34 

33.902.4 

94 

93.806.6 

154 

153.610.7 

214 

213.5 

14.9 

274 

273.3 

19.1 

35 

34.902.4 

95 

94.806.6 

155 

154.610.8 

215 

214.5 

15.0 

275 

274.3 

19.2 

36 

35.902.5 

96 

95.806.7 

156 

155.610.9 

216 

215.5 

15.1 

276 

275.3 

19.3 

37 

36.902.6 

97 

96.806.8 

157 

156.611.0 

217 

216.5 

15.1 

277 

276.3 

19.3 

38 

37.902.7 

98 

97.806.8 

158 

157.611.0 

218 

217.5 

15.2 

278 

277.3 

19.4 

39 

38.902.7 

99 

98.806.9 

159 

158.6 

11.1 

219 

218.5 

15.3 

279 

278.3 

19  5 

40 

39.902.8 

100 

99.8 

07.0 

160 

159.6 

11.2 

220 

219.5 

15.3 

280  279.3 

19.5 

41 

40.902.9 

101 

100.8 

J7.0 

161 

160.611.2 

221 

220.5 

15.4 

28] 

280.3 

19.6 

42 

41.902.9 

102 

101.807.1 

162 

161.6 

11.3 

222 

221.5 

15.5 

282 

281.3 

19.7 

43 

42.903.0 

103 

102.7107.2 

163 

162.  G 

11.4 

223 

222.5 

15.6 

283 

282.3 

19.7 

44 

43.903.1 

104 

103.7 

07.3 

164 

163.6 

11.4 

224 

223.5 

15.6 

284 

283.3 

19.8 

45 

44.903.1 

105 

104.7 

07.3 

165 

164.6 

11.5 

225 

224.5 

15.7 

285 

284.3 

19.9 

46 

45.9 

03.2 

106 

105.7 

07.4 

166 

165.6 

11.6 

2'26 

225.4 

15.8 

286 

285.3 

20.0 

47 

46.9 

03.3 

107 

106.7 

07.5 

167 

166.6 

11  6 

227 

226.4 

15.8 

287 

286.3 

20.0 

48 

47.903.3 

108 

107.7 

07.  5 

168 

167.6 

11.7 

228 

227.4 

15.9 

288 

287.3 

20.1 

49 

48.903.4 

109 

108.7 

07.6 

169 

168.6 

11.8 

229 

228.4 

16.0 

289 

288.3 

20.2 

50 

49.903.5 

11C 

109.7 

07.7 

17C 

169.6 

11.9 

230 

229.4 

16.0 

29C 

289.3 

20.2 

51 

50.  £ 

03.  G 

111 

110.7 

07.7 

171 

170.  b 

11.9 

231 

230.4 

16.1 

291 

290.3 

•20.3 

52 

51.  i 

03.6 

115 

111.7 

07.8 

172 

171.6 

12.0 

l)0f) 

•vi 

231.4 

16.2 

292 

291.3 

20.4 

53 

52.  i 

03.7 

IK 

112.7 

07.9 

17S 

172.  C 

12. 

233 

232.4 

16.3 

29S 

292.3 

20.4 

54 

53.  i 

03.8 

114 

113.7 

08.0 

174 

173.6 

12. 

234 

233.4 

16.3 

294 

293.3 

20.5 

55 

54.  { 

103.8 

HE 

114.7 

08.0 

111 

174.  C 

12. 

23E 

234.4 

16.4 

29c 

294.3 

20.6! 

56 

55.1 

103.9 

IK 

115.7 

08. 

176 

175.6 

12. 

23C 

235.4 

16.6 

29t 

295.3 

20.6 

57 

56.1 

>04.0 

I  11" 

116.7 

08. 

ITi 

176.  C 

12. 

23r 

236.4 

16.  E 

297 

296.3 

20.7 

58 

57.1 

>04.0 

i  lit 

117.7 

08. 

17* 

177.  e 

12. 

236 

237.4 

16.6 

296 

297.3 

20.8 

59 

58.1 

>04.1 

111 

118.7 

08. 

171 

178.6 

12. 

231 

238.4 

16.7 

291 

298.3 

20.9; 

60 

59.1 

>04.2 

12( 

119.7 

08.4 

18( 

179.612. 

24( 

239.4 

16.7 

30C 

299.3 

20.9 

Dist 

Dej: 

»  Lat. 

Dist 

Dcp. 

Lat 

Dist 

Do,). 

Lat 

Dist 

DCP. 

Lat. 

Dist. 

Dcp. 

Lat, 

For  86  Degrees. 

208                                         TABLE  IV. 

DIFFERENCE  OF   LATITUDE   AND  DEPARTURE   FOR  5  DEGREES. 

[list. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

Ol.O 

00.1 

61 

60.8 

05.3 

121 

120.5 

10.5 

181 

180. 

15.8 

241 

240.1 

21.0 

2 

02.0 

00.2 

62 

61.8 

05.4 

122 

121.5 

10.6 

182 

181. 

15.9 

242 

241.1 

21.1 

3 

03.0 

00.3 

63 

62.8 

05.5 

123 

122.5 

10.7 

183 

182. 

15.9 

243 

242.1 

21.2 

4 

04.0 

00.3 

64 

63.805.6 

124 

123.5 

10.8 

184 

183. 

16.0 

244 

243.1 

21.3 

5 

05.0 

00.4 

65 

64.8 

05.7 

125 

124.5 

10.9 

185 

184. 

16.1 

245 

244.1 

21.4 

6 

06.0 

00.5 

66 

65.7 

05.8 

126 

125.5 

11.0 

186 

185. 

16.2 

246 

245.1 

21.4 

7 

07.0 

00.6 

67 

66.7 

05.8 

127 

126.5 

11.1 

187 

186. 

16.3 

247 

246.1 

21.5 

8 

08.0 

00.7 

68 

67.7 

05.9 

128 

127.5 

11.2 

188 

187. 

16.4 

248 

247.1 

21.6 

9 

09.0 

J0.8 

6'J 

68.7 

06.0 

129 

128.5 

11.2 

189 

188. 

16.5 

249 

248.1 

21.7 

10 

10.0 

00.9 

70 

69.7 

06.1 

130 

129.5 

11.3 

190 

189. 

16.6 

250 

249.0 

21.7 

11 

11.0 

01.  0 

7i 

70.7 

06.2 

131 

130.5 

11.4 

191 

190. 

16.6 

251 

25J.O 

21.9 

12 

12.0 

01.0 

72 

71.7 

06.3 

132 

131.5 

11.5 

192 

191. 

16.7 

252 

251.0 

22.0 

13 

13.0 

01.1 

73 

72.7 

06.4 

133 

132.5 

11.6 

193 

192. 

16.8 

253 

252.0 

22.1 

14 

13.9 

01.2 

74 

73.7 

lJ-6.4 

134 

133.5 

11.7 

194 

193.3 

16.9 

254 

253.0 

22.1 

15 

14.9 

01.3 

75 

74.7 

06.5 

135 

134.5 

11.8 

195 

194.3 

17.0 

255 

254.0 

22.2 

16 

15.9 

01.4 

76 

75.7 

06.6 

136 

135.5 

11.9 

196 

195.3 

17.1 

256 

255.0 

22.3 

17 

16.9 

01.5 

77 

76.7 

06.7 

137 

136.5 

11.9 

197 

196.3 

17.2 

257 

256.0 

22.4 

18 

17.9 

01.0 

78 

77.7 

06.8 

138 

137.5 

12.0 

198 

197.2 

17.3 

258 

257.0 

22.5 

19 

18.9 

01.7 

79 

78.7 

06.9 

139 

138.5 

12.1 

199 

198.2 

17.3 

259 

258.0 

22.6 

20 

19.9 

dl.7 

80 

79.7 

07.0 

140 

139.5 

12.2 

200 

199.2 

17.4 

260 

259.0 

22.7 

21 

20.9 

01.8 

81 

«0  .  V 

07.1 

141 

140.5 

12.3 

201 

200.2 

1775 

261 

260.01     22.7 

22 

21.9 

Jl.9 

82 

81.7 

07.1 

142 

141.5 

12.4 

202 

201.2 

17.6 

262 

261.0 

22.8 

23 

22.9 

02.0 

83 

82.7 

07.2 

143 

142.5 

12.5 

203 

202.2 

17.7 

263 

262.0 

22.9 

24 

23.9 

02.1 

84 

83.7 

07.3 

144 

143.5 

12.6 

204 

203.2 

17.8 

264 

263.0 

23.0 

25 

24.9 

02.2 

85 

84.7 

07.4 

145 

144.4 

12.6 

205 

204.2 

17.9 

265 

264.0 

23.1 

26 

25.9 

02.3 

86 

85.7 

07.5 

146 

145.4 

12.7 

206 

205.2 

18.0 

266 

265.0 

23.2 

27 

26.9 

02.4 

87 

86.7 

07.6 

147 

146.4 

12.8 

207 

208.  '2 

18.0 

267 

266.0 

23.3 

28 

27.9 

02.4 

88 

87.7 

07.7 

148 

147.4 

12.9 

208 

207.2 

18.1 

268 

267.0 

23.4 

29 

28.9 

02.5 

89 

88.7 

07.8 

149 

148.4 

13.0 

209 

208.2 

18.2 

269 

268.0 

23.4 

30 

29.9 

02.  G 

90 

89.7 

07.8 

150 

149.4 

13.1 

210 

209.2 

18.3 

270 

269.0 

23.5 

31 

30.9 

02.  'i 

91 

90.  'i 

07.9 

151 

150.4 

13.2 

211 

'2  10.  2 

18.4 

271 

270.0 

23.6 

32 

31.9 

02.  b 

92 

91.  € 

08.0 

15i 

151.4 

13.2 

212 

211.2 

18.5 

272 

271.0 

23.7 

33 

32.9 

02.9 

93 

92.  C 

08.1 

153 

152.4 

13.3 

213 

212.2 

18.6 

273 

272.0 

23.8 

34 

33.9 

03.0 

94 

93.  C 

08.2 

154 

153.4 

13.4 

214 

213.2 

18.7 

274 

273.0 

23.9 

35 

34.9 

03.1 

95 

94.  G 

08.3 

155 

154.4 

13.5 

215 

214.2 

18.7 

275 

274.0 

24.0 

36 

35.9 

03.1 

9G 

95.6 

08.4 

15b 

155.4 

13.6 

216 

215.2 

J8.8 

276 

274.9 

24.1 

37 

36.9 

03:2 

97 

.96.6 

08.5 

157 

156.4 

13.7 

217 

216.2 

18.9 

277 

275.9 

24.1 

38 

37.9 

03.3 

98 

97.6 

08.5 

158 

157.4 

13.8 

218 

217.2 

19.0 

278 

276.9 

24.2 

39 

38.9 

03.4 

99 

98.6 

08.6 

159 

158.4 

13.9 

219 

218.2 

19.1 

279 

277.9 

24.3 

40 

39.8 

03.5 

100 

99.  G 

08.7 

160 

159.4 

13.9 

220 

219.2 

19.2 

280 

278.9 

24.4 

41 

40.8 

03.6 

101 

100.G 

08.8 

16i 

ICO.  4 

14.0 

221 

220.2 

19.3 

281 

279.9 

24.5 

42 

41.8 

03.7 

102 

101.6 

08.9 

162 

161.4 

14.1 

222 

221.2 

19.3 

282 

280.9 

24.6 

43 

12.8 

03.7 

103 

102.6 

09.0 

163 

162.4 

14.2 

223 

222.2 

19.4 

283 

281.9 

24.7 

44 

43.8 

03.  b 

104 

103.  C 

09.1 

164 

163.4 

14.3 

224 

223.1 

19.5 

284 

282.9 

24.8 

45 

44.8 

03.9 

105 

104.  G 

09.2 

165 

164.4 

14.4 

225 

224.1 

19.6 

285 

283.9 

24.8' 

46 

45.8 

04.0 

106 

105.6 

09.2 

166 

165.4 

14.5 

226 

225.1 

19.7 

286 

284.9 

24.9 

47 

46.8 

04.1 

107 

106.6 

09.3 

167 

166.4 

14.6 

227 

226  1 

19.8 

287 

285.9 

25.0 

48 

47.8 

04.2 

108 

107.  C 

09  4 

]68 

167.4 

14.6 

228 

227.1 

19.9 

288 

286.9 

25.1 

49 

48.8 

04.3 

109 

108.  C 

09.5 

169 

168.4 

14.7 

229 

228  1 

20.0 

289 

287.9 

25.2 

50 

49  8 

04.4 

110 

109.  G 

09.6 

170 

169.4 

14.8 

230 

229.1 

20.0 

290 

288.9 

25.3 

51 

50.8 

04.4 

111 

110.6 

09.7 

171 

170.3 

14.9 

231 

230.1 

20  1 

291 

289.9 

25.4! 

52 

51.8 

04.5 

112 

111.6 

09.8 

172 

171.3 

15.0 

232 

231.1 

20.2 

292 

290.9 

25.41 

53 

52.8 

04.6 

113 

112.  C 

09.8 

173 

172.3 

15.1 

233 

232.1 

20.3 

293 

291.9 

25.5 

54 

53.8 

04.7 

114 

113.  C 

09.9 

174 

173.3 

15.2 

234 

233.1 

20.4 

294 

292.9 

25.6 

55 

51.8 

04.8 

115 

114.6 

10.0 

175 

174.3 

15.3 

235 

234.1 

20.5 

295 

293.9 

25.7 

56 

55.8 

04.9 

116 

115.6 

10.1 

176 

175.3 

15.3 

236 

235.1 

20.6 

296 

294.9 

25  8 

57 

56.8 

05.0 

117 

116.6 

10.2 

177 

176.3 

15.4 

237 

236.  1 

20.7 

297 

295.9 

25.9 

58 

57.8 

05.1 

118 

117.  C 

10.3 

178 

177.3 

15.5 

238 

237.1 

20.7 

298 

296.9 

26.0 

59 

58.8 

05.1 

119 

118.5 

10.4 

179 

178.3 

15.6 

239 

238.1 

20.8 

299 

297.9 

26.1 

60 

59.8 

05.2 

120 

119.5 

10.5 

180 

179.3 

15.7 

240 

239.1 

20.9 

300 

298.9 

26.1 

[list. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

)ist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  85  Degrees. 

TABLE  IV.                                          209 

DIFFERENCE    OF   LATITUDE  AND  DEPARTURE  FOR  6   DEGREES. 

Dist. 

Lat,  Dep 

Dist. 

Lat. 

Dep 

Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

01.000.1 

61 

60.706.4 

121 

120.3 

12.6 

181 

180.0 

18.9 

241 

239.7 

25.2 

2 

02.000.2 

62 

61.7 

06.5 

122 

121.3 

12.8 

182 

181.0 

19.0 

242 

240.7 

25.3 

3 

03.0 

00.3 

63 

62.706.6 

123 

122.3 

12.9 

183 

182.0 

19.1 

243 

241.7 

25.4 

4 

04.000.4 

64 

63.606.7 

124 

123.3 

13.0 

184 

183.0 

19.2 

244 

242.7 

25.5 

5 

05.000.5 

65 

64.606.8 

125 

124.3 

13.1 

185 

184.0 

19.3 

245 

243  7 

25.6 

6 

06.0 

00.6 

66 

65.606.9 

126 

125.3 

13.2 

186 

185.0 

19  4 

24.6 

244.7 

25.7 

7 

07.0 

00.7 

67 

66.607.0 

127 

126.3 

13.3 

187 

186.0 

19.5 

247 

245.  1) 

25.8 

8 

J8.0 

00.8 

68 

67.607.1 

128 

127.3 

13.4 

188 

187.0 

19.7 

248 

246.6 

25.9 

9 

09.0 

00.9 

69 

6*.  6  07.  2 

129 

128.3 

13.5 

189 

188.0 

19.8 

249 

247.6 

26.0 

10 

09.9 

01.0 

70 

69.607.3 

130 

129.3 

13.6 

190 

189.0 

19.9 

250 

248.6 

26.1 

11 

10.9 

01.1 

71 

70.607.4 

131 

130  3 

13.7 

191 

190.0 

'M  0 

251 

249.6 

^0.2 

12 

11.9 

01.3 

72 

71.607.5 

132 

131.3 

13.8 

192 

190.9 

2o!i 

252 

250.6 

20.3 

13 

12.9 

01.4 

73 

72.607.6 

133 

132.3 

13.9 

193 

191.9 

20.2 

253 

251.6 

26.4 

14 

13.9 

01.5 

74 

73.607.7 

134 

133.314  0 

194 

192.9 

20.3 

254 

252.0 

26.6 

15 

14.0 

01.6 

75 

74.607.8 

135 

134.3 

14.1 

195 

193.9 

20.4 

255 

253  6 

26.7 

16 

15.9 

01.7 

76 

75.6|07.9 

136 

135.3 

14.2 

196 

194.9 

20.5 

256 

254.6 

26.8 

17 

16.9 

01.8 

77 

76.608.0 

137 

136.2 

14.3 

197 

195.9 

20.6 

257 

255.6 

26.9 

18 

17.9 

01.9 

78 

77.608.2 

138 

137.2 

14.4 

198 

196.9 

20.7 

258 

250.0 

27.0 

19 

18.9 

02.0 

79 

78.6'08.3 

139 

138.  '2 

14.5 

199 

197.9 

20.8 

259 

257.6 

27.1 

20 

19.9 

12.1 

80 

79.608.4 

140 

139.2 

14.6 

200 

198.9 

20.9 

260 

258.  <) 

27.2 

Ul 

M.9 

01.  -L 

81 

80.608.5 

141 

140.2 

14.7 

201 

199.9 

21.0 

201 

259.6 

27.3 

22 

21  9 

02  3 

82 

81.6i08.6 

142 

141.2 

14.8 

202 

200.9 

21.1 

262 

200.6 

27.4 

23 

22.9 

02.4 

83 

82.508.7 

143 

142.2 

14.9 

203 

201.9 

21.2 

263 

261.6 

27.5 

24 

23.9 

02.5 

84 

83  5!08.8 

144 

143.2 

15.1 

204 

202.9 

21.3 

264 

262.6 

27.6 

25 

24.9 

02.6 

85 

84.508.9 

145 

144.2 

15.2 

205 

203.9 

21.4 

265 

263.5 

27.7 

26 

25.9 

02.7 

86 

85.509.0 

146 

145  2 

15.3 

206 

204.9 

21.5 

266 

264.5 

27.8 

27 

26.9 

02.8 

87 

86.5U9.1 

147 

146.2 

15.4 

207 

205.9 

21.6 

267 

265.5 

27.9 

28 

27.8 

02.9 

88 

87.509.2 

148 

147.2 

15".  5 

208 

206.9 

21.7 

268 

266.5 

28.0 

29 

28.8 

03.0 

89 

88.509.3 

149 

148.2 

15.  C 

209 

207.9 

21.8 

269 

267.5 

28.1 

30 

29.8 

03.1 

90 

89.509.4 

150 

149.2 

15.7 

210 

208.8 

22  0 

270 

268.5 

28.2 

31 

30.8 

03.2 

91 

90.509.5 

151 

150.2 

15.8 

211 

209.8 

22.1 

271 

269.5 

28.3 

32 

31.8 

03.3 

92 

91.509.6 

152 

161.2 

15.9 

212 

210.8 

22.2 

272 

270.5 

28.4 

33 

33.* 

03.4 

93 

92.509.7 

153 

152.2 

16.0 

213 

211.8 

22.3 

273 

271.5 

28.5 

34 

33.8 

03.6 

94 

93.509.8 

154 

153.2 

16.1 

214 

212.8 

22.4 

274 

272.5 

28.6 

35 

34  8 

03.7 

95 

94.509.9 

155 

154.2 

16.2 

215 

213.8 

22.5 

275 

273.5 

28.7 

36 

Jo.  8 

03.8 

96 

95.510.0 

156 

155.1 

16.3 

216 

214.8 

22.6 

276 

274.5 

28.8 

37 

30.8 

03.9 

97 

96.510.1 

157 

156  1 

16.4 

217 

215.8 

22.7 

277 

275.5 

29.0 

38 

37.8 

04.0 

98 

97.5J10.2 

158 

157.1 

16.5 

218 

216.8 

22.8 

278 

276.5 

29.1 

39 

38.8 

04.1 

99 

98.510.3 

159 

158.1 

16.6 

219 

217.8 

22.9 

279 

277.5 

29.2 

40 

39.  8 

04.2 

10U 

99.510.5 

160 

159.1 

16.7 

220 

218.8 

23.0 

280 

278.5 

29.3 

41 

10.8 

04.3 

101 

100.410.0 

101 

160.1 

16.8 

221 

219.8 

23.1 

281 

279.5 

29.4 

42 

41.8 

04.4 

102 

101.410.7 

162 

161.1 

16.9 

222 

220.8 

23.2 

282 

280.5 

29.5 

43 

42.8 

04  5 

103 

102.410.8 

163 

162.1 

17.0 

223 

221.8 

23.3 

283 

281.4 

29.6 

44 

43.8 

04.6 

104 

103.4 

10.9 

164 

163.1 

17.1 

224 

222.8 

23.4 

284 

282.4 

29.7 

45 

14  8 

04.7 

105 

104.4 

11.0 

165 

164.1 

17.2 

225 

223.8 

23.5 

285 

283.4 

29.8 

46 

15.7 

04.8 

106 

105.4 

11.1 

166 

165  1 

17.4 

226 

224.8 

23.6 

286 

284.4 

29.9 

47 

46.7 

04.9 

107 

106^411.2 

167 

166.1 

17  5 

227 

225.8 

23.7 

287 

285.4 

30.0 

48 

47.7 

05.0 

108 

107.4 

11.3 

168 

167.1 

17.6 

228 

226.8 

23.8 

288 

286.4 

30.1 

49 

48.7 

05.1 

109 

108.4 

11.4 

169 

168.1 

17.7 

229 

227.7 

23.9 

289 

287.4 

30.2 

50 

19.7 

05.2 

110 

109.411.5 

170 

169.1 

17.8 

230 

228.7 

24.0 

290 

288.4 

30.3 

51 

50  7 

05.3 

111 

110.4 

11.6 

171 

170.1 

17.9 

231 

229.7 

24.1 

291 

2ts9.4 

30.4 

52 

51.7 

05.4 

112 

111.4 

11.7 

172 

171.1 

18.0 

232 

230.7 

24.3 

292 

290.4 

30.5 

53 

52.7 

05.5 

113 

112.411.8 

173 

172.1 

18.1 

233 

231.7 

24.4 

293 

291.4 

30.6 

54 

53.7 

05.6 

114 

113.411.9 

174 

173.0 

18.2 

234 

232.7 

24.5 

294 

292.4 

30.7 

55 

54.7 

05.7 

115 

114.412.0 

175 

174.0 

18.3 

235 

233.7 

24.6 

295 

293.4 

30.8 

56 

55.7 

05.9 

116 

115.4 

12.1 

176 

175.0 

18.4 

236 

234.7 

24.7 

296 

294.4 

30.9 

57 

56.7 

06.0 

117 

116.4 

12.2 

177 

176.0 

18.5 

237 

235.7 

24.8 

297 

295.4 

31.0 

58 

57.7 

06.1 

118 

117.412.3 

178 

177.0 

18.6 

238 

236.7 

24.9 

298 

296.4 

31.1 

59 

58.7 

06.2 

119 

118  312  4 

179 

178.0 

18.7 

239 

237.7 

25.0 

'2!)',) 

297.4 

31.3 

60 

59  7 

06.3 

120 

119.3 

12.5 

180 

179.0 

18.8 

240 

238.7 

25.1 

300 

198.4 

31.4 

Dist, 

Dep 

Lat. 

Dist, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  84  Degrees. 

210                                          TABLE  IV. 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE   FOR    7    DEGREES. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep  Dist. 

Lat, 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

01.0 

00.1 

61 

60.5 

07.4 

121 

120.1 

14.7 

181 

179.7 

22.1 

241 

239.2 

29.4 

2 

02.0 

00.  i 

62 

61  5 

07.6 

122 

121.1 

14.9 

182 

180.6 

22.2 

242 

240.2 

29  5 

3 

03.0 

00.4 

63 

62.5 

07.7 

123 

122.1 

15.0 

183 

181.6 

22.3 

243 

•241.2 

29.6 

4 

04  0 

00.6 

64 

63.507.8 

124 

123.1 

15.1 

184 

182.6 

22.4 

244 

242.2 

29.7 

5 

05.0 

00.6 

63 

64.5 

07.9 

125 

124.1 

15.2 

185 

183.6 

22.5 

245 

243.2 

29.9 

6 

06.0 

00.7 

66 

65.5 

08.0 

126 

125.1 

15.4 

186 

184.6 

22.7 

246 

244.2 

30  0 

7 

03  9 

00.9 

67 

66.5 

08.2 

127 

126  1 

15.5 

187 

185.6 

22.8 

247 

245.2 

30.1 

8 

07.9 

01.  0 

68 

67.5 

08.3 

128 

127.0 

15.6 

188 

186.6 

22.9 

2-18 

246.2 

30.2 

9 

08.9 

01.1 

69 

68.5 

08.4 

129 

128.0 

15.7 

189 

187.6 

23  0 

249 

247.1 

30.  C 

10 

09.9 

01.  i 

70 

69.5 

08.5 

130 

129.0 

15.8 

190 

188.6 

23.2 

250 

248.1 

30.5 

11 

10.  y 

Ol.o 

71 

70.  & 

08.7 

131 

130.  0 

16.0 

191 

i»y.(j 

23.  b 

251 

249.1 

30.6 

ia 

11.9 

01.5 

72 

71.5 

08.8 

132 

131.0 

16.1 

192 

190.6 

23.4 

252 

250.1 

30.7 

13 

12.9 

01.  0 

73 

72.5 

08.9 

133 

132.0 

16.2 

193 

191.6 

23.5 

253 

251.1 

30.8 

14 

13  9 

01.7 

74 

73.4 

09.0 

134 

133.0 

16.3 

194 

192.6 

23.6 

254 

252.1 

31.0 

15 

14.9 

01.8 

75 

74.4 

09.1 

135 

134.0 

16.5 

195 

193.5 

23.8 

255 

253.1 

31.1 

10 

15.9 

01.9 

76 

75.4 

09.3 

136 

135.0 

16.6 

196 

194.5 

23.9 

256 

254.1 

31.2 

17 

1G.9 

02.] 

77 

76.4 

09.4 

137 

136.0 

16.7 

197 

195.5 

24.0 

257 

255.1 

31.3 

18 

17.9 

02.2 

I8 

77  4 

09.5 

138 

137.0 

16.8 

198 

196.5 

24.1 

258 

256.1 

31.4 

19 

18.9 

02.3 

79 

78.4 

09.6 

139 

138.0 

16.9 

199 

197.5 

24.3 

259 

257.1 

31.0 

20 

19.9 

02  4 

80 

79.4 

09.7 

140 

139.0 

17.1 

200 

198.5 

24.4 

260 

258.1 

31.7 

iJi 

20.8 

02.6 

81 

80.4 

09.9 

141 

139.9 

17.2 

201 

199.5 

24.5 

261 

259.1 

31.8 

22 

21.8 

02.7 

82 

81.4 

10.0 

142 

140.9 

17.3 

202 

200.5 

24.6 

262 

260.0 

31.9 

23 

22.8 

02.8 

83 

82.4 

10.1 

143 

141.9 

17.4 

203 

201.5 

24.7 

263 

261.0 

32.1 

24 

23.8 

02.9 

81 

83.4 

10.2 

144 

142.9 

17.5 

204 

202.5 

24.9 

264 

262.0 

32.2 

25 

24.8 

03.0 

85 

84.4 

10.4 

145 

143.9 

17.7 

205 

203.5 

25.0 

265 

263.0 

32.3 

2G 

25.8 

C3  i. 

86 

85.4 

10.  f. 

146 

144.9 

17.8 

206 

204.5 

25.1 

260 

264.0 

32.4 

27 

26.8 

03.3 

87 

86.4 

10.6 

147 

145.9 

17.9 

207 

205.5 

25.2 

2G7 

265.0 

32.5 

28 

27.8 

03.4 

88 

87.3 

10.7 

148 

146  9 

18.0 

208 

206.4 

25.3 

268 

266.0 

32.7 

29 

28.8 

03.5 

89 

88.3 

10.8 

149 

147.9 

18.2 

209 

207.4 

25.5 

269 

267  0 

32.8 

30 

29.8 

03.7 

90 

89  3 

11.0 

150 

148.9 

18.3 

210 

208.4 

25.6 

270 

268.0 

32.9 

3i 

30.8 

03.8 

9i 

90.3 

11.1 

151 

149.9 

18.4 

211 

209.4 

25.7 

271 

269  .  0 

33.0 

32 

31.8 

03.9 

92 

91.3 

11.2 

152 

150  9 

18.5 

212 

210.4 

25.8 

272 

270.0 

33.1 

33 

32.8 

04.0 

93 

92.3 

11.3 

153 

151.9 

18.6 

213 

211.4 

26.0 

273 

271.0 

33.3 

3i 

33.7 

04.1 

94 

93.3 

11.5 

154 

152.9 

18.8 

214 

212.4 

26.1 

274 

272.0 

33.4 

35 

34.7 

04.3 

95 

94.3 

11.6 

155 

153.8 

18.9 

215 

213.4 

26.2 

275 

273.0 

33.5 

33 

35.7 

04.4 

90 

95.3 

11.7 

156 

154.8 

19.0 

216 

214  4 

26.3 

276 

273.9 

33.6 

37 

33.7 

04.5 

97 

96.3 

11.8 

157 

155.8 

19.1 

217 

215.4 

26.4 

277 

274.9 

33.8 

38 

37.7 

04.6 

98 

97.3 

11.9 

158 

156.8 

19.3 

218 

216.4 

26.  G 

278 

275.9 

33.9 

39 

38.7 

04.8 

99 

98.3 

12.1 

159 

157.8 

19.4 

219 

217.4 

26.7 

279 

276.9 

34.0 

40 

39.7 

04.9 

100 

99.3 

12.2 

160 

158.8 

19.5 

220 

218.4 

26.8 

280 

277.9 

34.1 

41 

40.  '< 

05.0 

101 

100.* 

12.3 

161 

159.8 

19.6 

221 

219.4 

26.9 

281 

278.9 

34.2 

42 

41.7 

05.1 

102 

101.2 

12.4 

162 

160.8 

19.7 

222 

220.3 

27.1 

282 

279.9 

34.4! 

43 

42.7 

05.2 

103 

102.2 

12.6 

163 

161.8 

19.9 

223 

221.3 

27.2 

283 

280,9 

34.5 

4i 

43.7 

05.4 

101 

103.2 

12.7 

164 

162.8 

20.0 

224 

222.3 

27.3 

284 

281.9 

34.C 

45 

44.7 

05.5 

105 

104.2 

12.8 

165 

163.8 

20.1 

225 

223.3 

27.4 

285 

282.9 

34.7 

40 

45.7 

05.6 

106 

105.2 

12.9 

166 

164.8 

20.2 

228 

224.3 

27.5 

28G 

283.9 

34.9 

47 

46.6 

05.7 

107 

106.2 

13.0 

167 

165.8 

20.4 

227 

225.3 

27.7 

287 

284.9 

35.0 

43 

17.6 

05.  b 

108 

107.2 

13.2 

168 

166.7 

20.5 

228 

226.3 

27.8 

288 

285.9 

35.1 

49 

18.  C 

06.0 

109 

108.2 

13.3 

169 

167.7 

20.6 

229 

227.3 

27.9 

289 

286.8 

35.2 

50 

49.6 

06  1 

110 

109.2 

13.4 

170 

168.7 

20.7 

230 

228.3 

28.0 

290 

287.8 

35.3 

5i 

50.  b 

0(3.2 

111 

110.2 

13.5 

171 

169.7 

20.8 

231 

229.3 

28.2 

29ll  288.8 

35.5 

52 

51.6 

06.3 

112 

111.2 

13.6 

172 

170.7 

21.0 

232 

230.3 

28.3 

292 

289.8 

35.6 

53 

52.6 

06.5 

113 

112.2 

13.8 

173 

171.7 

21.1 

233 

231.3 

28.4 

293 

290.8 

35.7 

54 

53.6 

06.6 

114 

113.  2 

13.9 

174 

172.7 

21.2 

234 

232.3 

28.5 

294 

291.8 

35.8 

55 

54.6 

06.7 

115 

114.1 

14-0 

175 

173.7 

21.3 

235 

233.2 

28.6 

295 

292.8 

30.0 

58 

55.6 

06.8 

116 

115.1 

14.1 

176 

174.7 

21.4 

236 

234.2 

28.8 

296 

293.8 

36.1 

57 

56.6 

06.9 

117 

116.1 

14.3 

177 

175.7 

21.6 

237 

235.2 

28.9 

297 

294.8 

36.2 

58 

57.6 

07.1 

118 

117.1 

14.4 

178 

176.7 

21.7 

238 

236.2 

29.0 

298 

295.8 

36.3 

59 

58.6 

07.2 

119 

118.1 

14.5 

179 

177.7 

21.8 

239 

237.2 

29.1 

299 

296.8 

36.4 

CO 

59.6 

07.3 

120 

119.1 

14.6 

180 

178.7 

21.9 

240 

238.2 

29.2 

300 

297.8 

36.6 

Dist. 

Dcp 

Lat. 

Dist, 

Dep. 

Lat.iflist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Hist. 

Dep. 

Lat. 

For  83  Degrees. 

TABLE  IV.                                          211 

DIFFERENCE   OF   LATITUDE   AND   DEPARTURE  FOR  8  DEGREES. 

Dist.lLat.JDep  Dist. 

Lat, 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat, 

Dep. 

1 

01.000.1 

61 

60.4 

08.5 

121 

119.8 

16.8 

181 

179.2 

25.2 

241 

238.7 

33.5 

2 

02.000  3 

62 

61.4 

08.6 

122 

120.817.0 

182 

180.2 

25.3 

242 

239.6 

33.7 

3 

03.000.4 

63 

62  4 

08.8 

123 

121.817.1 

183 

181.2 

25.5 

243 

240.6 

33.8 

4 

04.000.6 

64 

63.408.9 

124 

122.817.3 

184 

182.2 

25.6 

244 

241.6 

34.0 

5 

05.0J00.7 

65 

64.409.0 

125 

123.817.4 

185 

183.2 

25.7 

245 

242.6 

34.1 

6 

05.900.8 

66 

65.409.2 

126 

124.817.5 

186 

184.2 

25.9 

246 

243.6 

34.2 

7 

06  901.0 

67 

66.309.3 

127 

125.817.7 

187 

185.2 

26.0 

247 

244.6 

34.4 

8 

07.901.1 

68 

67.309.5 

128 

126.817.8 

188 

186.2 

26.2 

248 

245.6 

34.5 

9 

08.901.3 

69 

68.309.6 

129 

127.718.0 

189 

187.2 

26.3 

249 

246.6 

34.7 

10 

09.901.4 

70 

69.309.7 

130 

128.718.1 

190 

188.2 

26.4 

250 

247.6 

34.8 

11 

10.901.5 

71 

70.3 

09.9 

131 

129.7 

18.2 

191 

189.1 

26.6 

251 

248  6 

34.9 

12 

11  901.7 

72 

71.3 

10.0 

132 

130.7 

18.4 

192 

190.1 

26.7 

252 

249^5 

35.1 

13 

12.901  8 

73 

72.3 

10.2 

133 

131.7 

18.5 

193 

191.1 

26.9 

253 

250.5 

35.2 

14 

13.901.9 

74 

73  3 

10.3 

134 

132.7 

18.6 

194 

192.1 

27  0 

254 

251.5 

35.3 

15 

14.802.1 

75 

74.3 

10.4 

135 

133.7 

18.8 

195 

193.1 

27.1 

255 

252.5 

35.5 

16 

15.802.2 

76 

75.3 

10.6 

136 

134.7 

18.9 

196 

194.1 

27.3 

256 

253.5 

35.6 

17 

16.802.4 

77 

76.3 

10.7 

137 

135.7 

19.1 

197 

195.1 

27.4 

257 

254.5 

35.8 

18 

17.8'02.5 

78 

77.2 

10.9 

138 

136.7 

19.2 

198 

196.1 

27.6 

258 

255.5 

35.9 

19 

18.802.6 

79 

78  2 

11.0 

139 

137.7 

19.3 

199 

197.1 

27.7 

259 

256.5 

36.0 

20 

19.802.8 

80 

79.2 

11.1 

140 

13-!.  6 

19.5 

200 

198.1 

27.8 

260 

257.5 

36.2 

21 

20.802.9 

81 

80.2 

11.3 

141 

13J.6 

19.6 

201 

199.0 

28.0 

261 

258  .  5 

36.3 

22 

21.803.1 

82 

81.2 

11.4 

142 

140.6 

19.8 

202 

200.0 

28.1 

262 

259.5 

36.5 

23 

22.803.2 

83 

82.2 

11.6 

143 

141.6 

19.9 

203 

201.0 

28.3 

263 

260.4 

36.6 

24 

23.803.3 

84 

83.2 

11.7 

144 

142.6 

20.0 

204 

202.0 

28.4 

264 

261.4 

36.7 

25 

24.803.5 

85 

84.2 

11.8 

145 

143.6 

20.2 

205 

203.0 

28.5 

265 

262.4 

36.9 

-26 

25.703.6 

86 

85.2 

12.0 

146 

144.6 

20.3 

206 

204  0 

28.7 

266 

263.4 

37.0 

27 

26.703.8 

87 

86.2 

12.1 

147 

145.6 

20.5 

207 

205.0 

28.8 

267 

264.4 

37.2 

28 

27.703.9 

88 

87.1 

12.2 

148 

146.6 

20.6 

208 

206.0 

28.9 

268 

265.4 

37.3 

29 

28.704.0 

89 

88.1 

12.4 

149 

147.5 

20.7 

209 

207.0 

29.1 

269 

266.4 

37.4 

30 

29.704.2 

90 

89.1 

12.5 

150 

148.5 

20.9 

210 

208.0 

29.2 

270 

267.4 

37.6 

31 

30.  7  04.  ii 

91 

90.1 

12.7 

151 

14y.5 

21.0 

211 

208.9 

29  4 

271 

268.4 

37.7 

32 

31.704.5 

92 

91.1 

12.8 

152 

150.5 

21.2 

212 

209.9 

29.5 

272 

269.4 

37.9 

33 

32.704.6 

93 

92.1 

12.9 

153 

151.5 

21.3 

213 

210.9 

29.6 

273 

270.3 

38.0 

34 

33.704.7 

94 

93.1 

13.1 

154 

152.5 

21.4 

214 

211.9 

29.8 

274 

271.3 

38.1 

35 

34.704.9 

95 

94.1 

13.2 

155 

153.5 

21.6 

215 

212.9 

29.9 

275 

272.3 

38.3 

36 

35.605  0 

9G 

95.1 

13.4 

156 

154.5 

21.7 

216 

213.9 

30.1 

276 

273.3 

38.4 

37 

J6.  605.1 

97 

96.1 

13.5 

157 

155.5 

21.9 

217 

214.9 

30.2 

277 

274.3 

38.6 

38 

37.605.3 

98 

97.0 

13.6 

158 

156.5 

22.0 

218 

215.9 

30.3 

278 

275.3 

38.7 

39 

H8.605.4 

99 

98.0 

13.8 

159 

157.5 

22.1 

219 

216.9 

30.5 

279 

276.3 

38.8 

40 

39.605.6 

100 

99.0 

13.9 

160 

158.4 

22.3 

220 

217.9 

30.6 

280 

277.3 

39.0 

41 

40.605.7 

101 

100.0 

14.1 

101 

159.4 

22.4 

221 

218  8 

30.8 

281 

278.3 

39.1 

42 

11.605.8 

102 

101.0 

14.2 

162 

160.4 

22.5 

222 

219.8 

30.9 

282 

279.3 

39.2 

43 

42.606.0 

103 

102.0 

14.3 

163 

161.4 

22.7 

223 

220.8 

31.0 

283 

280.2 

39.4 

44 

43.606.1 

104 

103  0 

14.5 

164 

162  4 

22.8 

224 

221.8 

31.2 

284 

281.2 

39.5 

45 

44.606.3 

105 

104.0 

14.6 

165 

163.4 

23.0 

225 

222.8 

31.3 

285 

282.2 

39.7 

46 

45.606.4 

106 

105.0 

14  8 

166 

164.4 

23.1 

226 

223.8 

31.5 

286 

283.2 

39.8 

47 

46.506.5 

107 

106.0 

14.9 

167 

165.4 

23.2 

227 

224.8 

31.6 

287 

284.2 

39.9 

48 

47.506.7 

108 

106.9 

15.  0 

168 

166.4 

23.4 

228 

225.8 

31.7 

288 

285.2 

40.1 

49 

48.506.8 

109 

107.9 

15.2 

169 

167.4 

23.5 

229 

226.8 

31.9 

289 

286.2 

40.2 

50 

49.507.0 

110 

108.9 

15.3 

170 

168.3 

23.7 

230 

227.8 

32.0 

290 

287.2 

40.4 

51 

50.507.1 

111 

109.9 

15.4 

171 

109.3 

23.8 

231 

228.8 

32.1 

291 

288.2 

40.5 

52 

51.507.2 

112 

110.9 

15  6 

172 

170.3 

23.9 

232 

229.7 

32.3 

292 

289.2 

40.6 

53 

52.507.4 

113 

111.9 

15.7 

173 

171.3 

24.1 

233 

230.7 

32.4 

293 

290.1 

40.8 

54 

53.507.5 

114 

112.9 

15.9 

174 

172.3 

24.2 

234 

231.7 

32.6 

294 

2yl  1 

40.9 

55 

54.507.7 

115 

113.9 

16.0 

175 

173.3 

24.4 

235 

232.7 

32.7 

295 

292'.! 

41.1 

56 

55.507.8 

116 

114.9 

16.1 

176 

174.3 

24.5 

236 

233.7 

32.8 

296 

293.1 

41.2 

57 

56.407.9 

117 

115.9 

16.3 

177 

175.3 

24.6 

237 

234.7 

33.0 

297 

294.1 

41.3 

58 

57.408.1 

118 

116.9 

16.4 

178 

176.3 

24.8 

238 

235.7 

33.1 

298 

295.1 

41.5 

59 

58.408.2 

119 

117.8 

16.6 

179 

177.3 

24.9 

239 

236.7 

33.3 

299 

296.1 

41.6 

60 

59.408.4 

120 

118.8 

16.7 

180 

178.2 

25.1 

240 

237.7 

33.4 

300 

297.1 

41.8 

Dist. 

Dep  Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

(list. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  82  Degrees. 

212 

TABLE  IV. 

DIFFERENCE  OF   LATITUDE   AND   DEPARTURE  FOR  9  DEGREES. 

Dist, 

Lat. 

Dep 

Dist. 

Lat. 

JDep 

Dist. 

Lat, 

Dep 

Dist, 

Lat. 

Dep.  jDist. 

Lat. 

Dep. 

l 

01.0 

00.2 

61 

60.209.5 

121 

119.5 

18.9 

181 

178.8 

28.3 

241 

238,0 

37.7 

2 

02.0 

00.3 

62 

61.209.7 

122 

120.5 

19.1 

182 

179.8 

28.5 

242 

239.0 

37.9 

3 

03.0 

00.5 

63 

62.209.9 

123 

121.5 

19.2 

183 

180.7 

28.6 

243 

240.0 

38.0 

4 

04.0 

00.6 

64 

63.210.0 

124 

122.5 

19.4 

184 

181.7 

28.8 

244 

241.0 

38.2 

5 

04.9 

00.8 

65 

64.210.2 

125 

123.5 

19.6 

185 

182.7 

28.9 

245 

242.0 

38.3 

6 

05.9 

00.9 

66 

65.210.3 

126 

124.4 

19.7 

186 

183.7 

29.1 

246 

243.0 

38.5 

7 

00.  9 

01.1 

67 

66.210.5 

127 

125.4 

19.9 

187 

184.7 

29.3 

247 

244.0 

38.6 

8 

07.9 

01.3 

68 

67.2:10.6 

128 

126.4 

20.0 

188 

185.7 

29.4 

248 

244.9 

38.8 

9 

08.9 

01.4 

69 

68.210.8 

129 

127.4 

20.2 

189 

186.7 

29.6 

249 

245.9 

39.0 

10 

09.9 

01.6 

70 

69.111.0 

130 

128.420.3 

190 

187.7     29.7 

250 

246.9 

39  1 

11 

10.  9 

01.7 

71 

70.111.1 

131 

129.4 

20.5 

191 

188.6     29.9 

251 

•247.9 

39.3 

12 

11.9 

01.9 

72 

71.111.3 

132 

130.4 

20.6 

192 

189.6 

30.0 

25. 

248.9 

39.4 

13 

12.8 

02.0 

73 

72.111.4 

133 

131.4 

20.8 

193 

190.6 

30.2 

253 

249.9 

39.6 

14 

13.8 

02.2 

74 

73.111.6 

134 

132.4 

•21.0 

194 

191.6 

3'J.3 

254 

250.9 

39.7 

15 

14.8 

02.3 

75 

74.  11!!.  7 

135 

133.3 

21.1 

195 

192.6 

30.5 

255 

251.9 

39.9 

16 

15.8 

02.5 

76 

75.1 

11.9 

136 

134.3 

21.3 

196 

193.6 

30.7 

256 

252.8 

40.0 

17 

16.8 

02.7 

77 

76.112.0 

137 

135.3 

21.4 

197 

194.6 

30.8 

257 

253.8 

40  2, 

18 

17.8 

02.8 

78 

77.012.2 

138 

136.3 

21.6 

198 

195.6 

31.0 

258 

254.8 

40.4 

19 

18  8 

03.0 

79 

78.012.4 

139 

137.3 

21.7 

199 

196. 

81.1 

259 

255.8 

40.5' 

20 

19.8 

03.1 

80 

79.012.5 

140 

138.3 

21.9 

200 

197. 

31.3 

260 

256.8 

40.7 

21 

20.7 

03.3 

81 

80.012.7 

141 

139.3 

22.1 

201 

198. 

31.4 

261 

'257.8 

4U.8, 

22 

21.7 

03  4 

82 

81.012.8 

142 

140.3 

22.2 

202 

199. 

31.6 

262 

258.8 

41.0 

23 

22.7 

03.6 

83 

82.013.0 

143 

141.2 

22.4 

203 

200. 

31.8 

263 

259.8 

41.1 

24 

23.7 

03.8 

84 

83.013.1 

144 

142.2 

22.5 

204 

201. 

31.9 

264 

260. 

41.3 

25 

24.7 

03.9 

85 

84.0 

13.3 

145 

143.2 

22.7 

205 

202. 

32.1 

265 

261. 

41.5 

26 

25.7 

04.1 

86 

84.913.5 

146 

144.2 

22.8 

206 

203. 

32.2 

266 

262. 

41.6 

27 

26.7 

04.2 

87 

85.913.6 

147 

145.2 

23.0 

207 

204. 

32.4 

267 

263. 

41  8 

28 

27.7 

04.4 

88 

86.913.8 

148 

146.2 

23.2 

208 

205.4 

32.5 

268 

264. 

41  9 

29 

28.6 

04.5 

89 

87.9jl3.9 

149 

147  2 

23.3 

209 

206.4 

32.7 

269 

265. 

42.1 

30 

29.6 

04.7 

90 

88.9 

14.1 

150 

148.2 

23.5 

210 

207.4 

32.9 

270 

266. 

42.2 

31 

JO.  6 

04.8 

91 

89.9 

14.2 

151 

149.1 

23.6 

211 

208.4 

33.0 

271 

267. 

42.4 

32 

31.6 

05.0 

92 

90.914.4 

152 

150.1 

23.8 

212 

209.4 

33.2 

272 

268. 

4-2.6 

33 

32.  C 

05.2 

93 

91.914.5 

153 

151.1 

23.9 

213 

210.4 

33.3 

273 

269. 

42.7 

34 

33.6 

05.3 

94 

92.814.7 

154 

152.1 

24.1 

214 

211.4 

33.5 

274 

'270.6 

42  9 

35 

34.6 

05.5 

95 

93.814.9 

155 

153.1 

24.2 

215 

212.4 

33.6 

275 

271.6 

43.0 

36 

35.6 

05.6 

96 

94.8 

15.0 

156 

154.1 

24.4 

216 

213.3 

33.8 

276 

272.6 

43  .2 

37 

36.5 

05.8 

97 

95.8 

15.2 

157 

155.1 

24.6 

217 

214.3 

33.9 

277 

273.6 

43  3 

38 

37.5 

05.9 

98 

96.815.3 

158 

156.1 

24.7 

218 

215.3 

34.1 

278 

274.6 

43.5 

39 

38.5 

06  1 

99 

97.815.5 

159 

157.0 

24.9 

219 

216.3 

34.3 

279 

275.6 

43.6 

40 

39  5 

06.3 

100 

98.815.6 

160 

158.0 

25.0 

220 

217.3 

34.4 

280 

276.6 

43  8 

41 

10.5 

06.4 

101 

99.815.8 

1G1 

159.0 

25.2 

221 

218.3 

34.6 

281 

277.5 

44  0 

42 

41.5 

06.6 

102 

100.7 

16.0 

162 

160.0 

25.3 

222 

219.3 

34.7 

282 

278.5 

44.1 

43 

42.5 

06.7 

103 

101.7 

16.1 

163 

161.0 

25.5 

223 

220.3 

34.9 

283 

279.5 

44  3 

44 

43.5 

06.9 

104 

102.7 

16.3 

164 

162.0 

25.7 

224 

221.2 

35.0 

284 

280.5 

44.4 

45 

14.4 

07.0 

105 

103.7 

16.4 

165 

163.0 

25.8 

225 

•222.2 

35  2 

285 

281.5 

44  6 

46 

45.4 

07.2 

106 

104.7 

16.6 

166 

164.0 

26.0 

226 

223.2 

35.4 

286 

282.5 

44.7 

47 

46.4 

07.4 

107 

105.7 

16.7 

167 

164  9 

26.1 

227 

224.2 

35.5 

287 

283.5 

44.9 

48 

47.4 

07.5 

108 

106.7 

16.9 

168 

165.9 

26.3 

228 

225.2 

35.7 

288 

284.5 

45.1 

49 

48.4 

07.7 

109 

107.7 

17.1 

169 

166.9 

26.4 

229 

226.2 

35  8 

289 

285.4 

45.2 

50 

49.4 

07.8 

110 

108.6 

17.2 

170 

167.9 

26.6 

230 

227.2 

36.0 

290 

286.4 

45.4 

51 

30.4 

08.0 

111 

109.6 

17.4 

171 

168.9 

26.8 

231 

228.2 

36.1 

291 

287.4 

45.5! 

52 

51.4 

08.1 

112 

110.6 

17.5 

172 

169.9 

26.9 

ooo 

229.1 

36.3 

292 

288.4 

45.71 

53 

52.308.3 

113 

111.6 

17.7 

173 

170.9 

27.1 

233 

230.1 

36.4 

293 

289.4 

45.8 

54 

53.308.4 

114 

112.6 

17.8 

174 

171.9 

27.2 

234 

231.1 

36.6 

294 

290.4 

46.0 

55 

54.3'08.6 

115 

113.6 

18.0 

175 

172.8 

27.4 

235 

232.1 

36.8 

295 

291.4 

46.1 

56 

55.3 

08.8 

116 

114.6 

18.1 

176 

173.8 

27.5 

236 

233.1 

36.9 

296 

292.4 

46.3 

57 

56.3 

08.9 

117 

115.6 

18.3 

177 

174.8 

27.7 

237 

234.1 

37.1 

297 

293.4 

46.5 

58 

57.3 

09.1 

118 

116.5 

18  5 

178 

175.8 

27.8 

238 

235.1 

37.2 

298 

294  3 

46.6 

59 

58.3 

09.2 

119 

117.5 

18.6 

179 

176.8 

28.0 

239 

236.1 

37.4 

299 

295.3 

46.8 

60 

59.309.4 

120 

118.5 

18.8 

180 

177.8 

28.2 

240 

237.0 

37.5 

300 

296.3 

46.9 

Dist. 

Dep 

Lat. 

Dist, 

Dcp. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Mst. 

Dep. 

Lat. 

For  81  Degrees. 

FABLE  iv.                             213 

DIFFERENCE    OF    LATITUDE  AND  DEPARTURE  FOR  10    DEGREES. 

Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

01.0 

00.2 

61 

60.1 

10.6 

121 

119.2 

21.0 

181 

178.3 

31.4 

241 

237.3 

41.8 

2 

02.000.3 

62 

61.1 

10.8 

122 

120.1 

21.2 

182 

179.2 

31.6 

242 

238.3 

42.0 

3 

03.000.5 

63 

62.0 

10.9 

123 

121.1 

21.4 

183 

180.2 

31.8 

243 

239.3 

42.2 

4 

03.900.7 

64 

63.0 

11.1 

124 

122.1 

21.5 

184 

181.2 

32.0 

244 

240.3 

42.4 

6 

04.900.9 

65 

64.0 

11.3 

125 

123.1 

21.7 

185 

182.2 

32.1 

245 

241.3 

42  5 

6 

05.9 

01.0 

66 

65.0 

11.5 

126 

124.1 

21.9 

186 

183.2 

32.3 

246 

242.3 

42.7 

7 

06.9 

01.2 

67 

66.0 

11.6 

127 

125.1 

22.1 

187 

184.2 

32.5 

247 

243.2 

42.9 

8 

07.9 

01.4 

68 

67.0 

11.8 

128 

126.1 

22.2 

188 

185.1 

32.6 

248 

244.2 

43.1 

9 

08.901.6 

69 

68.0 

12.0 

129 

127.0 

22.4 

189 

186.1 

32.8 

249 

245.2 

43.2 

10 

09.801.7 

70 

68.9 

12.2 

130 

128.0 

22.6 

190 

187.1 

33.0 

250 

246.2 

43.4 

11 

10.801.9 

71 

69.9 

12.3 

131 

129  0 

22.7 

191 

188.1 

33  2 

251 

247.2 

43.6 

12 

11.802.1 

72 

70.9 

12.5 

132 

130.0 

22.9 

192 

189.1 

33.3 

252 

248.2 

43.8 

13 

12.8 

02.3 

73 

71.9 

12.7 

133 

131.0 

23.1 

193 

190.1 

33.5 

253 

249.2 

43.9 

14 

13.8 

02.4 

74 

72.9 

12.8 

134 

132.0 

23  3 

194 

191.0 

33.7 

254 

250.1 

44.1 

15 

14.8 

02.6 

75 

73.9 

13.0 

135 

132.9 

23.4 

195 

192.0 

33.9 

255 

251  1 

44.3 

16 

15.8 

02.8 

76 

74.8 

13.2 

136 

133.9 

23.6 

196 

193.0 

34.0 

256 

252.1 

44.5 

17 

16.7 

03.0 

77 

75.8 

13.4 

137 

134.9 

23.8 

197 

194.0 

34  2 

257 

253.1 

44.6 

18 

17.7 

03.1 

78 

76.8 

13.5 

138 

135.9 

24.0 

198 

195.0 

34.4 

258 

254.1 

44.  8j 

19 

18.7 

03.3 

79 

77.8 

13.7 

139 

136.9 

24.1 

199 

196.0 

34.6 

259 

255.1 

'45.0 

20 

19.7 

03.5 

80 

78.8 

13.9 

140 

137.9 

24.3 

200 

197.0 

34.7 

260 

256.1 

45  1 

21 

20.7 

03.6 

81 

79.8 

14.1 

141 

138.9 

24.5 

201 

197.9 

34.9 

261 

257.0 

45.3 

22 

21  7 

03  8 

82 

80.8 

14.2 

142 

139.8 

24.7 

202 

198.9 

35.1 

262 

258.0 

45.5 

23 

22.7 

04.0 

83 

81.7 

14.4 

143 

140.8 

24.8 

203 

199.9 

35.3 

263 

259.0 

45.7 

24 

•23.6 

04.2 

84 

82.7 

14  6 

144 

141.8 

25.0 

204 

200.9 

35.4 

264 

260.0 

45.8 

25 

24.6 

04.3 

85 

83.7 

14.8 

145 

142.8 

25.2 

205 

201.9 

35.6 

265 

261.0 

46.0 

26 

25.6 

04.5 

86 

84.7 

14.9 

146 

143.8 

25.4 

206 

202.9 

35.8 

266 

262.0 

46.2 

27 

•26.  G 

04.7 

87 

85.7 

15.1 

147 

144.8 

25.5 

207 

203.9 

35.9 

267 

262.9 

46.4 

28 

•27.6 

04.9 

88 

86.7 

15.3 

148 

145.8 

25.7 

208 

204.8 

36.1 

268 

263.9 

46.5 

29 

28.6 

05.0 

89 

87.6 

15  5 

149 

146.7 

25.9 

209 

205.8 

36.3 

269 

264.9 

46.7 

30 

29.5 

05.2 

90 

88.6 

15.6 

150 

147.7 

26.0 

210 

206.8 

36.5 

270 

265.9 

46.9 

31 

30.5 

05.4 

91|    89.6 

15.8 

151 

148.7 

26.2 

211 

207.8 

36.6 

271 

266.  9 

47.1 

32 

31.5 

05.6 

92 

90.6 

16.0 

152 

149.7 

26.4 

212 

208.8 

36.8 

272 

267.9 

47.2 

33 

32.5 

05.7 

93 

91.6 

16.1 

153 

150.7 

26.6 

213 

209.8 

37.0 

273 

268.9 

47.4 

34 

33.5 

05.9 

94 

92.6 

16.3 

154 

151.7 

26.7 

214 

210  7 

37.2 

274 

269.8 

47.6 

35 

34.5 

06.1 

95 

93.6 

16.5 

155 

152.6 

26.9 

215 

211.7 

37.3 

275 

270.8 

47.8 

3G 

35.5 

06.3 

96 

94.5 

16.7 

156 

153.6 

27.1 

216 

212.7 

37.5 

276 

271.8 

47.9 

37 

36.4 

06.4 

97 

95.5 

16.8 

157 

154.6 

27  3 

217 

213.7 

37.7 

277 

272.8 

48.1 

38 

37.4 

06.6 

98 

96.5 

17.0 

158 

155.6 

27.4 

218 

214.7 

37.9 

278 

273.8 

48.3 

39 

38.4 

06.8 

99 

97.5 

17.2 

159 

156.6 

27.6 

219 

215.7 

38.0 

279 

274.8 

48.4 

40 

39.4 

06.9 

100 

98.5 

17.4 

160 

157.6 

27.8 

220 

216  7 

38.2 

280 

275.7 

48.6 

41 

40.4 

07.1 

101!     99.5 

17.5 

161 

158.6 

28.0 

'221 

217.6 

38.4 

281 

276.7 

48.8 

42 

41.4 

07.3 

102  100.5 

17.7 

162 

159.5 

28.1 

222 

218.6 

38.5 

282 

277.7 

49.0 

43 

42.3 

07  5 

103 

101.4 

17.9 

163 

160.5 

28.3 

223 

219.6 

38.7 

283 

278.7 

49.1 

44 

43.3 

07.6 

104 

102.4 

18.1 

164 

161.5 

28.5 

224 

220.6 

38  9 

284 

279.7 

49.3 

45 

44  3 

07.8 

105 

103.4 

18.2 

165 

162.5 

28.7 

225 

221.6 

39.1 

28o 

280.7 

49.5 

4G 

45.3 

08.0 

106 

104.4 

18.4 

160 

163.5 

28  8 

226 

222.6 

39.2 

286 

281.7 

49.7 

47 

46.3 

08.2 

107 

105.4 

18.6 

167 

164  5 

29.0 

227 

223.6 

39.4 

287 

282.6 

49.8 

48 

47.3 

08.3 

108 

106.4 

18.8 

168 

165.4 

29.2 

228 

224.5 

39.6 

288 

283.6 

50.0 

49 

48.3 

08.5 

109 

107.3 

18.9 

169 

166.4 

29.3 

229 

225.5 

39.8 

289 

284.6 

50.2 

50 

49.2 

08.7 

110 

108.3 

19.1 

170 

167.4 

29.5 

230 

226.5 

39.9 

290 

285.6 

50.4 

51 

50.2 

08.9 

111 

109.3 

19.3 

171 

168.4 

29.7 

'231 

227.5 

40.1 

291 

286.6 

50.5 

52 

51.2 

09.0 

112 

110.3 

19.4 

172 

169.4 

29.9 

23'2 

228.5 

40.3 

292 

287  6 

50.7 

53 

52.2 

09.2 

113 

111.3 

19.6 

173 

170.4 

30.0 

233 

229.5 

40.5 

293 

288.5 

50.9 

54 

53.2 

09.4 

114 

112.3 

19.8 

174 

171.4 

30.2 

234 

230.4 

40.6 

294 

289.5 

51.1 

55 

54.2 

09.6 

115 

113.3 

20.0 

175 

172.3 

30.4 

235 

231.4 

40.8 

'295 

290.5 

51.2 

5G 

55.1 

09.7 

116 

114.2 

20.1 

176 

173.3 

30.6 

236 

232.4 

41.0 

296 

291.5 

51  4 

57 

56.  1 

09.9 

117 

115.2 

•20.3 

177 

174.3 

30.7 

237 

233.4 

41.2 

297 

292.5 

51  6 

53 

57.1 

10.1 

118 

116  2 

•20.5 

178 

175.3 

30.9 

238 

234.4 

41.3 

298 

293  5 

51.7 

59 

58.1 

10.2 

119 

117  2 

20  7 

179 

176.3 

31.1 

239 

235.4 

41.5 

299 

294.5 

51.9 

60 

59  1 

10.4 

120 

118.2 

20.8 

180 

177.3 

31.3 

240 

236.4 

41.7 

300 

295.4 

52.1 

Dist. 

Dep 

Lat. 

Dist, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat, 

For  80  Degrees. 

214                                         TABLE  IV. 

DIFFERENCE  OF    LATITUDE   AND  DEPARTURE   FOR  11  DEGREES. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist, 

Lat. 

Dep. 

l 

01.0 

00.2 

61 

59.9 

11.6 

121 

118.8 

23.1 

181 

177.7 

34.5 

241 

236.6 

46.0 

9 

02.0 

00.4 

62 

60.9 

11.8 

122 

119.8 

,23.3 

182 

178.7 

34.7 

242 

237.6 

46.2 

3 

02.9 

00.6 

63 

61.8 

12.0 

123 

120.7 

23.5 

183 

179.6 

34.9 

243 

238.5 

46.4 

4 

03.9 

00.8 

64 

62.8 

12.2 

124 

121.7 

23.7 

184 

180.6 

35.1 

244 

239.5 

46.6 

5 

04.9 

01.0 

65 

63.8 

12.4 

125 

122.7 

23.9 

185 

181.6 

35.3 

245 

240.5 

46.7 

6 

05.9 

01.1 

66 

64.8 

12.6 

126 

123.7 

24.0 

186 

182.6 

35.5 

246 

241.5 

46.9 

7 

06.9 

01.3 

67 

65.8 

12.8 

127 

124.7 

24.2 

187 

183.6 

35.7 

247 

242.5 

47.1 

8 

07.9 

01.5 

68 

66.8 

13.0 

128 

125.6 

24.4 

188 

184.5 

35.9 

248 

243.4 

47.3 

9 

U8.8 

01.7 

69 

67.7 

13.2 

129 

126.6 

24.6 

189 

185.5 

36.1 

249 

244.4 

47.5 

10 

09.8 

01.9 

70 

68.7 

13.4 

130 

127.6 

24.8 

190 

186.5 

36.3 

250 

245.4 

47.7 

11 

10.8 

02.  J 

71 

69.7 

13.5 

131 

128.6 

25.0 

191 

187.5 

36.4 

251 

246.4 

47.9 

12 

11.8 

02.3 

72 

70.7 

13.7 

132 

129.6 

25.2 

192 

188.5 

36.6 

252 

247.4 

48.1 

13 

12.8 

02.5 

73 

71.7 

13.9 

133 

130.6 

25.4 

193 

189.5 

36.8 

253 

248.4 

48.3 

14 

13.7 

02.7 

74 

72.6 

14.1 

134 

131.5 

25.6 

194 

190.4 

37.0 

254 

249.3 

48.5 

15 

14.7 

02.9 

75 

73.6 

14.3 

135 

132.5 

25.8 

195 

191.4 

37.2 

255 

250.3 

48.7 

16 

15.7 

03.1 

76 

74.6 

14.5 

136 

133.5 

26.0 

196 

192.4 

37.4 

256 

251.3 

48.8 

17 

16.7 

03.2 

77 

75.6 

14.7 

137 

134.5 

26.1 

197 

193.4 

37.6 

257 

252.3 

49.0 

18 

17.7 

03.4 

78 

76.6 

14.9 

138 

135.5 

26.3 

198 

194.4 

37.8 

258 

253.3 

49.2 

19 

18.7 

03.  C 

79 

77.5 

15.1 

139 

136.4 

26.5 

199 

195.3 

38.0 

259 

254.2 

49.4 

20 

19.6 

03.8 

80 

78.5 

15.3 

140 

137.4 

26.7 

200 

196.3 

38.2 

260 

255.2 

49  6 

81 

20.6 

04.0 

81 

79.5 

15.5 

141 

138.4 

26.9 

^01 

197.3 

38.4 

261 

256  .  2 

49.8 

22 

21.6 

04.  '2 

82 

80.5 

15.6 

142 

139.4 

27  1 

202 

198.3 

38.5 

262 

257.2 

50.0 

23 

22.6 

04.4 

'83 

81.5 

15.8 

143 

140.4 

27.3 

203 

199.3 

38.7 

263 

258.2 

50.2 

24 

23.6 

04.6 

84 

82.5 

16.0 

144 

141.4 

27.5 

204 

200.3 

38.9 

264 

259.1 

50.4 

25 

24.5 

04.8 

85 

83.4 

16.2 

145 

142.3 

27.7 

205 

201.2 

39  1 

265 

260.1 

50.6 

26 

25.5 

05.0 

86 

84.4 

16.4 

146 

143.3 

27.9 

206 

202.2 

39.3 

266 

261.1 

50.8 

27 

26.5 

05.2 

87 

85.4 

16.6 

147 

144.3 

28.0 

207 

203.2 

39.5 

267 

262  1 

50.9 

28 

27.5 

05.3 

88 

86.4 

16.8 

148 

145.3 

28.2 

208 

204.2 

39.7 

268 

263.1 

51.1 

29 

28.5 

05.5 

89 

87.4 

17.0 

149 

146.3 

28.4 

209 

205.2 

39.9 

269 

264.1 

51.3 

30 

29.4 

05.7 

90 

88.3 

17.2 

150 

147.2 

28.6 

210 

206.1 

40.1 

270 

265.0 

51.5 

31 

30.4 

05.9 

91 

89.3 

17.4 

151 

148.2 

28.8 

211 

207  .  1 

40.3 

27J 

266.0 

51.7 

32 

31.4 

06.1 

92 

90.3 

17.6 

152 

149.2 

29.0 

212 

208.1 

40.5 

272 

267.0 

51.9 

33 

32.4 

06.3 

93 

91.3 

17.7 

153 

150.2 

29.2 

213 

209.1 

40.6 

273 

268.0 

52.1 

34 

33.4 

06.5 

94 

92.3 

17.9 

154 

151.2 

29.4 

214 

210.1 

40.8 

274 

269.0 

52.3 

35 

34.4 

06.7 

95 

93.3 

18.1 

155 

152.2 

29.6 

215 

211.0 

41.0 

275 

269.9 

52.5 

3G 

35.3 

06.9 

96 

94.2 

18.3 

156 

153.1 

29.8 

216 

212.0 

41.2 

276 

270.9 

52.7 

37 

36.3 

07.1 

97 

95.2 

18.5 

157 

154.1 

30.0 

217 

213.0 

41.4 

277 

271.9 

52.9 

38 

37.3 

07.3 

98 

96.2 

18.7 

158 

155.1 

30.1 

218 

214.0 

41.6 

278 

272.9 

53.0 

39 

38.3 

07.4 

99 

97.2 

18.9 

159 

156.1 

30.3 

219 

215.0 

41.8 

279 

273.9 

53  2 

40 

39.3 

07.6 

100 

98.2 

19.1 

160 

157.1 

30.5 

220 

216.0 

42.0 

280 

274.9 

53.4 

41 

iO.2 

07.8 

101 

99.1 

19.3 

161 

158.0 

30.7 

221 

216.9 

4^ 

281 

275.8 

53.6 

42 

41.2 

08.0 

102 

100.1 

19.5 

162 

159.0 

30.9 

222 

217.9 

42.4 

282 

276.8 

53.8 

43 

12.2 

08.2 

103 

101.1 

19.7 

163 

160.0 

31.1 

223 

218.9 

42.6 

283 

277.8 

54.0 

44 

43.2 

08.4 

104 

102.1 

19.8 

164 

161.0 

31.3 

224 

219.9 

42.7 

284 

278.8 

54.2 

45 

44.2 

08.6 

105 

103.1 

20.0 

165 

162.0 

31.5 

225 

220.9 

42.9 

285 

279.8 

54.4 

40 

45.2 

08.8 

106 

104.1 

20.2 

166 

163.0 

31.7 

226 

221.8 

43.1 

286 

280.7 

54.6 

47 

46.1 

09.0 

107 

105.0 

20.4 

167 

163.9 

31.9 

227 

222.8 

43.3 

287 

281.7 

54.8 

48 

47.1 

09.2 

108 

106.0 

20.6 

168 

164.9 

32.1 

228 

223.8 

43.5 

288 

282.7 

55.0 

49 

48.1 

09.3 

109 

107.0 

20.8 

169 

165.9 

32.2 

229 

224.8 

43.7 

289 

283.7 

55.1 

50 

49.1 

09.5 

110 

108.0 

21.0 

170 

166.9 

32.4 

230 

225.8 

43.9 

290 

284.7 

55.3 

51 

50.1 

09.7 

111 

109.0 

21.2 

171 

167.9|32.6 

231 

226.8 

44.1 

291 

285.7 

55.5 

52 

51.0 

09.9 

112 

109.9 

21.4 

172 

168.832.8 

232 

227.7 

44.3 

292 

286.6 

55  7 

53 

•32.0 

10.1 

113 

110.9 

21.6 

173 

169.8 

33.0 

233 

228.7 

44.5 

293 

287.6 

55.9 

54 

53.0 

10.3 

114 

111.9 

21.8 

174 

170.8 

33.2 

234 

229.7 

44.6 

294 

288.6 

56.1 

55 

54  0 

10.5 

115 

112.9 

21.9 

175 

171.8 

33.4 

235 

230.7 

44.8 

295 

289.6 

56.3 

5G 

55.0 

10.7 

116 

113.9 

22.1 

176 

172.8 

33.6 

236 

231.7 

45.0 

296 

290.6 

56.5 

57 

56.0 

10.9 

117 

114.9 

22.3 

177 

173.7 

33.8 

237 

232.6 

45.2 

297 

291.5 

56.7 

58 

56  9 

11.1 

118 

115.8 

22.5 

178 

174.7 

34.0 

238 

233.6 

45.4 

298 

292.5 

56.9 

59 

57.9 

11.3 

119 

116.8 

22.7 

179 

175.7 

34.2 

239 

234.6 

45.6 

299 

293.5 

57.1 

60 

58.9 

11.4 

120 

117.8 

22.9 

180 

176.7 

34.3 

240 

235.6 

45.8 

300 

294.5 

57.2 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist.  Dep. 

Lat. 

For  79  Degrees. 

TABLE  IV.                                           215 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE   FOR  12  DEGREES. 

Hist. 

Lat. 

Dei, 

list. 

Lat. 

Dcp 

Dist. 

Lat. 

Dep 

ist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

31.0 

00.  21 

61 

59.7 

12.7 

121 

118.4 

25.2 

181 

177.0 

37.  6- 

241 

235.7 

50.1 

•I 

3-2.0 

00.4! 

6i 

60.612.9 

122 

119.3 

25.  41 

182 

178.0 

37.8 

212 

236.7 

50.3 

3 

32.9 

00.  61 

63 

61.6 

13.1 

123 

120.3 

25.6! 

183 

179.0 

38.0 

243 

237.7 

50.5 

4 

)3.9 

00.8 

64 

62.6 

13.3 

124 

121.3 

25.8? 

184 

180.0 

38.3 

244 

238.7 

50.7 

5 

54.9 

01.0 

65 

63.6 

13.  5i 

125 

122.3 

26.  0| 

185 

181.0 

38.5 

245 

239.6 

50.9 

6 

1)5.9 

01.2 

66 

64.6 

13.7 

126 

123.2 

26.2' 

186 

181.9 

38.7; 

246 

240.6 

51.1 

7 

06.8 

01.5 

67 

65.5 

13.9 

127 

124.2 

26.4 

187 

182.9 

38.9 

247 

241.6 

51.4 

8 

07.8 

01.7 

68 

66.5 

14.1 

128 

125.2 

26.6| 

188 

183.9 

39.1 

248 

242.6 

51.6 

9 

08.8 

01.9 

69 

67.5 

14.3 

129 

126.2 

26.8 

189 

184.9 

39.3! 

249 

243.6 

51.8 

10 

J9.8 

12.1 

70 

68.5 

14.6 

130 

127.2 

27.  0' 

190 

185.8 

39.5 

250 

244.5 

52.0 

11 

10.8 

J2  .  3 

71 

69.4 

14.8 

131 

128.1 

27.  2| 

191 

186.8 

39.7 

251 

245.5 

52.  V 

13 

11.7 

02.5 

72 

70.4 

15.0 

132 

129.1 

27  4 

192 

187.8 

39.9 

252 

246.5 

52.4 

13 

12.7 

02.7 

73 

71.4 

15.2 

133 

130.1 

27.7 

193 

188.8 

4.0.1 

253 

247.5 

52.6 

14 

13.7 

02.  9 

74 

72.4 

15.4 

134 

131.1127.9 

194 

189.8 

40.3; 

254 

248.4 

52.8 

13 

14.7 

03.1 

75 

73.4 

15.6 

135 

132.0 

28.  1' 

195 

190.7 

40.5 

255 

249.4 

53.0 

16 

15.7 

03.3 

76 

74.3 

15.8 

136 

133.0 

28.3' 

196 

191.7 

40.8 

256 

25'3.4 

53.2 

17 

16.6 

)3.5 

77 

75.3 

16.0 

137 

134.0 

28.  51 

197 

192.7 

41.0 

257 

251.4 

53.4 

18 

17.6 

03.7 

78 

76.3 

16.2 

138 

135.0 

28.7: 

198 

193.7 

41.2 

258 

252.4 

53.6 

19 

18.6 

04.0 

79 

77.3 

16.  41 

139 

136.0 

28.9: 

199 

194.7 

41.  41 

259 

253.3 

53.8 

20 

19.  (3 

04.2 

80 

78.3 

16.6 

140 

136.9 

29  1 

200 

195.6 

41.  6 

260 

254.3 

54.1 

•21 

^0.5 

04.4 

81 

79.2 

10.6 

141 

137.9 

29.3 

201 

196.6 

"iTTS; 

261 

255  .  3 

54.3 

22 

21.5 

04.6 

82 

80.2 

17.0 

142 

138.9 

29.5 

202 

197.6 

42.0 

262 

256.3 

54.5 

23 

22.5 

04.8 

83 

81.2 

17.3 

143 

139.9 

29.7' 

203 

198.6 

42.2 

263 

257.3 

54.7 

'24 

23.5 

05.0 

81 

82.2 

17.5 

144 

140.9 

29.9 

204 

199.5 

42.4 

264 

258.2 

54.9 

25 

24.5 

J5.2 

85 

83.1 

17.7 

145 

141.8 

30.1 

205 

200.5 

42.6 

265 

259.2 

55.1 

ii6 

25.4 

05.4 

86 

84.1 

17.9 

146 

142.8 

30.4 

206 

201.5 

42.8 

266 

260.2 

55.3 

27 

26.4 

05.6 

87 

85.1 

18.1 

147 

143.8 

30.6 

207 

202.5 

43.0 

267 

261.2 

55.5 

28 

27.4 

05.8 

88 

86.1 

18.3 

148 

144.8 

30.8 

208 

203.5 

43.2 

268 

262.1 

55.7 

29 

28.4 

06.0 

89 

87.1 

18.5 

149 

145.7 

31.0 

209 

204.4 

43.5 

269 

263.1 

55.9 

30 

29.  ;-> 

06.2 

90 

88.0 

18.7 

150 

146.7 

31.2 

210 

205.4 

43.7 

270 

264.1 

56.1 

31 

30,3 

06.4 

9i 

89.0 

18.9 

151 

147.7 

31  4 

211 

206.4 

43.9 

271 

265.1 

56.3 

32 

31.3 

06.7 

92 

90.0 

19.1 

152 

148.7 

31.6 

212 

207.4 

44.1 

272 

266.1 

56.6 

33 

32.3 

06.9 

93 

91.0 

19.3 

153 

149.7 

31.8 

213 

208.3 

44.3 

273 

267.0 

56.8 

34 

33.3 

07.1 

94 

91.9 

19.5 

154 

150.6 

32.0 

214 

209.3 

44.5 

274 

268.0 

57.0 

35 

34.2 

07.3 

95 

92.9 

19.8 

155 

151.6 

32.2! 

215 

210.3 

44.7 

275 

269.0 

57.2 

So 

35.2 

07.5 

96 

93.9 

20.0 

156 

152.6 

32.4 

216 

211.3 

44.9 

276 

270.0 

57.4 

37 

3(5.2 

07.7 

97 

94.9120.2 

157 

153.6 

32.6 

217 

212.3 

45.1 

277 

270.9 

57.6 

38 

37.2 

07.9 

98 

95.920.4 

158 

154.5 

32.9 

218 

213.2 

45.3 

278 

271.9 

57.8 

39 

38.1 

08.1 

99 

96.8 

20.6 

159 

155.5 

33.1 

219 

214.2 

45.5 

279 

272.9 

58.0 

40 

39.1 

08.3 

100 

97.8 

20.8 

160 

156.5 

33.3 

220 

215.2 

45.7 

280 

273.9 

58.2 

41 

40.  J 

u8.5 

101 

98.8J21.0 

161 

157.5 

33.5 

221 

216.2 

45.9 

281 

274.9 

58.4 

42 

11.1 

08.7 

102 

99.8121.2 

162 

158.5 

33.7 

222 

217.1 

46.2 

282 

275.8 

58.6 

43 

12.1 

08.9 

103 

100.7 

21.4 

163 

159.4 

33.9 

223 

218.1 

46.4 

283 

276.8 

58.8 

44 

43.0 

09.1 

104 

101.7 

•21.  ( 

164 

160.4 

34.1 

224 

219.1 

46.6 

284 

277.8 

59.0 

45 

44.0 

09.4 

105 

102.7 

21.8 

165 

161.4 

34.3 

225 

220.1 

46.8 

285 

278.8 

59.3 

46 

45.0 

09.6 

106 

103.7 

22.0 

166 

162.4 

34.5 

226 

221.1 

47.0 

286 

279.8 

59.5 

47 

46.0 

09.8 

107 

104.7 

22.2 

167 

163.4 

34.7 

22" 

222  0 

47.2 

287 

280.7 

59  7 

48 

47.0 

10.0 

108 

105.  C 

22  5 

168 

164.3 

34.9 

228 

223.0 

47  4 

288 

281.7 

59.9 

49 

47.9 

10.2 

109 

106.  C 

22.7 

169 

165.3 

35.1 

229 

224  0 

47.6 

289 

282.7 

60.1 

50 

48  9 

10.4 

110 

107.  C 

22.9 

170 

166.3 

35.3 

230 

225.0 

47.8 

290 

283.7 

60.3 

51 

19.  9 

10.0 

111 

108.623.1 

171 

167.2 

35.  fa 

231 

226.0 

48.0 

291 

284.6 

60.5 

52 

50.9 

10.8 

112 

109.623.3 

172 

168.  2 

35.8 

232 

226.9 

48.2 

292 

285.6 

60.7 

53 

51.8 

11.0 

113 

110.523.5 

173 

169.  S 

36.0 

233 

227.0 

48.4 

293 

286.6 

60.9 

54 

52.  8 

11.2 

114 

111.523.7 

174 

170.  i 

36.2 

234 

228.9 

48.7 

294 

287.  C 

61.1 

55 

53.8 

11.4 

115 

112.523.9 

175 

171.  S 

36.4 

235 

229.9 

48.9 

295 

288.  C 

61.3 

56 

54.8 

11.6 

11C 

113.524.1 

176 

172.5 

36.6 

236 

230.6 

49.1 

29G 

289.5 

61.5 

57 

55.8 

11.9 

117 

114.424.3 

177 

173.] 

36.8 

237 

231.8 

49.3 

297 

290.5 

61.7 

58 

56.7 

12.1 

lie 

115.424.5 

178 

174.1 

37.0 

238 

232.8 

49.5 

298 

291.  E 

62.0 

59 

57.7 

12.3 

11£ 

116.424.7 

179 

175.] 

37.2 

23f 

233.8 

49.7 

298 

292.  C 

62.2 

60 

58.7 

12  5 

12( 

117.4 

124.9 

ISO 

176.] 

37.4 

24C 

234.8 

49.9 

30C 

293.4 

62.4 

Dixt 

!Dep 

Lat 

Dist. 

Dcp. 

Lat 

ftist 

Dcp. 

Lat 

Dist 

Dcp. 

Lat. 

Dist. 

Dcp. 

Lat. 

For  78  Degrees. 

216                                          TABLE  IV. 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE  FOR  13  DEGREES. 

Dist. 

Lat. 

Dep  'Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

l 

31.0 

30.2 

61 

59.413.7 

121 

117.9 

27.2 

181 

176.4 

40.7 

241 

234.8 

54.2 

2 

91.900.4 

62 

60  413.9 

122 

118.927.4 

182 

177.3 

40.9 

242 

235.8 

54  4 

3 

D2.900.7 

63 

61.414.2 

123 

119.827.7 

183 

178.3 

41.2 

243 

236.8 

54.7 

4 

03.900.9 

64 

62.4 

14.4 

124 

120.827.9 

184 

179.3 

41.4 

244 

237.7 

54.9 

5 

04.901.1 

65 

63.3 

14.6 

125 

121.828.1 

185 

180.3 

41.6 

245 

238.7 

55.1 

6 

05-801.3 

66 

64.3 

14.8 

126 

122.828.3 

186 

181.2 

41.8 

246 

239.7 

55  3 

7 

06.8 

01.6 

67 

65.3 

15  1 

127 

123  7 

28.6 

187 

182.2 

42.1 

247 

240.7 

55.6 

8 

07.8 

)1.8 

68 

66.3 

15.3 

128 

124.7 

28.8 

188 

183.2 

42.3 

248 

241.  C 

55.8 

9 

>8.8 

02.0 

69 

67.2 

15.5 

129 

125.7 

29.0 

189 

184.2 

42.5 

249 

242.6 

56.0 

1(1 

09.7 

02.2 

70 

68.2 

15.7 

130 

126.7 

•29.2 

190 

185.1 

42.7 

250 

243.6 

56.2 

11 

10.7 

02.5' 

71 

t>y.2 

iO.O 

131 

127.629.5 

191 

180.1 

43.0 

251 

244.6 

50.5 

12 

11.7 

02.7 

72 

70.2 

16.2 

132 

128.6 

29.7 

192 

187.1 

43.2 

252 

245.5 

56.7 

13 

12.7 

02.9 

73 

71.1 

16.4 

133 

129.6 

29.9 

193 

188.1 

43.4 

253 

246.5 

56.9 

14 

13  6 

03.1 

74 

72.1 

16.  G 

134 

130.6 

30.1 

194 

189.0 

43.6 

254 

247.5 

57.1 

15 

14.6 

03.4 

75 

73.1 

16.9 

135 

131.5 

30.4 

195 

190.0 

43.9 

255 

248.5 

57.4 

16 

15.6 

03.6 

76 

74.1 

17.1 

136 

132.5 

30.6 

196 

191.0 

44.1 

256 

249.4 

57.6 

17 

16.6 

03.8 

77 

75.0 

17.3 

137 

133.5 

30.8 

197 

192.0 

44.3 

257 

250  4 

57.8 

18 

17.504.0 

78 

76.0 

17.5 

138 

134.5 

31.0 

108 

192.9 

44.5 

258 

251.4 

58.0 

19 

18.5 

04.3 

79 

77.0 

17.8 

139 

135.4 

31.3 

199 

193.9 

44.8 

259 

252.4 

58.3 

20 

19.5 

04.5 

80 

77.9 

18.0 

140 

136.4 

31.5 

200 

194.9 

45.0 

260 

253.3 

58.5 

21 

20.504.7 

81 

78.9 

18.2 

141 

137.431.7 

'201 

195.8 

45.2 

261 

254.3 

58.7 

22 

21.404.9 

82 

79.9 

18.4 

142 

138.431  9 

202 

196.8 

45.4 

262 

255.3 

58.9 

23 

22.4 

05.2 

83 

80.9 

18.7 

143 

139.332.2 

203 

197.8 

45.7 

263 

256.3 

59.2 

24 

23.4 

05.4 

84 

81.8 

18.9 

144 

140.3'32.4 

204 

198.8 

45.9 

264 

257.2 

59.4 

25 

24.405.6 

85 

82.8 

19.1 

145 

141.332.6 

205 

199.7 

46.1 

265 

258.2 

59.6 

26 

25.305  8 

86 

83.8 

19  3 

146 

142.332.8 

20G 

200.7 

46.3 

266 

259.2 

19.8 

27 

26.306.1 

87 

84.8 

19.6 

147 

143.233.1 

207 

201.7 

46.6 

267 

260.2 

60.1 

28 

27.306.3 

88 

85.7 

19.8 

148 

144.233.3 

208 

202.7 

46.8 

268 

261.1 

60.3 

29 

28.306.5 

89 

86.7 

20.0 

149 

145.2 

33.5 

209 

203.6 

47.0 

269 

262  1 

60.5 

30 

29  206.7 

90 

87.7 

20.2 

150 

146.2 

33.7 

210 

204.6 

47.2 

270 

263.1 

60.7 

31 

30.2 

07.0 

91 

88.7 

20.5 

151 

147.1 

34.0 

211 

205.6 

47.5 

27  i|  204.1 

61.0 

32 

31.2 

C7.2 

92 

89.6 

20.7 

152 

148.1 

34.2 

212 

206.6 

47.7 

2721  265.0 

61.2 

33 

32.2 

07.4 

93 

90.6 

20.9 

153 

149.1 

34.4 

213 

207.5 

47.9 

273 

266.0 

61.4 

34 

33.1|07.6 

94 

91  6 

21.1 

154 

150.1 

34.6 

214 

208.5 

48.1 

274 

267.0 

61.6 

35 

34.107.9 

95 

92.6 

21.4 

155 

151.0 

34.9 

215 

209.5 

48.4 

275 

268.0 

61.9 

36 

35.1 

08.1 

96 

93.5 

21.6 

156 

152.035.1 

216 

210.5 

48.6 

276 

268.9 

62.1 

37 

36.1 

08.3 

97 

94.5 

21.8 

157 

153.0 

35.3 

217 

211.4 

48.8 

277 

269.9 

62.3 

38 

37.0 

08.5 

98 

95.5 

22.0 

158 

154.0 

OO  .  L 

218 

212.4 

49.0 

278 

270.9 

62.5 

39 

38.0d8.8 

99 

96.5 

22.3 

159 

154.9 

35.8 

219 

213.4 

49.3 

279 

271.8 

62.8 

40 

39.009.0 

100 

97.4 

22.5 

160 

155.9 

36.0 

220 

214.4 

49.5 

280 

272.8 

63.0 

41 

39.9|09.2 

101 

98.4 

22.7 

161 

156.9 

36.2 

221 

215.3 

49.7 

281 

273.8 

03.2 

42 

40.909.4 

102 

99.4 

22.9 

162 

157.8 

36.4 

222 

216.3 

49.9 

282 

274.8 

63.4 

43 

41.9 

09.7 

103 

100.4 

23.2 

163 

158.8 

36.7 

223 

217.3 

50.2 

283 

275.7 

63.7 

44 

42.9 

09.9 

104 

101.3 

23.4 

164 

159.8 

36.9 

224 

218.3 

50.4 

284 

276.7 

63.9 

45 

43.8 

10.1 

105 

102.3 

23.6 

165 

160.8 

37.1 

225 

219.2 

50.6 

285 

277.7 

64.1 

46 

44.8 

10.3 

106 

103.3 

•23.8 

166 

161.7 

37.3 

226 

220.2 

50.8 

286 

278.7 

64.3 

47 

45.8 

10.6 

107 

104.3 

24.1 

167 

162.7137.6 

227 

221.2 

51.1 

287 

279.6 

64.6 

48 

46.8 

10.8 

108 

105.2 

24.3 

168 

163.737.8 

228 

222.2 

51.3 

288 

280.  C 

64.8 

49 

47.7 

11.0 

109 

106.2 

24.5 

109 

164.7 

38.0 

229 

223.1 

51.5 

289 

281.6 

65.0 

50 

48  7 

11.2 

110 

107.2 

24.7 

170 

165.6 

38.2 

230 

224.1 

51.7 

290 

282.6 

65.2 

51 

49.7 

11.5 

111 

108.2 

25.0 

171 

166.638.5 

231 

225.1 

52.0 

291 

283.5 

65.5 

52 

50.7 

11.7 

112 

109.1 

25  2 

172 

167.6 

38.7 

232 

226.1 

52.2 

292 

284.5 

65.7 

53 

51.6 

11.9 

113 

110.1 

25.4 

173 

168.6 

•38.9 

233 

227.0 

52.4 

293 

285.5 

65.9 

54 

52.6 

12.1 

114 

111.1 

25.6 

174 

169.539.1 

234 

228.0 

52.6 

294 

280.5 

66.1 

55 

53.6 

12.4 

115 

112.1 

25.9 

175 

170.5 

39.4 

235 

229.0 

52.9 

295 

287.4 

66.4 

56 

54.6 

12.6 

116 

113.0 

26.1 

176 

171.5 

39.6 

236 

230.0 

53.1 

296 

288.4 

66.6 

57 

55.5 

12.8 

117 

114.0 

20.3 

177 

172.539.8 

237 

230.9 

53.3 

297 

289.4 

66.8 

58 

56.5 

13.0 

118 

115.0 

26.5 

178 

173.440.0 

238 

231.9 

53.5 

298 

290.4 

67.0 

59 

57.5 

13.3 

119 

116.0 

26.8 

179 

174.440.3 

239 

232.9 

53.8 

299 

2al.3 

67.3 

CO 

58.5 

13.5 

120 

116.9 

27.0 

180 

175.4 

40.5 

240 

233.8 

54.0 

300 

292.3 

67.5 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

'Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  77  Degrees. 

TABLE  IV.                                           217 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE  FOR  14  DEGREES. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

01.0 

00.2 

61 

59.2 

14.8 

121 

117.4 

•29.3 

181 

175.6 

43.8 

241 

233.8 

58.3 

2 

01.9 

00.5 

62 

60.2 

15.0 

12'2 

118.4 

29.5 

182 

176.6 

44.0 

242 

234.8 

58.5 

3 

02.9 

00.7 

63 

61.1 

15.2 

123 

119.3 

29.8 

183 

177.6 

44.3 

243 

235.8 

58.8 

4 

03.9 

01.0 

64 

62.1 

15.5 

124 

120.3 

30.0 

184 

178.5 

44.5 

244 

236.8 

59.0 

5 

04.9 

01.2 

65 

63.1 

15.7 

125 

121.3 

30.2 

185 

179.5 

44.8 

245 

237.7 

59.3 

6 

05.8 

01.5 

66 

64.0 

16.0 

126 

122.3 

30.5 

186 

180.5 

45.0 

246 

238.7 

59.5 

7 

06.8 

01.7 

67 

65.0 

16.2 

127 

123.2 

30.7 

187 

181.4 

45.2 

247 

239.7 

59.8 

8 

07.8 

01.9 

68 

66.0 

16.5 

128 

124.2 

31.0 

188 

182.4 

45.5 

248 

240.6 

60.0 

9 

08.7 

02.2 

69 

67.0116.7 

129 

125.2 

31.2 

189 

183.4 

45.7 

249 

241.6 

60.2 

10 

09.7 

02.4 

70 

67.9!l6.9 

130 

126.1 

31.4 

190 

184.4 

46.0 

250 

242.6 

60  5 

11 

10.7 

02.7 

71 

68.917.2 

131 

1-27.1 

31.7 

191 

1S5.3 

46.2 

251 

243.5 

60.7 

12 

1.6 

02.9 

72 

69.9J17.4 

132 

128.1 

31.9 

192 

186.3 

46.4 

25. 

244.5 

61.0 

13 

12.6 

03.1 

73 

70.817.7 

133 

129.0 

32.2 

193 

187.3 

46.7 

253 

'245.5 

61.2 

14 

13.6 

03.4 

74 

71.817.9 

134 

130.0 

32.4 

194 

188.2 

46.9 

254 

246.5 

61.4 

15 

14.6 

03.6 

75 

72.8'l8.1 

135 

131.0 

32.7 

195 

189.2 

47.2 

255 

247.4 

61.7 

16 

15.5 

03.9 

76 

73.718.4 

136 

132.0 

32.9 

196 

190.2 

47.4 

256 

248.4 

61.9 

17 

16.5 

04.1 

77 

74.718.6 

137 

132.9 

33.1 

197 

191.1 

47.7 

257 

249.4 

62  2 

18 

7.5 

04.4 

78 

75.7 

18.9 

138 

133  9 

33.4 

198 

192.1 

47.9 

258 

250.3 

62.4 

19 

8  4 

04.6 

79 

76.719.1 

139 

134.9 

33  6 

199 

193.1 

48.1 

250 

251.3 

62.7 

20 

19.4 

04.8 

80 

77.619.4 

140 

135.8 

33.9 

200 

194.1 

48.4 

260 

252.3 

62.9 

21 

20.4 

05.1 

81 

78.619.6 

141 

136.8 

34.1 

201 

195.0 

48.6 

261 

•253  .  i: 

(33.1 

22 

21.3 

05  3 

82 

79.6 

19.8 

142 

137.8 

34.4 

202 

196.0 

48.9, 

262 

254.2 

63.4 

23 

22.3 

05.6 

83 

80.5 

20.1 

143 

138.8 

34.6 

203 

197.0 

49.1 

263 

255.2 

63.6 

24 

23.305.8 

84 

81.5 

20.3 

144 

139.7 

34.8 

204 

197.9 

49.4 

264 

256  .  2 

63.9 

25 

24.3 

06.0 

85 

82.5 

20.6 

145 

140.7 

35.1 

205 

198.9 

49.6 

265 

257.1 

64.1 

26 

25.2 

06.3 

86 

83.4 

20.8 

146 

141.7 

35.3 

206 

199.9 

49.8 

266 

258.1 

64.4 

27 

26.2 

06.5 

87 

84.421.0 

147 

142.6 

35.6 

207 

200.9 

50.1 

267 

259.1 

64.6 

28 

27.2 

06.  81 

88 

85.421.3 

148 

143.6 

35.8 

208 

201.8 

50.3 

268 

260.0 

64  8 

29 

28.1 

07.  0| 

89 

86.421.5 

149 

144.6 

36.0 

209 

202.8 

50.6 

269 

261.0 

65.1 

30 

29.1 

07.3 

90 

87.321.8 

150 

145.5 

36.3 

210 

203.8 

50.8 

270 

262.0 

65.3 

31 

30.1 

17.5 

91 

88.  322.  U 

151 

146.536.5 

211 

204.7 

51.0 

27  J 

203.0 

65.6 

32 

31.0 

07.7 

92 

89.3 

22.3 

152 

147.5 

36.8 

212 

205.7 

51.3 

272 

263.9 

65.8 

33 

32.0 

08.0 

93 

90.222.5 

153 

148.5 

37.0 

213 

206.7 

51  5 

27b 

264.9 

66.0 

34 

33.0 

08.2 

94 

91.2*2.7 

154 

149.4 

37.3 

214 

207.6 

51.8 

274 

265.9 

66.3 

35 

34.0 

08.5 

95 

92.223.0 

155 

150.4 

37.5 

215 

208.6 

52.0 

275 

2G6.8 

66.5 

36 

34.9 

08.7 

96 

93.1 

23.2 

156 

151.4 

37.7 

216 

209.6 

52.3 

276 

267.8 

66.8 

37 

35.9 

09.0 

97 

94.1 

23.5 

157 

152.3 

38.0 

217 

210.6 

52.5 

277 

268  8 

67.0 

38 

36.9 

09.2 

98 

95.1 

23.7 

158 

153.3 

38.2 

218 

211.5 

52.7 

278 

269.7 

67.3 

39 

37.8 

09.4 

99 

96.1 

24.0 

159 

154.3 

38.5 

219 

212.5 

53.0 

279 

270.7 

67.5 

40 

38.8 

09.7 

100 

97.0 

24.2 

160 

155.2 

38.7 

220 

213.5 

53.2 

280 

271.7 

67  7 

41 

39.8 

09.9 

101 

98.0 

24.4 

161 

156.2 

38.9 

221 

214.4 

53.5 

281 

2  •  2  .  7 

U8.0 

42 

40.8 

10.2 

102 

99.0 

24.7 

162 

157.2 

39.2 

222 

215.4 

53.7 

282 

273.6 

68.2 

43 

41.7 

10.4 

103 

99.924.9 

163 

158.2 

39.4 

223 

216.4 

53.9 

283 

274.6 

68  5 

44 

42.7 

10.6 

104 

100.925.2 

164 

159.1 

39.7 

224 

217.3 

54.2 

284 

275.  b 

68.7 

45 

43.7 

10.9 

105 

101.925.4 

165 

160.1 

39.9 

225 

218.3 

54  4 

285 

276.5 

68.9 

46 

44.6 

11.1 

100 

102.925.6 

166 

161.1 

40.2 

226 

219.3 

54.7 

286 

277.5 

69.2 

47 

45.6 

11.4 

107 

103.825.9 

167 

162.0 

40.4 

227 

220.3 

54.9 

287 

278.  i 

69.4 

48 

46.6 

11.6 

108 

104.826.1 

168 

163.0 

40  6 

228 

221.2 

55.2 

288 

279.4 

69.7 

49 

47.5 

11.9 

109 

105.826.4 

169 

164.0 

40.9 

229 

222.2 

55  4 

289 

280.4 

69.9 

50 

48.5 

12.1 

110 

106.726.6 

170 

165.0 

41.1 

230 

223.2 

55.6 

290 

281.4 

70.2 

51 

49.5 

12.3 

111 

107.726.9 

171 

165.9 

41.4 

231 

2^4.1 

55.9 

291 

282.4 

70.4 

52 

50.5 

12.6 

112 

108.727.1 

172 

166.9 

41.6 

232 

225.1 

56.1 

292 

283  .  3 

70.6 

53 

51.4 

12.8 

113 

109.6'27.3 

173 

167.9 

41.9 

233 

226.1 

56.4 

293 

284.3 

70.9 

54 

52.4 

13.1 

114 

110.6 

27.6 

174 

168.8 

42.1 

234 

227.0 

56.6 

294 

2«5.3 

71.1 

55 

53.4 

13.3 

115 

111.6 

27.8 

175 

169.8 

42.3 

235 

228.0 

56.9 

295 

286.2 

71.4 

56 

54.3 

13.5 

116 

112.  G 

28.1 

176 

170.8 

42.6 

236 

229.0 

57.1 

296 

287.2 

71.6 

57 

55.  > 

13.8 

117 

113.5 

•28.3 

177 

171.7 

42.8 

237 

230.0 

57.3 

297 

288.2 

71.9 

58 

56.3 

14.0 

118 

114.5 

28  6 

178 

172.7 

43.1 

238 

230.9 

57.6 

298 

289.1 

72.1 

59 

57.2 

14.3 

119 

115.5 

•28.  8 

179 

173.7 

43.3 

239 

231.9 

57.8 

299 

290.1 

72.3 

60 

58.2 

14.5 

120 

116.4 

29  0 

180 

174.7 

43.5 

240 

232.9 

58.1 

300 

291.1 

72.6 

Dist 

Dep 

Lat. 

Dist 

Dep. 

Lat 

IHst. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  76  Degrees. 

218                                          TABLE  IV. 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE  FOR  15  DEGREES. 

Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist, 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

l 

1.0 

U0.3 

61 

58.9 

15.8 

121 

116.9 

31.3 

181 

174.8 

46.8 

241 

232.8 

62.4 

2 

01  9 

1)0.5 

62 

59.9 

16.0 

122 

117.8 

31.6 

182 

175.8 

47.1 

242 

233.8 

62.6 

3 

32.9 

00.8 

63 

60.9 

16.3 

123 

118  8 

31.8 

183 

176.8 

47.4 

243 

234.7 

62.9 

4 

J3.9 

01.0 

64 

61.8 

16.6 

124 

119.8 

32  1 

184 

177.7 

47.6 

244 

235  7 

63.2 

5 

J4.8 

01.3 

65 

62.8 

16.8 

125 

120.7 

32.4 

185 

178.7 

47.9 

245 

236.7 

63.4 

6 

j5.8 

01.6 

66 

63.8 

17.1 

126 

121.7 

32.6 

186 

179.7 

48.1 

246 

237.6 

63.7 

7 

6.8 

01.8 

67 

64.7 

17.3 

127 

122.7 

32.9 

187 

180.6 

48.4 

247 

238.6 

63.9 

8 

37.7 

02.1 

68 

65.7 

17.6 

128 

123.6 

33.1 

188 

181.6 

48.7 

248 

239.5 

64.2 

9 

J8  7 

02.3 

69 

66.6 

17.9 

129 

124.6 

33.4 

189 

182.6 

48.9 

249 

240.5 

64.4 

10 

39.7 

02.6 

70 

67.6 

18.1 

130 

125.6 

33.6 

190 

183.5 

49.2 

250 

241.5 

64.7 

11 

10.6 

02.8 

71 

68.6 

18.4 

131 

126.5 

33.9 

191 

184.5 

49.4 

251 

242.4 

65.0 

IS 

1  6 

03.1 

72 

69.5 

18.6 

132 

127.5 

34.2 

192 

185.5 

49.7 

252 

243.4 

65.2 

18 

2.6 

03  4 

73 

70.5 

18.9 

133 

128.5 

34.4 

193 

186.4 

50.0 

253 

244.4 

65.5 

14 

3.5 

03.6 

74 

71.5 

19.2 

134 

129.4 

34.7 

194 

187.4 

50  2 

254 

245.3 

65.7 

15 

4.5 

03.9 

75 

72.4 

19.4 

435 

130.4 

34.9 

195 

188.4 

50.5 

255 

246.3 

66.0 

16 

15.5 

04.1 

76 

73.4 

19.7 

136 

131.4 

35.2 

196 

189.3 

50.7 

256 

247.3 

66.3 

17 

16.4 

04.4 

77 

74.4 

19.9 

137 

132.3 

35.5 

197 

190.3 

51.0 

257 

248.2 

66.5 

18 

7.4 

04.7 

78 

75.3 

20.2 

138 

133.3 

35.7 

198 

191.3 

51.2 

258 

249.2 

66.8 

19 

8.4 

04.9 

79 

76  3 

20.4 

139 

134.3 

36.0 

199 

192.2 

51.5 

259 

250.2 

67.0 

20 

19.3 

05.2 

80 

77  3 

20.7 

140 

135.2 

36.2 

200 

193.2 

51.8 

260 

251  .  1 

67.3 

21 

20.o 

05.4 

81 

78.2 

21.0 

141 

136.2 

36.5 

201 

194.2 

52.0 

261 

252.1 

67.6 

22 

21.3 

05.7 

82 

79.2 

21  .2 

142 

137.2 

36.8 

202 

195.1 

52.3 

262 

253.1 

67.8 

23 

22.2 

06.0 

83 

80.2 

21.5 

143 

138.1 

37.0 

203 

196.1 

52.5 

263 

254.0 

68.1 

24 

23.2 

06.2 

84 

81.1 

21.7 

144 

139.1 

37.3 

204 

197.0 

52.8 

264 

255.0 

68.3 

25 

24.1 

06.5 

85 

82.1 

22.0 

145 

140.1 

37.5 

205 

198.0 

53.1 

265 

256.0 

68.6 

2G 

25.1 

06.7 

86 

83.1 

22.3 

146 

141.0 

37.8 

206 

199.0 

53.3 

266 

256.9 

68.8 

27 

26.1 

07.0 

87 

84.0 

22.5 

147 

142.0 

38.0 

207 

199.9 

53.6 

267 

257.9 

69.1 

28 

27.0 

07.2 

88 

85.0 

22.8 

148 

143.0 

38.3 

208 

200.9 

53.8 

268 

258.9 

69.4 

29 

28.0 

07.5 

89 

86.0 

23.0 

149 

143.9 

38.6 

209 

201.9 

54.1 

269 

259.8 

69.6 

30 

29.0 

07.8 

90 

86.9 

23.3 

150 

144.9 

38.8 

210 

202.8 

54.4 

270 

260.8 

69.9 

31 

29.9 

08.0 

91 

87.9 

23.6 

151 

145.9 

39.1 

211 

203.8 

54.6 

271 

261.8 

70.1 

32 

30.9 

08.3 

92 

88.9 

23.8 

152 

146.8 

39.3 

212 

204.8 

54.9 

272 

262.7 

70.4 

33 

31.9 

08.5 

93 

89.8 

24.1 

153 

147.8 

39.6 

213 

205.7 

55.1 

273 

263.7 

70.7 

34 

32.8 

08.8 

94 

90.8 

24.3 

154 

148.8 

39.9 

214 

206.7 

55.4 

274 

264.7 

70.9 

35 

33.8 

09.1 

95 

91.8 

24.6 

155 

149.7 

40.1 

215 

207.7 

55.6 

275 

265.6 

71.2 

36 

34.8 

09.3 

96 

92.7 

24.8 

156 

150.7 

40.4 

216 

208.6 

55.9 

276 

266.6 

71.4 

37 

35.7 

09.6 

97 

9a.7 

25.1 

157 

151.7 

40.6 

217 

209.6 

56.2 

277 

267.6 

71.7 

38 

36.7 

09.8 

98 

94.7 

25.4 

158 

152.6 

40.9 

218 

210.6 

56.4 

278 

268.5 

72.0 

39 

V7.7 

10.1 

99 

95.6 

25.6 

159 

153.6 

41.2 

219 

211.5 

56.7 

279 

269.5 

72.2 

40 

38.6 

10.4 

100 

96.6 

25.9 

160 

154.5 

41.4 

220 

212.5 

56.9 

280 

270.5 

72.5 

41 

39.6 

10.6 

101 

97.6 

26.1 

161 

155.5 

41.7 

221 

213  5 

57.2 

281 

271.4 

72.7 

42 

40.6 

10.9 

102 

98.5 

26.4 

162 

156.5 

41.9 

222 

214.4 

57.5 

282 

272.4 

73.0 

43 

±1.5 

11.1 

103 

99.5 

26.7 

163 

157.4 

42.2 

223 

215.4 

57.7 

283 

273.4 

73.2 

44 

42.5 

11.4 

104 

100.5 

26.9 

164 

158  4 

42.4 

224 

216.4 

58.0 

284 

274.3 

73.5 

45 

43.5 

11.6 

105 

101.4 

27.2 

165 

159.4 

42.7 

225 

217.3 

58.2 

285 

275.3 

73.8 

46 

44.4 

11.9 

106 

102.4 

27.4 

166 

160  3 

43.0 

226 

218.3 

58.5 

286 

276.3 

74.0 

47 

45.4 

12.2 

107 

103.4 

27.7 

167 

161.3 

43.2 

227 

219.3 

58.8 

287 

277.2 

74.3 

48 

46.4 

12.4 

108 

104.3 

28.0 

168 

162.3 

43.  b 

228 

220.2 

59.0 

288 

278.2 

74.5 

49 

47.3 

12.7 

109 

105.3 

28.2 

169 

163.2 

43.7 

229 

221.2 

59.3 

289 

279.2 

74.8 

50 

48.3 

12.9 

110 

106.3 

28.5 

170 

164.2 

44.0 

230 

222.2 

59.5 

290 

280.1 

75.1 

51 

49.  a 

13.2 

111 

107.2 

28.7 

171 

165.2 

44.3 

231 

223.1 

59.8 

291 

281.1 

75.3 

52 

o0.2 

L3.5 

112 

108.2 

29.0 

172 

166.1 

44.5 

232 

224.1 

60.0 

292 

282.1 

75.6 

53 

51.2 

13.7 

113 

109.1 

29.2 

173 

167.1 

44.8 

233 

225.1 

60.3 

293 

283.0 

75.8 

54 

52.2 

14.0 

114 

110.1 

29.5 

174 

168.1 

45.0 

234 

226.0 

60.6 

294 

284.0 

76.1 

55 

53.1 

14.2 

115 

111.1 

29.8 

175 

169.0 

45.3 

235 

227.0 

60.8 

295 

284.9 

76.4 

56 

54.1 

14.5 

116 

112.  C 

'30.0 

176 

170.0 

45.6 

236 

228.0 

61.1 

296 

285.9 

76  6 

57 

55.1 

14.8 

117 

113.  C 

30.3 

177 

171.0 

45.8 

237 

228.9 

61.3 

297 

286.9 

76  9 

58 

56.  C 

15.0 

118 

114  C 

30.5 

178 

171.9 

46.1 

238 

229.9 

61.6 

298 

287.8 

77.1 

59 

57.  ( 

15.3 

119 

114.  S 

30  8 

17S 

172.9 

46.3 

239 

230.9 

61.9 

299 

288.8 

77  4 

60 

68  C 

15.5 

120 

115.  S 

31.1 

18CJ 

173.9 

46.6 

240 

231.8 

62.1 

30U 

289.8 

77.6 

Dist 

Der 

Lat 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

For  75  Degrees. 

TABLE  IV.                                           219 

DIFFERENCE  OF    LATITUDE   AND  DEPARTURE   FOR  16  DEGREES. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist, 

Lat. 

Dep. 

1 

01.0 

00.3 

61 

58.6 

16.8 

121 

116.3 

33.4 

181 

174.0 

49.9 

241 

231.7 

66.4 

2 

01.900.6 

62 

59.6 

17.1 

122 

117.3 

33.6 

18J 

174.9 

50.2 

242 

232.6 

66.7 

3 

02.900.8 

63 

60.6 

17.4 

123 

118.2 

33.9 

183 

175.9 

50.4 

243 

233.6 

67.0 

4 

03.801.1 

64 

61.5 

17.6 

124 

119.2 

34.2 

184 

176.9 

50.7 

244 

234.5 

67.3 

5 

04.8 

01.4 

65 

62.5 

17.9 

125 

120.2 

34.5 

185 

177.8 

51.0 

245 

235.5 

67.5 

G 

05.8 

01.7 

66 

63.4 

18.2 

126 

121.1 

34.7 

186 

178.8 

51.3 

246 

236.5 

67.8 

7 

06.7 

01.9 

67 

64.4 

18.5 

127 

122.1 

35.0 

187 

179.8 

51.5 

247 

237.4 

68.1 

8 

07.7 

02.2 

68 

65.4 

18.7 

128 

123.0 

35.3 

188 

180.7 

51.8 

248 

238.4 

68.4 

9 

,8.7 

02.5 

69 

66.3 

19.0 

129 

124.0 

35.6 

189 

181.7 

52.1 

249 

239.4 

68.6 

10 

')9.6 

02.8 

70 

67.3 

19.3 

130 

125.035.8 

19,. 

182.6 

52.4 

250 

240.3 

68.9 

11 

10.  b 

U3.0 

71 

68.2 

19.6 

131 

125.936.1 

191 

163.6 

52.6 

251 

241.3 

69.2 

12 

11.5 

03.3 

72 

69.2 

19.8 

132 

126.9 

36.4 

192 

184.6 

52.9 

252 

242.2 

69.5 

13 

12.5 

03.6 

73 

70.2 

20.1 

133 

127.8 

36.7 

193 

185.5 

53.2 

253 

243.2 

69.7 

14 

13.5 

J3  9 

74 

71.1 

20.4 

134 

128.8 

36.9 

194 

186.5 

53.5 

254 

244.2 

70.0 

15 

14.4 

04.1 

75 

72.1 

20.7 

135 

129.8 

37.2 

195 

187.4 

53.7 

255 

245.1 

70.3 

1C 

15.4 

04.4 

7C 

73.1 

20.9 

136 

130.7 

37.5 

196 

188.4 

54.0 

256 

246.1 

70.6 

17 

16.3 

04.7 

77 

74.0 

21.2 

137 

131.7 

37.8 

197 

189.4 

54.3 

257 

247.0 

70.8 

18 

17.3 

05.0 

78 

75.0 

21.5 

138 

132.7 

38.0 

198 

190.3 

54.6 

258 

248.0 

71.1 

19 

18.3 

05.2 

79 

75.9 

21.8 

139 

133.6 

38.3 

199 

191.3 

54.9 

259 

249.0 

71.4 

'^0 

19.2 

J5.5 

80 

76.9 

22.1 

140 

134.6 

38.6 

200 

192.3 

55.1 

260 

249.9 

71.7 

21 

.0.2 

05.8 

81 

77.9 

22.3 

141 

135.5 

38.9 

20i 

193.2 

55.4 

2(51 

25u  .  9 

71.9 

22 

21.1 

06.1 

82 

78.8 

22.6 

142 

136.5 

39  1 

202 

194.2 

55.7 

262 

251.9 

72.2 

23 

22.1 

06.3 

83 

79.8 

22.9 

143 

137.5 

39.4 

203 

195.1 

56.0 

263 

252.8 

72.5 

24 

23.1 

06.6 

84 

80.7 

23.2 

144 

138.4 

39.7 

204 

196.1 

56.2 

264 

253.8 

72.81 

25 

24.0 

06.9 

85 

81.7 

23.4 

145 

139.4 

40.0 

205 

197.1 

56  5 

265 

254.7 

73.0 

26 

25.0 

07.2 

86 

82.1 

23.7 

146 

140.3 

40.2 

206 

198.0 

56.8 

266 

255.7 

73.3 

27 

26.0 

07.4 

87 

83.6 

24.0 

147 

141.3 

40.5 

207 

199.0 

57.1 

267 

256.7 

73.6 

28 

26.9 

07.7 

88 

84.6 

24.3 

148 

142.3 

40.8 

208 

199.9 

57.3 

268 

257.6 

73.9 

29 

27.9 

08.0 

89 

85.6 

24.5 

149 

143.2 

41.1 

209 

200.9 

57.6 

269 

258.6 

74.1 

30 

28.8 

08.3 

90 

86.5 

24.8 

150 

144.2 

41.3 

210 

201.9 

57.9 

270 

259.5 

74.4 

31 

29.8 

08.5 

91 

87.5 

25.1 

161 

145.2 

41.6 

211 

202.8 

58.2 

27  J 

260.5 

74.7 

32 

30.8 

08.8 

92 

88.4 

25.4 

152 

146.1 

41.9 

212 

203.8 

58.4 

272 

261.5 

75.0 

33 

31.7 

09.1 

93 

89.4 

25.6 

153 

147.1 

42.2 

213 

204.7 

58.7 

273 

262.4 

75.2 

34 

32.7 

09.4 

94 

90.4 

25.9 

154 

148.0 

42.4 

214 

205.7 

59.0 

274 

263.4 

75.5 

35 

33.6 

09.6 

95 

91.3 

26.2 

155 

149.0 

42.7 

215 

206.7 

59.3 

275 

264.3 

75.8 

36 

34.6 

09.9 

96 

92.3 

26.5 

156 

150.0 

43.0 

216 

207.6 

59.5 

276 

265.3 

76.1 

37 

35.6 

10.2 

97 

93.2 

26.7 

157 

150.9 

43.3 

217 

208.6 

59.8 

277 

266.3 

76.4 

38 

36.5 

10.5 

98 

94.2 

27.0 

158 

151.9 

43.6 

218 

209.6 

60.1 

278 

267.2 

76.6 

39 

37.5 

10.7 

99 

95.2 

27.3 

159 

152.8 

43.8 

219 

210.5 

60.4 

279 

268.2 

76  9 

40 

38.5 

11.0 

100 

96.1 

27.6 

160 

153.8 

44.1 

220 

211.5 

60.6 

280 

269.2 

77.2 

41 

39.4 

11.3 

101 

97.1 

27.8 

161 

154.8 

44.4 

221 

212.4 

60.9 

281 

270.1 

77.5 

42 

40.4 

11.6 

102 

98.0 

28.1 

162 

155.7 

44.7 

222 

213.4 

61.2 

282 

271.1 

77.7 

43 

11.3 

11.9 

103 

99.0 

28.4 

163 

156.7 

44.9 

223 

214.4 

61.5 

283 

272.0 

78.0 

44 

42.3 

12.1 

104 

100.0 

28.7 

164 

157.6 

45.2 

224 

215.3 

61.7 

284 

273.0 

78.3 

45 

43.3 

12.4 

105 

100.9 

28.9 

165 

158.6 

45.5 

225 

216.3 

62.0 

285 

274.0 

78.6 

46 

44.2 

12.7 

106 

101.9 

29.2 

166 

159.6 

45.8 

226 

217.2 

62.3 

286 

244.9 

78.8 

47 

45.2 

13.0 

107 

102.9 

29.5 

167 

160.5 

46.0 

227 

218.2 

62.6 

287 

275.9 

79.1 

48 

46.1 

13.2 

108 

103.8 

29.8 

168 

161.5 

46.3 

228 

219.2 

62.8 

288 

276.8 

79.4 

49 

47.1 

13.5 

109 

104.8 

30.0 

169 

162.5 

46.6 

229 

220.1 

63.1 

289 

277.8 

79.7 

50 

48.1 

13.8 

110 

105.7 

30.3 

170 

163.4 

46.9 

230 

221.1 

63.4 

290 

278.8 

79.9 

51 

49.0 

04.1 

111 

106.7 

30.6 

171 

164.4 

47.1 

231 

222.1 

63  7 

291 

279.7 

80.2 

52 

50.0 

14.3 

112 

107.7 

30.9 

172 

165.3 

47.4 

232 

223.0 

63.9 

292 

280.7 

80  5 

53 

•30.9 

14.6 

113 

108.6 

31.1 

173 

166.3 

47.7 

233 

224.0 

64.2 

293 

281.6 

80.8 

54 

51.9 

14.9 

114 

109.6 

31.4 

174 

167.3 

48.0 

234 

224.9 

64.5 

294 

282.6 

81.0 

55 

52.9 

15  2 

115 

110.5 

31.7 

175 

168.2 

48.2 

235 

225.9 

64.8 

295 

283.6 

81.3 

56 

53.8 

15.4 

116 

111.5 

32.0 

176 

169.2 

48.5 

236 

226.9 

65.1 

296 

284.5 

81.6 

57 

54.8 

15.7 

117 

112.5 

32.2 

177 

170.1 

48.8 

237 

227.8 

65.3 

297 

285.5 

81.9 

58 

55.8 

16.0 

118 

113.4 

32.5 

178 

171.1 

49.1 

238 

228.8 

65.6 

298 

286.5 

82.1 

59 

56.7 

16.3 

119 

114.4 

32.8 

179 

172.1 

49.3 

239 

229.7 

65.9 

299 

287.4 

82.4 

60 

57.7 

16.5 

120 

115.4 

33.1 

180 

173.0 

49.6 

240 

230.7 

66.2 

300 

288.4 

82.7 

Dist. 

Dcp 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  74  Degrees. 

220                                          TABLE  IV. 

DIFFERENCE    OF   LATITUDE  AND  DEPARTURE  FOR  17    DEGREES. 

Dist.  Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

oi.oloo.s 

61 

58  3 

17.8 

121 

115.7 

35.4 

181 

173.1 

52.9 

241 

230.5 

70.5 

2 

01  900.6 

62 

59.3 

18.1 

122 

116.7 

35.7 

182 

174.0 

53.2 

242 

231.4 

70.8 

3 

02.9U0.9 

63 

60.2 

18.4 

123 

117.6 

36.0 

183 

175.0 

53.5 

243 

232.4 

71.0 

4 

03.801.2 

64 

61.2 

18.7 

124 

118.6 

36.3 

184 

176.0 

53  8 

244 

233.3 

71.3 

5 

04.801  5 

65 

62.2 

19.0 

125 

119.5 

36.5 

185 

176.9 

54.1 

245 

234.3 

71  6 

6 

05.701.8 

66 

63.1 

19.3 

126 

120.5 

36.8 

186 

177  9 

54.4 

246 

235.3 

71.9 

7 

06.702.0 

67 

64.1 

19.6 

127 

121.5 

37.1 

187 

178.8 

54.7 

247 

236  2 

72.2 

8 

07.7 

02.3 

68 

65.0 

19.9 

128 

122.4 

37.4 

18S 

179.8 

55.0 

248 

237.2 

72.5 

9 

08.6 

02.6 

69 

66.0 

20.2 

129 

123.4 

37.7 

189 

180.7 

55.3 

249 

238.1 

72.8 

10 

09.602.9 

70 

66.9 

20.5 

130 

124.3 

38.0 

190 

181.7 

55.6 

250 

239.1 

73.1 

11 

10.5 

03.2 

7J 

67.920.8 

131 

125  338.3 

191 

182.7 

55  8 

251 

240.0 

73.4 

12 

11.5 

03.5 

72 

6S.  921.1 

132 

126.2 

38.6 

192 

183.6 

56.1 

252 

241.0 

73.7 

13 

12.4 

03.8 

73 

69.8 

21.3 

133 

127.2 

38.9 

193 

184.6 

56  4 

253 

241.9 

74.0 

14 

13.4 

04.1 

74 

70.8 

21.6 

134 

128.1 

39  2 

194 

185.5 

56.7 

254 

242.9 

74.3 

15 

14.3 

04.4 

75 

71.7 

21.9 

135 

129.1 

39.5 

195 

186.5 

57.1 

255 

243  9 

74.6 

16 

15.3 

04  .7 

7(5 

72.7 

22.2 

136 

130.1 

39.8 

196 

187.4 

57.3 

256 

244  8 

74.8 

17 

16.3 

05.0 

77 

73  6 

22.5 

137 

131.0 

40.1 

197 

188.4 

57  6 

257 

245.8 

75.1 

18 

17.2 

05.3 

78 

74.6 

22.8 

138 

132.0 

40.3 

198 

189.3 

57.9 

258 

246.7 

75.4 

19 

18.2 

05.6 

79 

75.5 

23.1 

139 

132.9 

40.6 

199 

190.3 

58.2 

259 

247.7 

75.7 

20 

19.1 

05.8 

80 

76.5 

23.3 

140 

133.9 

40.9 

200 

191  3 

58.5 

260 

248.6 

76  0 

541 

•20.1 

06.1 

81 

77.5 

23.7 

141 

134.841.2 

201 

192.2 

58.8 

261 

249.6 

76.3 

22 

21  006  4 

82 

78.4 

24.0 

142 

135.8 

41.5 

202 

193.2 

59.1 

262 

250.6 

76.6 

23 

22.006.7 

83 

79.4 

24.3 

143 

136.8 

41.8 

203 

194.1 

59.4 

263 

251  5 

76.9 

24 

23.0 

07.0 

84 

80.3 

24  6 

144 

137.7 

42.1 

204 

195.1 

59.6 

264 

252.5 

77.2 

25 

23.9 

07.3 

85 

81.3 

24.9 

145 

138.7 

42.4 

205 

196.0 

59.9 

265 

253.4 

77.5 

26 

24.907.6 

86 

82.2 

25.1 

146 

139  6 

42.7 

206 

197.0 

60.2 

266 

254.4 

77.8 

27 

25.807.9 

87 

83.2 

25.4 

147 

140.6 

43.0 

207 

198.0 

60.5 

267 

255.3 

78.1 

28 

26.8 

08.2 

88 

84.2 

25.7 

148 

141.5 

43.3 

208 

198.9 

60.8 

268 

256.3 

78.4 

29 

27.7 

08.5 

89 

85.1 

26  0 

149 

142.5 

43.6 

209 

199.  & 

61.1 

269 

257.2 

78.6 

30 

28.7 

08.8 

90 

83.1 

26.3 

150 

143.4 

43.9 

210 

200.8 

61.4 

270 

258.2 

78.9 

31 

29.  b 

0971 

91 

87.0 

26.6 

151 

144.4 

44.1 

iill 

201.8 

61.7 

271 

259  2 

79.2,' 

32 

30.6 

09.4 

92 

88.0 

26.9 

152 

145.4 

44.4 

212 

202.7 

62.0 

272 

260.1 

79.51 

33 

31.6:09.6 

93 

88.9 

27.2 

153 

146.3 

44.7 

213 

203.7 

62.3 

273 

261.1 

79.8 

34 

32.509.9 

94 

89.927.5 

154 

147.3 

45.0 

214 

204.6 

62.6 

274 

262.0 

80.1 

35 

33.510.2 

95 

90.8 

27.8 

155 

148.2 

45.3 

215 

205.6 

62.9 

275 

263.0 

80.4 

3G 

34.4110.5 

96 

91.8 

28.1 

156 

149.2 

45.6 

216 

206.6 

63.2 

276 

263.9 

80.71 

37 

35.4 

10.8 

97 

92.8 

28.4 

157 

150.1 

45.9 

217 

207.5 

63.4 

277 

264.9 

81.0 

38 

36.3 

11.1 

98 

93.7 

28.7 

158 

151.1 

46.2 

218 

208.5 

63.7 

278 

265.9 

81.3 

39 

37.3 

11.4 

99 

94.7 

28.9 

159 

152.1 

46.5 

219 

209.4 

64.0 

279 

266.8 

81.6 

40 

38.3 

11.7 

100 

95.6 

29.2 

160 

153.0 

46.8 

220 

210.4 

64.3 

280 

267.8 

81.9 

41 

39.2 

12.0 

101 

96.6 

29.5 

161 

154.0J47.1 

221 

211.3 

64.6 

281 

208.  7 

82.2 

42 

40.2 

12.3 

102 

97.5 

29.8 

162 

154.9|47.4 

222 

212.3 

64.9 

282 

269.7 

82.4 

43 

41  1 

12.6 

103 

98.5 

30.1 

163 

155.9 

47.7 

223 

213.3 

65.2 

283 

270.6 

82.7 

44 

42.1 

12.9 

104 

99.5 

30.4 

164 

156.8 

47.9 

224 

214.2 

65.5 

284 

271.6 

83.0 

45 

43.0 

13  2 

105 

100.4 

30.7 

165 

157.8 

48.2 

225 

215.2 

65.8 

285 

272.5 

83.3 

46 

14.0 

13.4 

106 

101.4 

31.0 

166 

158.7 

48.5 

226 

216.1 

66.1 

286 

273.5 

83.6 

47 

44.9 

13.7 

107 

102.331.3 

167 

159  7 

48.8 

227 

217.1 

66.4 

287 

274.5 

83.9 

48 

45.9 

14.0 

108 

103.331.6 

168 

160.7 

49.1 

228 

218.0 

66.7 

288 

275.4 

84.2 

49 

46.9 

14.3 

109 

104.231.9 

169 

161.6 

49.4 

229 

219.0 

67.0 

289 

276.4 

84.5 

50 

47.8 

14.6 

110 

105.2 

32.2 

170 

162.6 

49.7 

230 

220.0 

67.2 

290 

277.3 

84.8 

51 

48.8 

14.9 

111 

106.1 

32.5 

171 

163.5 

50.0 

231 

220.9 

67.5 

291 

278.3 

&5.1 

52 

49.7 

15.2 

112 

107.1 

32.7 

172 

164.5 

50.3 

232 

221.9 

67.8 

292 

279.2 

85.4 

53 

50.7 

15.5 

113 

108.1 

33.0 

173 

165.4 

50.6 

233 

222.8 

68.1 

293 

280.2 

85.7 

54 

51.6 

15.8 

114 

109.0 

33.3 

174 

166.4 

50.9 

234 

223.8 

68.4 

294 

281.2 

86.0 

55 

52.6 

16.1 

115 

110.0 

33.6 

175 

167.4 

51.2 

235 

224.7 

68.7 

295 

282.1 

86.2 

56 

53.6 

16.4 

116 

110.9 

33.9 

176 

168.3 

51.5 

236 

225.7 

69.0 

296 

283.1 

86.5 

57 

54.5 

16.7 

117 

111.9 

34.2 

177 

169.3 

51.7 

237 

226.6 

69.3 

297 

284.0 

86.8 

58 

55.5 

17.0 

118 

112.8 

34.5 

178 

170.2 

52.0 

238 

227.6 

69.6 

298 

285.0 

87.1 

59 

56.4 

17.2 

119 

113.834.8 

179 

171.2 

52.3 

239 

228.6 

69.9 

299 

285.9 

87.4 

60 

57.4 

17.5 

120 

114.8 

35.1 

180 

172.1 

52.6 

240 

229.5 

70.2 

300 

286.9 

87.7 

Dist, 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

'Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

For  73  Degrees. 

TABLE  IV.                                          221 

DIFFERENCE  OF   LATITUDE   AND  DEPARTURE   FOR  18  DEGREES. 

Dist. 

Lat. 

Dep 

Dist. 

Lat, 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep.  jj)ist. 

Lat. 

Dep. 

1 

01.0 

00.3 

61 

58.0 

18.9 

121 

115.1 

37.4 

181 

172.1 

55.  y|  241 

229.2 

74.5 

2 

01.9 

00.6 

62 

59.0 

19.2 

122 

116.037.7 

182 

173.1 

56.2|  242 

230.2 

74.8 

3 

02.9 

00.9 

63 

59.919.5 

123 

117.0 

38.0 

183 

174.0 

56.6 

243 

231.1 

75.1 

4 

03.8 

01.2 

64 

60.919.8 

124 

117.9 

38.3 

184 

175.0 

56.9 

244 

232.1 

75.4 

5 

04.8 

01.5 

65 

61.820.1 

125 

118.9 

38.6 

185 

175.9 

57.2 

245 

233.0 

75.7 

6 

05.7 

01.9 

66 

62.820.4 

126 

119.8 

38.9 

186 

176.9 

57.5 

246 

234.0 

76.0 

7 

06.7 

02.2 

67 

63.720.7 

127 

120.8 

39.2 

187 

177.8 

57.8 

247 

234.9 

76.3 

8 

07.6 

02.5 

68 

64.7 

21.0 

128 

121.7 

39.6 

188 

178.8 

58.1 

248 

235.9 

76.6 

9 

08.6 

02.8 

69 

65.6 

21.3 

129 

122.7 

39.9 

189 

179.7 

58.4 

249 

236.8 

76.9 

10 

09.5 

03.1 

70 

66.6 

21.6 

]30 

123.6 

40.2 

190 

180.7 

58.7 

250 

237.8 

77.3 

11 

10.5 

03.4 

71 

67.5 

21.9 

131 

124.6 

40.5 

191 

181.7 

59.0 

251 

238.7 

77.6 

12 

11.4 

03.7 

72 

68.5 

22.2 

132 

125.5 

40.8 

192 

182.6 

59.3 

252 

239.7 

77.9 

13 

12.4 

04.  ( 

73 

69.4 

22  6 

133 

126.5 

41.1 

193 

183.6 

59.6 

253 

240.6 

78.2 

14 

13.3 

04.3 

74 

70.4 

22^9 

134 

127.4 

41.4 

•194 

184.5 

59.9 

254 

241.6 

78.5 

15 

14.3 

04.  ( 

75 

71.3 

23.2 

135 

128.4 

41.7 

195 

185.5 

60.3 

255 

242.5 

78.8 

16 

15.2 

04.9 

76 

72.3 

23.5 

136 

129.3 

42.0 

196 

186.4 

60.6 

256 

243.5 

79.1 

17 

16.2 

05.3 

77 

73.223.8 

137 

130.3 

42.3 

197 

187.4 

60.9 

257 

244.4 

79.4 

18 

17.1 

05.6 

78 

74.2 

24.1 

138 

131.2 

42.6 

198 

188.3 

61.2 

258 

245.4 

79.7 

19 

18.1 

05.9 

79 

75.1 

24.4 

139 

132.2 

43.0 

199 

189.3 

61.5 

259 

246.3 

80.0 

20 

19.0 

06.2 

80 

76.1 

24.7 

140 

133.1 

43  3 

200 

190.2 

61.8 

260 

247.3 

80.3 

21 

M.O 

U6.5 

81 

77.0 

25.0 

141 

134.1 

43.6 

201 

191.2 

62.1 

'261 

24*.  2 

80.7 

22 

20.9 

06.8 

82 

78.0 

25.3 

142 

135.1 

43.9 

202 

192.1 

62.4 

262 

249.2 

81.0 

23 

21.9 

07.1 

83 

78.9 

25.6 

143 

136.0 

44.2 

203 

193.1 

62.7 

263 

250.1 

81.3 

24 

•22.8 

07.4 

84 

79.9 

26.0 

144 

137.0 

44.5 

204 

194.0 

63.0 

264 

251.1 

81.6 

25 

23.8 

07.7 

85 

80.8 

26.3 

145 

137.9 

44.8 

205 

195.0 

63.3 

265 

252.0 

81.9 

20 

24.7 

08.0 

86 

81.8 

26.6 

146 

138.9 

45.1 

206 

195.9 

63.7 

266 

253.0 

82.2 

27 

25.7 

08.3 

87 

82.7 

26.9 

147 

139.8 

45.4 

207 

196.9 

64.0 

267 

253.9 

82.5 

28 

26.  G 

08.7 

88 

83.7 

27.2 

148 

140.8 

45.7 

208 

197.8 

64.3 

268 

254.9 

82.8 

29 

27.6 

09.0 

89 

84.6 

27.5 

149 

141.7 

46.0 

209 

198.8 

64.6 

269 

255.8 

83.1 

30 

28.5 

09.3 

90 

85.6 

27.8 

150 

142.7 

46.4 

210 

199.7 

64.9 

270 

256.8 

83.4 

31 

29.  b 

09.6 

91 

86.5 

28.1 

151 

143.6 

46.7 

"211 

200.7 

65.2 

271 

257.7 

83.7 

32 

30.4 

09.9 

92 

87.5 

28.4 

152 

144.6 

47.0 

212 

201.6 

65.5 

272 

258.7 

84.1 

33 

31.4 

10.2 

93 

88.4 

28.7 

153 

145.5 

47.3 

213 

202.6 

65.8 

273 

259.6 

84.4 

34 

32.3 

10.5 

94 

89.4 

29.0 

154 

146.5 

47.6 

214 

203.5 

66.1 

274 

260.6 

84.7 

35 

33.3 

10.8 

95 

90.4 

29.4 

155 

147.4 

47.9 

215 

204.5 

66.4 

275 

261.5 

85.0 

33 

34.2 

11.1 

96 

91.3 

29.7 

156 

148.4 

48.2 

216 

205.4 

66.7 

276 

262.5 

85.3 

37 

35.2 

11.4 

97 

92.3 

30.0 

157 

149.3 

48.5 

217 

208.4 

67.1 

277 

263.4 

85.6 

38 

36.1 

11.7 

98 

93.2 

30.3 

158 

150.3 

48.8 

218 

207.3 

67.4 

278 

264.4 

85.9 

39 

37.1 

12.1 

99 

94.2 

30.6 

159 

151.2 

49.1 

219 

208.3 

67.7 

279 

265.3 

86.2 

40 

38.0 

12.4 

100 

95.1 

30.9 

160 

152.2 

49.4 

220 

209.2 

68.0 

280 

266.3 

86.5 

41 

39.0 

12.7 

101 

96.1 

31.2 

161 

153.1 

49.8 

221 

210.2 

68.3 

281 

267.2 

86.8 

42 

39.9 

13.0 

102 

97.0 

31.5 

162 

154.1 

50.1 

222 

211.1 

68.6 

282 

268.2 

87.1 

43 

40.9 

13.3 

103 

98.0 

31.8 

163 

155.0 

50\4 

223 

212.1 

68.9 

283 

269.1 

87.5 

44 

41.8 

13.6 

104 

98.9 

32.1 

164 

156.0 

50.7 

224 

213.0 

69.2 

284 

270.1 

87.8 

45 

42.8 

13.9 

105 

99.9 

32.4 

165 

156.9 

51.0 

225 

214.0 

69.5 

285 

271.1 

88.1 

46 

13.7 

14.2 

106 

100.8 

32.8 

166 

157.9 

51.3 

226 

214.9 

69.8 

286 

272.0 

88.4 

47 

44.7 

14.5 

107 

101.8 

33.1 

167 

158.8 

51.6 

227 

215  9 

70.  l! 

287 

273  0 

88  7 

48 

45.7 

14.8 

108 

102.7 

33  4 

168 

159  8 

51.9 

228 

216.8 

70.5 

288 

273.9 

89.0 

49 

46.6 

15.1 

109 

103.733.7 

169 

160.7 

52.2 

229 

217  8 

70.8 

289 

274.9 

89.3 

50 

47.6 

15  5 

110 

104.634.0 

170 

161.7 

52.5 

230 

218.7 

71.1 

290 

275.8 

89.6 

51 

18.5 

15.8 

111 

105.634.3 

171 

162.6 

52.8 

231 

219.7 

71.4 

291 

276.8 

89.9 

52 

49.5 

16.1 

112 

106.534.6 

172 

163.6 

53.2 

232 

220.6 

71.  7> 

292 

277.7 

90.2 

53 

50.4 

16.4 

113 

107.534.9 

173 

164.5 

53.5 

233 

221.6 

72.0, 

293 

278.7 

90.5 

54 

51.4 

16.7 

114 

108.435.2 

174 

165.5 

53.8 

234 

222.5 

72.3 

294 

279.6 

90.9 

55 

52.3 

17.0 

115 

109.435.5 

175 

166.4 

54.1 

235 

223.5 

72.6 

295 

280.6 

91.2 

56 

53.3 

17.3 

116 

110.335.8 

176 

167.4 

54.4 

236 

224.4 

72.9 

296 

281.5 

91.5 

57 

54.2 

17.6 

117 

111.336.2 

177 

168.3 

54.7 

237 

225.4 

73.2 

297 

282.5 

91.8 

58 

55.2 

17.9 

118 

112.236.5 

178 

169.3 

55.0 

238 

226.4 

73.5 

298 

283.4 

92.1 

59 

56.1 

18.2 

119 

113.236.8 

179 

170.2 

55.3 

239 

227.3 

73.9 

299 

284.4 

92.4 

GO 

>7.1 

18.5 

120 

114.1 

37.1 

180 

171.2 

55.6 

240 

228.3 

74.2 

300 

285.3 

92.7 

Dist.  Dep 

Lat. 

Dist. 

Dcp.  iLat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dcp. 

Lat. 

Dist. 

Dep. 

Lat, 

For  72  Degrees. 

222                                           T1BLE  IV. 

DIFFERENCE  OF  LATITUDE  AXD  DEPARTURE  FOR  19  DEGREES. 

Dist.  [Lat. 

Dep 

Dist. 

Lat. 

Dep| 

Dist. 

Lat, 

Dep! 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.3 

61 

57.7 

19  9 

121 

114.4 

39.4 

181 

171.1 

58.9 

241 

227.9 

78.5 

2 

01.9 

JO.  7 

62 

58  6 

:0.2 

122 

115.4 

39.7 

182 

172.1 

59.3 

242 

228.8 

78  8 

3 

02.8 

01.0 

63 

59.6 

20.5 

123 

116.3 

40.0 

183 

173.0 

59.6 

243 

229.8 

79.1 

4 

33.8 

01.3 

64 

60.5 

20.8 

124 

117.2 

40.4 

184 

174.0 

59.9 

244 

230.7 

79.4 

5 

04.7 

01.6 

6J 

61.5 

21.2 

125 

118.2 

40.  7, 

185 

174.9 

60.2 

245 

231.7 

79.8 

6 

05.7 

02.0 

66 

62.4 

21.5 

126 

119.1 

41.0 

186 

175.9 

60.6 

246 

232.6 

80.1 

7 

06.6 

02.3 

67 

63.3 

21.8 

127 

120  1 

41.3 

187 

176.8 

60.9 

247 

233.5 

80.4 

8 

07.  6 

02.6 

68 

64.3 

22.1 

128 

121.0 

41.7 

188 

177.8 

61.2 

248 

234.5 

80.7 

9 

)8.5 

02.9 

69 

65.2 

22.5 

129 

122.0 

42.0 

189 

178.7 

61.5; 

249 

235.4 

81  1 

10 

J9.5 

03.3 

70 

6J.2 

22.8 

130 

122.9 

42.3 

190 

179.6 

61.9' 

250 

236.4 

81.4 

11 

iO.4 

M  6 

71 

67.1 

z3.1 

131 

123.9 

42.6 

191 

ISO.  6 

62.2 

251 

237.3 

84.7 

12 

11.3 

03.9 

7z 

68.1 

23.4 

132 

124.8 

43.0 

192 

181.5 

62.5 

252 

238.3 

82.0 

13 

12.3 

J4.2 

73 

69.0 

23.8 

133 

125.8 

43.3 

193 

182.5 

62.8 

253 

239.2 

82.4 

14 

13.2 

04.6 

74 

70.0 

24.1 

134 

126.7 

43.6: 

194 

183.4 

63.2 

254 

240.2 

82.7 

15 

14.2 

04.9 

75 

70.9 

24.4 

135 

127.6 

44.0 

195 

184.4 

63.5 

255 

241.1 

83.0 

1C 

15.1 

05.2 

76 

71.9 

24.7 

136 

128.6 

44.3 

196 

185.3 

63.8 

256 

242.1 

83.3 

17 

16.1 

05.5 

77 

72.8 

25.1 

137 

129.5 

44.6 

197 

186.3 

64.1 

257 

243.0 

83.7 

18 

17.0 

05.9 

78 

73.8 

25.4 

138 

130.5 

44.9 

198 

187.2 

64.5 

258 

243.9 

84.0 

19 

18.006.2 

79 

74.7 

25.7 

139 

131.4 

45.3 

199 

188.2 

64.8 

259 

244.9 

84.3 

20 

18  906.5 

80 

75.6 

26.0 

140 

132.4 

45.6 

200 

189.1 

65.1 

260 

245.  b 

84.6 

zi 

19.9J06.8 

81 

76.  (3 

•26.4 

141 

133.3 

45.9 

201 

190.0 

65.4 

•261 

246.8 

85.0 

22 

20.8 

07.2 

82 

77.5 

26.7 

142 

134.3 

46.2 

202 

191.0 

65.8 

262 

247.7 

85.3 

23 

21.7 

07.5 

83 

78.5 

27.0 

143 

135.2 

46.6 

203 

191.9 

66.1 

263 

248.7 

85.6 

24 

22.7 

07.8 

84 

79.4 

27.3 

144 

136.2 

46.9 

204 

192.9 

66.4 

264 

249.6 

86.0 

25 

23.608.1 

85 

80.427.7 

145 

137.1 

47.2 

205 

193.8 

66.7 

265 

250.6 

86.3 

26 

24  608.5 

86 

81.328  0 

146 

138.0 

47.5 

206 

194.8 

67.1 

266 

251.5 

86.6 

27 

25.508.8 

87 

82.3 

28.3 

147 

139.0 

47.9 

207 

195.7 

67.4 

267 

252.5 

86.9 

28 

26.5 

09.1 

88 

83.2 

28.7 

148 

139.9 

48.2 

208 

196.7 

67.7 

268 

253.4 

87.3 

29 

27.4 

09.4 

89 

84.229.0 

149 

140.9 

48.5 

209 

197.6 

68.0 

269 

254.3 

87.6 

30 

23.4 

09  8 

90 

85.1 

29.3 

150 

141.8 

48.8 

210 

198.6 

68.4 

270 

255.3 

87.8 

31 

29.3 

10.1 

91 

86.0 

29.6 

151 

142.8 

49.2 

211 

199.5 

68.7 

27  J 

256.  ± 

68.2 

32 

30.3 

10.4 

92 

87.030.0 

152 

143.7 

49.5 

212 

200.4 

69.0 

272 

257.2 

88.6 

33 

31.2 

10.7 

93 

87.9 

30.3 

153 

144.7 

49.8 

213 

201.4 

69.3 

273 

258.1 

88.9 

34 

32.1 

11.1 

94 

88.9 

30.  C 

154 

145.6 

50.1 

214 

202.3 

69.7 

274 

259.1 

89.2 

35 

33.1 

11.4 

95 

89.8 

30.9 

155 

146.6 

50.5 

215 

203.3 

70.0 

275 

260.0 

89.5 

30 

34.0 

11.7 

96 

90.8 

31.3 

150 

147.5 

50.8 

216 

204.2 

70.3 

276 

261.0 

89.9 

37 

35.0 

12.  (J 

97 

91.7 

31.6 

157 

148.4 

51.1 

217 

205.2 

70.6 

277 

261.  i, 

90.2 

38 

35.9 

12.4 

98 

92.7 

31.9 

158 

149.4 

51.4 

21b 

206.1 

71.0 

278 

262.9 

90.5 

39 

36.9 

12.7 

99 

93.6 

32.2 

159 

150.3 

51.8 

219 

207.1 

71.3 

279 

263.8 

90.8 

40 

37.8 

13.0 

100 

94.6 

32.6 

160 

151.3 

52.1 

220 

208.0 

71.6 

280 

264.7 

91.2 

41 

38.  b 

13.3 

101 

95.5 

32.9 

161 

152.2 

52.4 

221 

209.0 

7-2.0 

281 

265.  '< 

91.5 

42 

39.7 

13.7 

102 

96.4 

33.2 

162 

153.2 

52.7 

222 

209.9 

72.3 

282 

266.6 

91.8 

43 

40.7 

14.0 

103 

97.4 

33.5 

163 

154.1 

53.1 

223 

210.9 

72.6 

283 

267.6 

92.1 

41 

41.0 

14.3 

104 

98.3 

33.9 

164 

155.1 

53.4 

224 

211.8 

72.9 

284 

268.5 

92.5 

45 

42.5 

14.7 

105 

99.3 

34.2 

165 

156.0 

53.7 

225 

212.7 

73.3 

285 

269.5 

92.8 

4G 

43.5 

15.0 

106 

100.2 

34.5 

166 

157.0 

54.0 

226 

213.7 

73.6 

28G 

270.4 

93.1 

47 

44.4 

15.3 

107 

101.2 

34.8 

167 

157.9 

54.4 

227 

214.6 

73.9 

287 

271.4 

93.4 

48 

45.4 

15.6 

108 

102.1 

35.2 

168 

158.8 

54.7 

228 

215.6 

74.2 

288 

272.3 

93.8 

49 

46.3 

16.0 

109 

103.1 

35.5 

169 

159.8 

55.6 

229 

216.5 

74.6 

289 

273.3 

94.1 

50 

47.3 

16.3 

110 

104.0 

35.8 

170 

160.7 

55.3 

230 

217.5 

74.9 

290 

274.2 

94.4 

51 

48.2 

16.6 

111 

105.0 

36.1 

171 

161.7 

55.7 

231 

218.4 

75/2 

291 

275.1 

94.7 

52 

49.2 

1619 

112 

105.9 

36.5 

172 

162.6 

56.0 

232 

219.4 

75.5 

292 

276.1 

95.1 

53 

50.1 

17.3 

113 

106.8 

36.8 

173 

163.6 

56.3 

233 

220.3 

75.9 

293 

277.0 

95.4 

54 

51.1 

17.6 

114 

107.8 

37.1 

174 

164.5 

56.6 

234 

221.3 

76.2 

294 

278.0 

95.71 

55 

52.0 

17.9 

115 

108.737.4 

175 

165.5 

57.0 

235 

222.2 

76.5 

295 

278.9 

96.0 

56 

52.9 

18.2 

116 

109.7 

37.8 

176 

166.4 

57.3 

236 

223.1 

76.8 

296 

279.9 

96.4 

57 

53.9 

18.6 

117 

110.6 

38.1 

177 

167.4 

57.6 

237 

224.1 

77.2 

297 

280.8 

96.7 

58 

54.8 

18.9 

118 

111.6 

38  4 

178 

168.3 

58.0 

238 

225.0 

77.5 

298 

281.8 

97.0 

59 

55.8 

19.2 

119 

112.5 

38.7 

179 

169.2 

58.3 

239 

226.0 

77.8 

299 

282.7 

97.3 

60 

56.7 

19.5 

120 

113.5 

39.1 

180 

170.2 

58.6 

240 

226.9 

78.1 

300 

283.7 

97.7 

riist. 

Dep 

Lat. 

m. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  71  Degrees. 

TABLE  IV.                                           223 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE  FOR  20  DEGREES. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.3 

61 

57.3 

20.9 

121 

113.7 

41.4 

181 

170.1 

61.9 

241 

226.5 

82.4 

2 

01.900.7 

62 

58.3 

21.2 

12-2 

114.6 

41.7 

182 

171.0 

62.2 

242 

227.4 

82.8 

3 

02.8 

01.0 

63 

59.2 

21.5 

123 

115.6 

42.1 

183 

172.0 

62.6 

243 

228  3 

83.1 

4 

03.8 

01.4 

64 

60.1 

21.9 

124 

116.5 

42.4 

184 

172.9 

62.9 

244 

229.3 

83.5 

5 

04.7 

01.7 

65 

61.1 

22.2 

125 

117.5 

42.8 

185 

173.8 

63.3 

245 

230.2 

83.8 

6 

05.6 

02.1 

66 

62.0 

22.6 

126 

118.4 

43.1 

186 

174.8 

63.6 

246 

231.2 

84.2 

7   OG.6 

02.4 

67 

63  0 

22  9 

127 

119.3 

43.4 

187 

175.7 

64  0 

247 

232.1 

84.5 

8  107.5 

02.7 

68 

63.9 

23.3 

128 

120.3 

43.8 

188 

176  7 

64.3 

248 

233.0 

84.8 

9  08.5 

03.1 

69 

64.8 

23.6 

129 

121.2 

44.1 

189 

177.6 

64.6 

249 

234.0 

85.2 

10  |09.4 

03.4 

70 

65.8 

23.9 

130 

122  2 

44.5 

190 

178.5 

65.0 

250 

234.9 

85  5 

11 

i0.3 

j3.8 

71 

66.7 

24.3 

131 

123.1 

44.8 

191 

179.5 

65.3 

251 

235.9 

85.8 

13 

11.3 

04.  1 

72 

67.7 

24.6 

132 

124.0 

45.1 

192 

180.4 

65.7 

252 

236.8 

86.2 

13 

12.2 

04.4 

73 

-  68  6 

25.0 

133 

125.0 

45.5 

193 

181.4 

66.0 

253 

237  7 

86.5 

14 

13.2 

04  8 

74 

69.5 

25.3 

134 

125.9 

45.8 

194 

182.3 

66  4 

254 

238.7 

86.9 

15 

14.1 

05.) 

75 

70  5 

25.7 

135 

126.9 

46.  5s 

195 

183.2 

66.7 

255 

239.6 

87.2 

16 

15.0 

0:>.5 

76 

71.4 

26.0 

136 

127.8 

46.5 

196 

184.2 

67.0 

256 

240.6 

87.6 

17 

16  0 

05.8 

77 

72.4 

26.3 

137 

128.7 

46.9 

197 

185.1 

67.4 

257 

241.5 

87  9 

18 

16.9 

06.2 

78 

73.3 

26.7 

138 

129  7 

47.2 

198 

186.1 

67.7 

258 

242.4 

88.2 

19 

17.9 

06  5 

79 

74.2 

27.0 

139 

130.6 

47  5 

199 

187.0 

68.1 

259 

243.4 

88.6 

20 

18.8 

<)6.8 

80 

75.2 

27.4 

140 

131.6 

47.9 

200 

187.9 

68.4 

260 

244  3 

88.9 

21 

19.7 

07.2 

81 

70.1 

27.7 

141 

132.5 

48.2 

201 

18W.9 

68.7 

261 

245.3 

89.3 

22 

20  7 

07.5 

82 

77.1 

28.0 

142 

133.4 

48.6 

202 

189.8 

69  1 

262 

246.2 

89.6| 

23 

21.6 

07.9 

83 

78.0 

28.4 

143 

134.4 

48.9 

203 

190  8 

69.4 

263 

247.1 

90.0 

24 

22.6 

08.2 

84 

78.9 

28.7 

144 

135.3 

49.3 

204 

191.7 

69.8 

264 

248.1 

90.3 

25 

•23.5 

08.6 

85 

79.9 

29.1 

145 

136.3 

49.6 

205 

192.6 

70.1 

265 

249.0 

90.6 

26 

24.4 

08-9 

86 

80.8 

29.4 

146 

137.2 

49.9 

206 

193.6 

70.5 

266 

250.0 

91.0 

27 

25.4 

09.2 

87 

81.8 

29.8 

147 

138.1 

50.3 

207 

194.5 

70.8 

267 

250.9 

91  3 

28 

•26.3 

09.6 

88 

82.7 

30.1 

148 

139.1 

50.6 

208 

195.5 

71.1 

268 

251.8 

91  7 

29 

•27.3 

J9.9 

89 

83.6 

30.4 

149 

140  0 

ol.O 

209 

196.4 

71.5 

269 

252.8 

92.0 

30 

2S.2 

10.3 

90 

84.6 

30.8 

150 

141.0 

51.3 

210 

197.3 

71.8 

270 

253.7 

92.3 

31 

29.1 

10.6 

91 

85.5 

31.1 

151 

141.9 

51.6 

211 

198.  b 

72.2 

271 

254.7 

92.7 

32 

30.1 

10.9 

92 

86.5 

31.5 

152 

142.8 

52.0 

212 

199.2 

72.5 

272 

255.6 

93.0 

33 

31.0 

11.3 

93 

87.4 

31.8 

153 

143.8 

52.3 

213 

200.2 

72.9 

273 

256.5 

93.4 

34 

31.9 

11.6 

94 

88.3 

32.1 

154 

144.7 

52.7 

214 

201.1 

73.2 

274 

257.5 

93.7 

35 

32.9 

i2.0 

95 

89.3 

32.5 

155 

145.7 

33.0 

215 

202.0 

73.5 

275 

258.4 

94.1 

36 

33.8 

12.3 

96 

90.2 

32.8 

156 

146.6 

53.4 

216 

203.0 

73.9 

276 

259.4 

94.4 

37 

34.8 

12.7 

97 

91.2 

33.2 

157 

147.5 

53.7 

217 

203.9 

74.2 

277 

260.3 

94.7 

38 

35.7 

13.0 

98 

92.1 

33.5 

158 

148.5 

54.0 

218 

204.  y 

74.6 

278 

261.2 

95.1 

39 

36.6 

13  3 

99 

93.0 

33.9 

159 

149.4 

54.4 

219 

205.8 

74.9 

279 

262.2 

95.4 

40 

37.0 

13  7 

100 

94.0 

34.2 

160 

150.4 

54.7 

220 

206.7 

75.2 

280 

263.1 

95.8 

41 

38.  fa 

14.0 

101 

94.9 

34.5 

161 

151.3 

-35.1 

221 

207.7 

75.6 

281 

264.1 

96.1 

42 

39  5 

14.4 

102 

95.8 

34.9 

162 

152.2 

55.4 

222 

208.6 

75.9 

282 

265.0 

96.4 

43 

40.4 

14.7 

103 

96.8 

35.2 

163 

153.2 

55.7 

223 

209.6 

76.3 

283 

265.9 

96.8 

44 

41.3 

15.0 

104 

97.7 

35.6 

164 

154.1 

56.1 

224 

210.5 

76.6 

284 

266.9 

97.1 

45 

42.3 

15.4 

105 

98.7 

35.9 

165 

155.0 

56.4 

225 

211.4 

77  0 

285 

267.8 

97.5 

46 

43.2 

15.7 

106 

99.6 

36.3 

166 

156.0 

56.8 

226 

212.4 

77  ..3 

286 

268.8 

97.8 

47 

44.  it 

16.1 

107 

100.5 

36.6 

167 

156.9 

57.1 

227 

213.3 

77.6 

287 

269.7 

98.2 

48 

45.1 

16.4 

108 

101.5 

36.9 

168 

157.9 

57  5 

228 

214.2 

78.0 

288 

270.6 

98.5 

49 

46.0 

16.8 

109 

102.4 

37.3 

169 

158.8 

57.8 

229 

215.2 

78.3 

289 

271.6 

98.8 

50 

47.0 

17.1 

110 

103.4 

37.6 

170 

159.7 

58.1 

230 

216.1 

78.7 

290 

272.5 

99.2 

61 

4V  .y 

IV.  4 

111 

104.3 

38.0 

171 

160.7 

58.5] 

231 

217.1 

79.0 

291 

273.5 

99.5 

52 

48.9 

17.8 

112 

105.2 

38.3 

172 

161.6 

.38.8 

232 

218  0 

79.3 

292 

274.4 

99  9 

53 

49.8 

18.1 

113 

106.2 

38.6 

173 

162.6 

•39.2 

233 

218.9 

79.7 

293 

275.3 

100.2 

5i 

50.7 

18.5 

114 

107.1 

39.0 

174 

163.5 

59.5 

234 

219.9 

80.0 

294 

276.3 

100.6 

55 

51  7 

18.8 

115 

108.1 

39.3 

175 

164.4 

59.9 

235 

220.8 

80.4 

295 

277.2 

100.9 

56 

52.6 

19.2 

116 

109.0 

39.7 

176 

165.4 

60.2 

236 

221  .  8 

80.7 

296 

278.1 

101.2 

57 

53.6 

19  5 

117 

109.9 

40.0 

177 

166.3 

60.5 

237 

222.7 

81.1 

297 

279.1 

101.6 

58 

54.5 

19.8 

118 

110.9 

40.4 

178 

167.3 

60.9 

238 

223.6 

81.4 

298 

280.0 

101.9 

59 

55.4 

20.2 

119 

111.8 

40.7 

179 

168.2 

61.2 

239 

224.6 

81.7 

299 

281.0 

102.3 

60 

56.4 

20.5 

120 

112.8 

41.0 

180 

169.1 

61.6 

240 

225.5 

82.1 

300 

281.9 

102.6 

DistJDep 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.  1  Lat. 

Dist. 

Dep. 

Lat. 

For  70  Degrees. 

224                                          TABLE  IV. 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE  FOR  21  DEGREES. 

Dist. 

Lat, 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

l 

00.9 

00.4 

61 

56.9 

21.9 

121 

113.0 

43.4 

181 

169.0 

64.9 

241 

225.0 

86.4 

2 

01.9 

00.7 

62 

57.9 

22.2 

122 

113.9 

43.7 

182 

169.9 

65.2 

242 

225.9 

86.7 

3 

02.8 

01.1 

63 

58.8 

22.6 

123 

114  8 

44.1 

183 

170.8 

65.6 

243 

226.9 

87.1 

4 

03.7 

01.4 

64 

59.7 

22.9 

124 

115.8 

44  4 

184 

171.8 

65.9 

244 

227  8 

87.4 

5 

04.7 

01.8 

65 

60.7 

23.3 

125 

116.7 

44.8 

185 

172.7 

66.3 

245 

228.7 

87.8 

6 

05.6 

02.2 

66 

61.6 

23.7 

126 

117.6 

15.2 

186 

173.6 

66.7 

246 

229.7 

88.2 

7 

16.5 

02.5 

67 

62.5 

24.0 

127 

118.6 

45.5 

187 

174.6 

67.0 

247 

230.6 

88.5 

8 

07.5 

02.9 

68 

63.5 

24.4 

128 

119.5 

45.9 

188 

175.5 

67.4 

248 

231.5 

88.9 

9 

08  4 

J3.2 

69 

64.4 

24.7 

129 

120.4 

16.2 

189 

176.4 

67.7 

249 

232.5 

89.2 

10 

09.3 

03.6 

70     65.4 

25.1 

130 

121.4 

46.  C 

190 

177.4 

68.1 

250 

233.4 

89.6 

11 

10.3 

03.9 

71 

66.3 

25.4 

131 

li-2.3 

16.91 

191 

178.3 

68.4 

25  1 

•234.5 

90.0 

12 

11.2 

J4.3 

72 

67.2 

25.8 

132 

123.2 

47.3 

192 

179.2 

68.8 

252 

235.3 

90.3 

13 

12.1 

04  7 

73 

68.2 

26.2 

133 

124.2 

47.7 

193 

180.2 

69.2 

253 

236.2 

90.7 

14 

13.1 

05.0 

74 

69.1 

26.5 

134 

125.1 

48.0 

194 

181.1 

69  5 

254 

237.1 

91.0 

15 

14.0 

05.4 

75 

70.0 

26.9 

135 

126.0 

48.4 

195 

182.0 

69.9 

255 

238.1 

91.4 

16 

14.5) 

05.  7 

76 

71.0 

.,7.2 

136 

127.0 

48.7 

196 

183.0 

70.2 

256 

239.0 

91.7 

17 

15.9 

06.1 

77 

71.9 

27.6 

137 

127.9 

49.1 

19? 

183.9 

70.6 

257 

239.9 

92.1 

18 

16.8 

06.5 

78     72.8 

28.0 

138 

128.8 

49.5 

198 

184.8 

71.0 

258 

240.9 

92.5 

19 

17.7 

06.8 

79     73  8 

28.3 

139 

129.8 

49.8 

199 

185.8 

71.3 

259 

241.8 

92.8 

20 

18.7 

07.2 

80     74  7 

28.7 

140 

130.7 

50.2 

200 

186.7 

71.7 

260 

242.7 

93.2 

21 

19.6 

07.5 

81,     75.6 

29.0 

141 

131.6 

oO.o 

'2ul 

167.6 

72.  U 

261 

243.  V 

93.5 

22 

20.5 

07.9 

82     76.6 

29.4 

142 

132.6 

30.9 

202 

188.6 

72.4 

262 

244.6 

93.9 

23 

21.5 

08.2 

83     77.5 

29.7 

!<•* 

133.5 

51.2 

203 

189.5 

72.7 

263 

245.5 

94.3 

24 

22.4 

08.6 

84     78.4 

30.1 

14* 

134.4 

51.6 

204 

190.4 

73.1 

264 

246.5 

94.6 

25 

23.3 

09.0 

85     79.4 

30.5 

145 

135.4 

12.0 

205 

191.4 

73.5 

265 

247.4 

95.0 

2G 

24.3 

09.3 

86 

80.3 

30.8 

146 

136.3 

52.3 

206 

192.3 

73.8 

266 

248.3 

95.3 

27 

25.2 

09.  7 

87 

81.2 

31.2 

147 

137.2 

32.7 

207 

193.3 

74.2 

267 

249.3 

95.7 

28 

26.1 

10.0 

88 

82.2 

31.5 

148 

138.2 

53.0 

208 

194.2 

74.5 

268 

250.2 

96.0 

29 

27.1 

10.4 

89     83.1 

31.9 

149 

139.1 

33.4 

209 

195.1 

74.9 

269 

251  .  1 

96.4 

3J 

28.0 

10.8 

90     84.0 

32.3 

150 

140.0 

53.8 

210 

196.1 

75.3 

270 

252.1 

96.8 

31 

28.  y 

11.1 

91 

85.0 

32.6 

151 

141.0 

54.1 

211 

197.0 

75.6 

271 

253  0 

97.1 

32 

29.9 

11.5 

92 

85.9 

33.0 

152 

141.9 

54.5 

212 

197.9 

76.0 

272 

253.9 

97.5 

33 

30.8 

11.8 

93 

86.8 

33.3 

153 

142.8 

54.8 

213 

198.9 

76.3 

273 

254.9 

97.8 

34 

31.7 

12.2 

94 

87.8 

33.7 

154 

143.8 

55.2 

214 

199.8 

76.7 

274 

255.8 

98.2 

35 

32.7 

12.5 

95 

88.7 

34.0 

155 

144.7 

55.5 

215 

200.7 

77.0 

275 

256.7 

98.6 

36 

33.6 

12  9 

96 

89.6 

34.4 

156 

145.6 

35.9 

216 

201.7 

77.4 

276 

257.7 

98.9 

37 

J4.5 

13.3 

97 

90.6 

34.8 

157 

146.6 

56.3 

217 

202.6 

77.8 

277 

258.6 

99.3 

38 

35.5 

13.6 

98 

91.5 

35.1 

158 

147.5 

56.6 

218 

203.5 

78.1 

278 

259.5 

99.6 

39 

36.4 

14.0 

99 

92.4 

35.5 

159 

148.4 

57.0 

219 

204.5 

78.5 

279 

260.5 

100.0 

40 

37.3 

14.3 

100 

93.4 

35.8 

160 

149.4 

57.3 

220 

205.4 

78.8 

280 

261.4 

100.3 

41 

38  3 

14.  V 

101 

94.3 

36.  '2 

161 

150.3 

57.7 

221 

206.3 

79.2 

281 

262.3 

100.7 

42 

39.2 

15.1 

102 

95.2 

36.6 

162 

151.2 

58.1 

222 

207.3 

79.6 

282 

263.3 

101.1 

43 

10.1 

15.4 

103 

96.2 

36.9 

163 

152.2 

58.4 

223 

208.2 

79.9 

283 

264.2 

101.4 

44 

11.1 

15.8 

104 

97.1 

37.3 

164 

153  1 

58.8 

224 

209.1 

80.3 

284 

265.1 

101.8 

45 

42.0 

16.1 

105 

98.0 

37.6 

165 

154.0 

59.1 

225 

210.1 

80.6 

285 

266.1 

102.1 

46 

42.9 

16.5 

106 

99.0 

38.0 

166 

155  0 

59.5 

226 

211.1) 

81.0 

286 

267.0 

102.5 

47 

43.9 

16.8 

107 

99.9 

38.3 

167 

155.9 

59.8 

227 

211.9 

81.3 

287 

267.9 

102.9 

48 

14.8 

17.2 

108 

100.8 

38.7 

168 

156:8 

60.2 

228 

212.9 

81.7 

288 

268.9 

103.2 

49 

45.7 

17.6 

109 

101.8 

39.1 

169 

157.8 

60.6 

229 

213.8 

82.1 

289 

269.8 

103.6 

50 

16.7 

17.9 

110 

102.7 

39.4 

170 

158.7 

60.9 

230 

214.7 

82.4 

290 

270.7 

103.9 

51 

47.6 

18.3 

111 

103.6 

39.8 

171 

159.6 

61.3 

231 

215.7 

82.8 

291 

271.7 

104.3 

52 

18.5 

18.6 

112 

104.6 

40.1 

172 

160.6 

61.6 

232 

216.6 

83.1 

292 

272  6 

104.6 

53 

49.5 

19.0 

113 

105.5 

40.5 

173 

161.5 

62.0 

233 

217.5 

83.5 

293 

273.5 

105.0 

54 

50.4 

19.4 

114 

106.4 

40.9 

174 

162.4 

62.4 

234 

218.5 

83.9 

204 

274.5 

105.4 

55 

51.3 

19.7 

115 

107.4 

41.2 

175 

163.4 

62.7 

235 

219.4 

84.2 

295 

275.4 

105.7 

50 

52.3 

20.1 

116 

108.3 

41.6 

176 

164.3 

63.1 

236 

220.3 

84.6 

296 

276.3 

106.1 

57 

53.2 

20.4 

117 

109.2 

41.9 

177 

165.2 

63.4 

237 

221.3 

84.9 

297 

277.3 

106  4 

58 

54.1 

20.8 

118 

110  2 

42.3 

178 

166.2 

63.8 

238 

222.2 

85.3 

298 

278  2 

106.8 

59 

55.1 

21.1 

119 

111.1 

42  6 

179 

167.1 

64.1 

239 

223.1 

85.6 

299 

279.1 

107  2 

60 

56.0 

21.5 

120 

112  0 

43.0 

180 

168.0 

64.5 

240 

224.1 

86.0 

300 

280.1 

107.5 

Dist; 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  69  Degrees. 

TABLE  IV.                                           225 

DIFFERENCE  OF    LATITUDE    AND  DEPARTURE   FOR  22  DEGREES. 

Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep  Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.4 

61 

56.6 

22.9 

121 

112.245.3 

181 

167.8 

67.8 

241 

223.5 

90.3 

2 

01.9 

00.7 

62 

67.523.2 

122 

113.1 

45.7    182 

168.7 

68.2 

242 

224.4 

90.7 

3 

02.8 

01.1 

63 

58.423.6 

123 

114.0J46.1    183 

169.7 

68.6 

243 

225.3 

91.0 

4 

03.7 

01.5 

64 

59.324.0 

124 

115.046.5 

184 

170.6 

68.9 

244 

226.2 

91.4 

5 

04.6 

01.9 

65 

60.324.3 

125 

115.946.8 

185 

171.5 

69.3 

245 

227.2 

91.8 

6 

05.6 

02.2 

66 

61.224.7 

126 

116.847.2    186 

172.5 

69.7 

246 

228.1 

92.2 

7 

16.5 

02.6 

67 

62.1'25.1 

127 

117.847.6 

187 

173.4 

70.1 

247 

229.0 

92.  £ 

8 

07.4 

03.0 

68 

63.025.5 

128 

118.747.9 

188 

174.3 

70.4 

248 

229.9 

92.  £ 

9 

•J8.3 

03.4 

69 

64.0,25.8 

129 

119.648.3 

189 

175.2 

70.8 

249  230.9 

93.3 

10 

09.3 

03.7 

70 

64.9!'26.2 

130 

120.548.7 

190 

176.2 

71.2 

250|  231.8 

93.7 

11 

10.2 

04.1 

71 

65.826.6 

131 

121.549.1 

~19~1 

177.1 

71.5 

251 

232.7 

94.  1 

12 

11.1 

04.5 

72 

66.8'27.0 

132 

122.449.4 

192 

178.0 

71.9 

252 

233.7 

94.4 

13 

12.1 

04.9 

73 

67.7127.3 

133 

123.349.8 

193 

178.9 

72.3 

253 

234.6 

94.8 

14 

13.0 

05.2 

74 

68.627.7 

134 

124.250.2 

194 

179.9 

72.7 

254 

235.5 

95.2 

15 

13.9 

05.6 

75 

69.528.1 

135 

125.2 

50.6 

195 

180.8 

73.0 

255 

236.4 

95.5 

16 

14.8 

06.0 

76 

70.528.5 

136 

126.150.9 

196 

181.7 

73.4 

256 

237.4 

95.  £ 

17 

15.8 

06.4 

77 

71.428.8 

137 

127.05l.3j|  197 

182.7 

73.8 

257 

238.3 

96.3 

18 

16.7 

06.7 

78 

72.329.2 

138 

128.051.7 

198 

183.6 

74.2 

258 

239.2 

96.6 

19 

17.6 

07.1 

79 

73.2:29.6 

139 

128.9 

52.1 

199 

184.5 

74.5 

259 

240.1 

97.  C 

20 

18.5 

07.5 

80 

74.230.0 

140 

129.852.4    200 

185.4 

74.9 

260 

241.1 

97.4 

21 

19.5 

07.  y 

81 

75.130.3    141 

130.7|52.8 

201 

186.4 

75.3 

261 

242.0 

97.  fc 

22 

20.4 

08.2 

82 

76.0 

30.7    142 

131.7 

53  2 

202 

187.3 

75.7 

262 

242.9 

98.1 

23 

21.3 

08.6 

83 

77.0 

31.1 

143 

132.653.6 

203 

188.2 

76.0 

263 

243.8 

98.5 

24 

22.3 

09.0 

84 

77.9 

31.5 

144 

133.553.9 

204 

189.1 

76.4 

264 

244.8 

98.  1 

25 

•23.2 

09.4 

85 

78.8 

31.8 

145 

134.454.3 

205 

190.1 

76  8 

265 

245.7 

99.  1 

26 

24.1 

09.7 

86 

79.732.2 

146 

135.454.7 

206 

191.0 

77.2 

266 

246.6 

99.6 

27 

25.0 

10.1 

87 

80.732.6 

147 

136.3 

55.1 

207 

191.9 

77.5 

267 

247  6 

100.0 

28 

26.0 

10.5 

88 

81.633.0 

148 

137.255.4 

208 

192.9 

77.9 

268 

248.5 

100.4 

29 

26.9 

10.9 

89 

82.533.3 

149 

138.255.8 

209 

193.8 

78.3 

269 

249.4 

100.8 

30 

27.8 

11.2 

90 

83.433.7 

150 

139.156.2 

210 

194.7 

78.7 

270 

250.3 

101.1 

31 

28.7 

11.6 

91 

84.434.1 

151 

140.056.6 

211 

195.6 

79.0 

271 

251  .  b 

101.  £ 

32 

29.7 

12.0 

92 

85.334.5 

152 

140.9(56.9 

212 

196.6 

79.4 

272 

252.2 

101.  t 

33 

30.6 

12.4 

93 

86.234.8 

153 

141.957.3 

213 

197.5 

79.8 

273 

253.1 

102.  £ 

34 

31.5 

12.7 

94 

87.2 

35.2 

154 

142.857.7 

214 

198.4 

80.2 

274 

254.0 

102.  C 

35 

32.5 

13.1 

95 

88.1 

35.6 

155 

143.758.1 

215 

199.3 

80.5 

275 

255.0 

103.  C 

36 

33.4 

13.5 

96 

89.0 

36.0 

156 

144.658.4 

216 

200.3 

80.9 

276 

255.9 

103.4 

37 

34.3 

13.9 

97 

89.9 

36.3 

157 

145.658.8 

217 

201.2 

81.3 

277 

256.8 

103.8 

38 

35.2 

14.2 

98 

90.9 

36.7 

158 

146.5 

59.2 

218 

202.1 

81.7 

278 

257.8 

104.1 

39 

36.2 

14.6 

99 

91.8 

37.1 

159 

147.459.6 

219 

203.1 

82.0 

279 

258.7 

104  5 

40  37.1 

15.0 

100     92.737.5 

160 

148.359.9 

220 

204.0 

82.4 

280 

259.6 

104.9 

41  138.0 

15.4 

101 

93.6 

37.8 

161 

149.360.3 

221 

204.9 

82.8 

281 

260.5 

106.3 

42 

38.9 

15.7 

102 

94.6 

38.2 

162 

150.260.7 

222 

205.8 

83.2 

282 

261.5 

105.6 

43 

39.9 

16.1 

103 

95.5 

38.6 

163 

151.1 

61.1 

223 

206.8 

83.5 

283 

262.4 

106.  t 

44 

40.8 

16.5 

104 

96.4 

39.0 

164 

152.1 

61.4 

224 

207.7 

83.9 

284 

263.3 

106.4 

45 

41.7 

16.9 

105 

97.439.3 

165 

153.0 

61.8 

225 

208.6 

84.3 

285 

264.2 

106.8 

46 

12.7 

17.2 

106 

98.339.7 

166 

153.9 

62.2 

226 

209.5 

84.7 

286 

265.2 

107.1 

47 

43.6 

17.6 

107 

99.240.1 

167 

154.8 

62.6 

227 

210.5 

85.0 

287 

266.1 

107.5 

48 

44.5 

18.0 

108 

100.140.5 

168 

155.862.9 

228 

211.4 

85.4 

288 

267.0 

107.9 

49 

45.4 

18.4 

109 

101.140.8 

169 

156.7163.3 

229 

212.3 

85.8 

289 

268.0 

108.3 

50 

46.4 

18.7 

110 

102.041.2 

170 

157.6J63.7 

230 

213.3 

86.2 

290 

268.9 

108.6 

51 

17.3 

19.1 

111 

102.941.6 

171 

158.5 

64.1 

231 

214.2 

86.5 

291 

269.8 

109.0 

52 

48.2 

19.5 

112 

103.842.0 

172 

159.5 

64.4 

232 

215.1 

86.9 

292 

270.7 

109.4 

53 

49.1 

19.9 

113 

104.842.3 

173 

160.4 

64.8 

233 

216.0 

87.3 

293 

271.7 

109.8 

54 

50.1 

20.2 

114 

105.742.7 

174 

161.3 

65.2 

234 

217.0 

87.7 

294 

272.6 

110.1 

55 

51.0 

20.6 

115 

106.643.1 

175 

162.3 

65.6 

235 

217.9 

88.0 

295 

273.5 

110.5 

56 

51.9 

21.0 

116 

107.643.5 

176 

163.2 

65.9 

236 

218.8 

88.4 

296 

274.4 

110.9 

57 

52.8 

21.4 

117 

108.543.8 

177 

164.1 

66.3 

237 

219.7 

88.8 

297 

275.4 

111.3 

58 

53.8 

21.7 

118 

109.444.2 

178 

165.066.7 

238 

220.7 

89.2 

298 

276.3 

111.6 

59 

54.7 

22.1 

119 

110.344.6 

179 

166.067.1 

239 

221.6 

89.5 

299 

277.2 

112.  C 

60 

55.6 

22  5 

120 

111.3 

45.0 

180 

166.9 

67.4 

240 

222.5 

89.9 

300 

278.2 

112.4 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

For  08  Degrees. 

226                                          TABLE  IV. 

DIFFERENCE    OF   LATITUDE  AND  DEPARTURE  FOR  23    DEGREES. 

Bist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.4 

61 

56  2 

23.8 

121 

111.447.3 

181 

166.6 

70.7 

241 

221.8 

94.2 

2 

01.8 

00.8 

62 

57.1 

24.2 

122 

112.347.7 

182 

167.5 

71.1 

242 

222.8 

94.5 

3 

)2.8 

01.2 

63 

58.0 

24.6 

123 

113.248.1 

183 

168.5 

71.5 

243 

223.7 

94.9 

4 

03.7 

01.6 

64 

58.9 

25.0 

124 

114.148.5 

184 

169.4 

71.9 

244 

224.6 

95.3 

5 

01.  602.0 

65 

59.8 

25.4 

125 

115.148.8 

185 

170.3 

72.3 

245 

225.5 

95  7 

6 

05.502.3 

66 

60.8 

25.8 

126 

116.049.2 

186 

171  2 

72.7 

246 

226.4 

96.1 

7 

06.402.7 

67 

61.7 

26.2 

127 

116.9 

19.6 

187 

172.1 

73.1 

247 

227.4 

96.5 

8 

07.403.1 

68 

62.6 

26.6 

128 

117.8 

50.0 

188 

173.1 

73.5 

24.8 

228  3 

96.9 

9 

08.303.5 

69 

63.5 

27.0 

129 

118.7 

50.4 

189 

174.0 

73.8 

249 

229.2 

97.3 

10 

09  203.9 

70 

64.4 

27.4 

130 

119.7 

50.8 

190 

174  9 

74.2 

250 

230.1 

97.7 

ll' 

10.] 

04.3 

71 

65.4 

27.7 

131 

120  6 

51/2 

191 

175.8 

74.6 

251 

231.0 

98.1 

12 

11.  0 

04.7 

72 

66.3 

28.1 

132 

121.5 

51.6 

192 

176.7 

75.0 

252 

232.0 

98.5 

13 

12.005.1 

73 

67.2 

28.5 

133 

122.4 

52.0 

193 

177.7 

75  4 

253 

232.9 

98  9 

14 

12.905.5 

74 

6H.1 

28.9 

134 

123.3")2  4 

194 

178.6 

75.8 

254 

233.8 

99.2 

15 

13.805.9 

75 

69.0 

29.3 

135 

124.3 

52.7 

195 

179  5 

76.2 

255 

234  7 

99.6 

16 

14.706.3 

70 

70.0 

29.7 

136 

125.2 

53.1 

196 

180.4 

76.6 

256 

235.6 

100.0 

17 

15.606.6 

77 

70  9 

30.1 

137 

126  1 

53.5 

197 

181.3 

77  0 

257 

236.6 

100.4 

18 

16.607.0 

78 

71.8 

30.5 

138 

127.0 

53.9 

198 

182.3 

77.4 

258 

237.5 

100.8 

19 

17.5 

07.4 

79 

72.7 

30  9 

139 

128.0 

54.3 

199 

183.2 

77.8 

259 

238.4 

101.2 

20 

18.4 

07.8 

80 

73.6 

31.3 

140 

128.954  7 

200 

184.1 

78.1 

260 

239.3 

101.6 

21 

19.308/2 

81 

74.631.6 

141 

129.855.1 

201 

185.0 

78.5 

261 

240.3 

102.0; 

22 

20  308  6 

82 

75.5 

32.0 

142 

130.755.5 

202 

185.9 

78.9 

262 

241.2 

102.4 

23 

21.209.0 

83 

76.4 

32.4 

143 

131.655.9 

203 

186.9 

79.3 

263 

242.1 

102-.8 

24 

22.109.4 

84 

77.3 

32  8 

144 

132.656.3 

204 

187.8 

79.7 

264 

243.0 

103/2 

25 

23.0 

09.8 

85 

78.233.2 

145 

133.556.7 

205 

188.7 

80.1 

265 

243.9 

103.5 

26 

23.9 

10  2 

8G 

79.2 

33.6 

146 

134  457.0 

206 

189.6 

80.5 

266 

244.9 

103.9 

27 

24.9 

10.5 

87 

80.1 

34.0 

147 

135.357.4 

207 

190.5 

80.9 

267 

245.8 

104.3 

28 

25.8 

10.9 

88 

81.0 

34.4 

148 

136.257.8 

208 

191.5 

81.3 

268 

246.7 

104  7 

29 

26.7 

11.3 

89 

81.9 

34.8 

149 

137.258.2 

209 

192.4 

81.7 

269 

247.6 

105.11 

30 

•27.6 

11.7 

90 

82.8 

35.2 

150 

138.1 

58.6 

210 

193.3 

82.1 

270 

248.5 

105.5 

31 

28.5 

12.1 

91 

83.  835.  C 

151 

139.059.0 

'211 

194.2 

82.4 

271 

249.5 

105.9 

32 

29.5 

12.5 

92 

84.7 

35.9 

152 

139  959.4 

212 

195.1 

82.8 

272 

250.4 

106.3 

33 

30.4 

12.9 

93 

85.6 

36.3 

153 

140.859.8 

213 

196.1 

83.2 

273 

251.3 

106.7 

34 

31.3 

13.3 

94 

86.5 

36.7 

154 

141  860.2 

214 

197  0 

83.6 

274 

252.2 

107.1 

35 

32.2 

13.7 

95 

87.4 

37.1 

155 

142.7 

60.6 

215 

197.9 

84.0 

275 

253.1 

107.5 

3G 

33.1 

14.1 

96 

88.4 

37.5 

156 

143.661.0 

'216 

198.8 

84.4 

276 

254.1 

107.8 

37 

34.1 

14.5 

97 

89.3 

37.9 

157 

144.561  3 

217 

199.7 

84.8 

277 

255.0 

108.2 

33 

35.0 

14.8 

98 

90.2 

38.3 

158 

145.461.7 

218 

200.7 

85.2 

278 

255.9 

108.6 

39 

35.9 

15.2 

99 

91.1 

38.7 

159 

146.462.1 

21<J 

201.6 

85.6 

279 

256.8 

109.0 

40 

36.8 

15.6 

100 

92.1 

39.1 

160 

147.3 

62.5 

220 

202.5 

86.0 

280 

257.7 

109.4 

41 

37.7 

16.0 

101 

93.0 

39.5 

161 

148.2 

62  9 

221 

203.4 

86.4 

281 

258.7 

1U9.8 

42 

38.7 

16.4 

102 

93.9 

39.9 

162 

149.1 

63.3 

222 

204.4 

86.7 

282 

259.6 

110.2 

43 

39  6 

16.8 

103 

94.8 

40.2 

163 

150.0 

63.7 

223 

205.3 

87.1 

283 

260.5 

110.6 

44 

40.5 

17  2 

104 

95.7 

40.6 

164 

151.0 

64.1 

224 

206.2 

87.5 

284 

261.4 

111.0 

45 

41  4 

17.6 

105 

96.7 

41.0 

165 

151.9 

64.5 

225 

207.1 

87.9 

285 

262.3 

111.4 

46 

42.3 

18.0 

10G 

97.6 

41.4 

166 

152.8 

64  9 

226 

208.0 

88.3 

286 

263.3 

111.7 

47 

43.3 

18.4 

107 

98.5 

41.8 

167 

153  7 

65.3 

227 

209.0 

88.7 

287 

264.2 

112.1 

43 

44.2 

18.8 

108 

99.4 

42.2 

168 

154.6 

65.6 

228 

209.9 

89.1 

288 

265.1 

112.5 

49 

45.1 

19.1 

109 

100.3 

42.6 

169 

155.6 

66.0 

229 

210.8 

89.5 

289 

266.0 

112.9 

50 

46.0 

19.5 

110 

101.3 

43.0 

170 

156.5 

66.4 

230 

211.7 

89.9 

290 

266.9 

113.3 

51 

46.9 

19.9 

111 

102.2 

43.4 

171 

157.4 

66.8 

231 

212.6 

90.3 

291 

267.9 

113.7 

52 

47.9 

20.3 

112 

103.1 

43  8 

172 

158.3 

67.2 

232 

213.6 

90.6 

292 

268.8 

114.1 

53 

48.8 

20.7 

113 

104.0 

44.2 

173 

159.2 

67.6 

233 

214.5 

91.0 

293 

269.7 

114.5 

54 

49.7 

21.1 

114 

104.9 

44.5 

174 

160.2 

68.0 

234 

215.4 

91.4 

294 

270.6 

114.9 

55 

50.6 

21.5 

115 

105.9 

44.9 

175 

161.1 

68.4 

235 

216.3 

91.8 

295 

271.5 

115.3 

56 

51.5 

21.9 

116 

106.8 

45.3 

176 

162.0 

68.8 

236 

217.2 

92.2 

296 

272.5 

115.7 

57 

52.5 

22.3 

117 

107.7 

45.7 

177 

162.9 

69.2 

237 

218.2 

92.6 

297 

273.4 

116.0 

58 

53.4 

22.7 

118 

108.6 

46.1 

178 

163.8 

69.6 

238 

219.1 

93.0 

298 

274.3 

116.4 

59 

54.3 

23.1 

119 

109.5 

46.5 

179 

164.869.9 

239 

220.0 

93.4 

299 

275.2 

116.8 

60 

55.2 

23.4 

120 

110.5 

46.9 

180 

165.7 

70.3 

240 

220.9 

93.8 

300 

276.2 

117.2 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

'Dist, 

Dep. 

Lat. 

For  G7  Degrees. 

TABLE  IV.                                           227 

DIFFERENCE  OF   LATITUDE   AND  DEPARTURE   FOE  24  DEGREES. 

9ist. 

LatJDep 

His!. 

Lat. 

!Vj.  I>ist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9:00.4 

61 

55.724.8 

121 

110.5 

49.2 

181 

165.4 

73.6 

241 

220.2 

y8.0 

2 

01.800.8 

62 

56.625.2 

122 

111.5 

49.6 

182 

166.3 

74.0 

242 

221.1 

98.4 

3 

02.7,01.2 

63 

57.625.6 

123 

112.4 

50.0 

183 

167.2 

74.4 

243 

222.0 

98.8 

4 

13.701.6 

64 

58.526.0 

124 

113.3 

50.4 

184 

168.1 

74.8 

244 

222.9 

99.2 

5 

04.602.0 

65 

59.426.4 

125 

114.2 

50.8 

185 

169.0 

75.2 

245 

223.8 

99.7 

6 

15.502.4 

6G 

60.  326.8 

126 

115.1 

51.1 

186 

169.9 

75.7 

246 

224.7 

100.1 

7 

16.4 

02.8 

67 

61.227.3 

127 

116.0 

51.7 

187 

170.8 

76.1 

247 

225.6 

100.5 

8 

07.303.3 

68 

62.1 

27.7 

128 

116.9 

52.1 

188 

171.7 

76.5 

248 

226.6 

100.9 

9 

08.203.7 

69 

63.028.1 

129 

117.8 

52.5 

189 

172.7 

76.9 

249 

227.5 

101.3 

10 

09.1 

04.1 

70 

63.9,28.5 

130 

118.8 

52.9 

190 

173.6 

77.3 

250 

228.4 

101.7 

Jl 

10.004.5 

71 

04.9,28.9 

131 

119.7 

53.3 

191 

174.5 

77.7 

251 

229.3 

102.1 

12 

11.  (04.  9 

72 

65.829.3 

132 

120.6 

53  7 

192 

175.4 

78.1 

252 

230.2 

102.5 

13 

11.9.05.3 

73 

6G.7i29.7 

133 

121.5 

54.1 

193 

176.3 

78.5 

253 

231.1 

102.9 

14 

12.805.7 

74 

67.630.1 

134 

122.4 

54.5 

194 

177.2 

78.9 

254 

232.0 

103.3 

15 

13.7 

06.1 

75 

68.530.5 

135 

123.3 

54.9 

195 

178.1 

79.3 

255 

233.0 

103.7 

16 

14.6 

06.5 

76 

69.430.9 

136 

124.2 

55.3 

196 

179.1 

79.7 

256 

233.9 

104.1 

17 

15.5 

06.9 

77 

70.331.3 

137 

125.2 

55.7 

197 

180.0 

80.1 

257 

234.8 

104.5 

18 

1G.4 

07.3 

78 

71.331.7 

138 

126.1 

56.1 

198 

180.9 

80.5 

258 

235.7 

104.9 

19 

17.4 

07.7 

79 

72.232.1 

139 

127.0 

56.5 

199 

181.8 

80.9 

259 

236.6 

105.3 

20 

18.308.1 

80 

73.132.5 

140 

127.9 

56.9 

200 

182.7 

81.3 

260 

237.5 

105.8 

21 

19.  '2 

08.5 

81 

74.032.9 

141 

128.8 

57.3 

201 

183.6 

81.8 

261 

238.4 

106.2 

22 

20.1 

08.9 

82 

74.933.4 

142 

129.7 

57.8 

202 

184.5 

82.2 

262 

239.3 

106.6 

23 

21.0 

09.4 

83 

75.833.8 

143 

130.6 

58.2 

203 

185.4 

82.6 

263 

240.3 

107.0 

24 

21.9 

09.8 

84 

76.734.2 

144 

131.  C 

58.6 

204 

186.4 

83.0 

264 

241.2 

107.4 

25 

22.8 

10.2 

85 

77.734.6 

145 

132.5 

59.0 

205 

187.3 

83.4 

265 

242.1 

107.8 

2G 

23.8 

10.6 

86 

78.635.0 

146 

133.4 

59.4 

206 

188.2 

83.8 

266 

243.0 

108.2 

27 

24.7 

11.0 

87 

79.535.4 

147 

134.3 

59.8 

207 

189.1 

84.2 

267 

243.9 

108.6 

28 

25.6 

11.4 

88 

80.4:35.8 

148 

135.2 

60.2 

208 

190.0 

84.6 

268 

244.8 

109.0 

29 

26.5 

11.8 

89 

81.336.2 

149 

136.1 

60.6 

209 

190.9 

85.0 

269 

245.7 

109.4 

30 

27.4 

12  .  -2 

90 

82.236.6 

150 

137.0 

61.0 

210 

191.8 

85.4 

270 

246.7 

109.8 

31 

28.  b 

12.0 

91 

83.  137.0 

151 

137.9 

61  4 

211 

192.8 

85.8 

271 

247.6 

110.2 

32 

29.2 

13.0 

92 

84.037.4 

152 

138.9 

61.8 

212 

193.7 

86.2 

272 

248.5 

110.6 

33 

30.1 

13.4 

93 

85.037.8 

153 

139.8 

62.2 

213 

194.6 

86.6 

273 

249.4 

111.0 

34 

31.1 

13.8 

94 

85.938.2 

154 

140.7 

62.6 

214 

195.5 

87.0 

274 

250.3 

111.4 

35 

32.0 

14.2 

95 

86.8 

38.6 

155 

141.  C 

63.0 

215 

196.4 

87.4 

275 

251.2 

111.9 

3C> 

32.9 

14.6 

9G 

87.739.0 

156 

142.5 

63.5 

216 

197.3 

87.9 

276 

252.1 

112.3 

37 

33.8 

15.0 

97 

88.6|39.5 

157 

143.4 

63.9 

217 

198.2 

88.3 

277 

253.1 

112.7 

38 

34.7 

15.5 

98 

89.539.9 

158 

144.3 

G4.3 

218 

199.2 

88.7 

278 

254.0 

113.1 

39 

35.6 

15.9 

99 

90.4 

40.3 

159 

145.3 

64.7 

219 

200.1 

89.1 

279 

254.9 

113.5 

40 

36.5 

1G.3 

100 

91.4 

40.7 

160 

14G.2 

65.1 

220 

201.0 

89.5 

280 

255.8 

113.9 

41 

37.5 

16.7 

101 

92.3 

41.1 

161 

147.1 

65.5 

221 

201.9 

89.9 

281 

256.7 

114.3 

42 

38.4 

17.1 

102 

93.2 

41.5 

162 

148.0 

65.9 

222 

202.8 

90.3 

282 

257.6 

114.7 

43 

39.3 

17.5 

103 

9i.l 

41.9 

163 

148.9 

66.3 

223 

203.7 

90.7 

283 

258.5 

115.1 

44 

40.2 

17.9 

104 

95.0 

42.3 

164 

149.8 

66.7 

224 

204.6 

91.1 

284 

259.4 

115.5 

45 

41.1 

18.3 

105 

95.9 

42.7 

165 

150.7 

67.1 

225 

205.5 

91.5 

285 

260.4 

115.9 

4G 

42.0 

18.7 

106 

96.8 

43.1 

166 

151.6 

67.5 

226 

208.5 

91.9 

286 

261.3 

116.3 

47 

42.9 

19.1 

107 

97.7 

43.5 

167 

152.6 

67.9 

227 

207  4 

92.3 

287 

262.2 

116  7 

48 

43  .9 

19.5 

108 

98.7 

43  9 

168 

153  5 

68.3 

228 

208.3 

92.7 

288 

263.1 

117.1 

49 

44.8 

19.9 

109 

99.6 

44.3 

169 

154.4 

68.7 

229 

209  2 

93.1 

289 

264.0 

117.5 

50 

45  7 

20.3 

110 

100.5 

44.7 

170 

155  3 

69.1 

230 

210.1 

93.5 

290 

264.9 

118.0 

51 

4(3.0 

20.7 

111 

101.4 

4571 

171 

15G.2 

Gb.  6 

231 

211.0 

94.0 

291 

265.8 

118.4 

52 

47.5 

21.2 

112 

102.3 

45.6 

172 

157.1 

70.0 

232 

211.9 

94.4 

292 

266  8 

118.8 

53 

48.4 

21.6 

113 

103.2 

46.0 

173 

158.0 

70.4 

233 

212.9 

94.8 

293 

267.7 

119.2 

54 

49.3 

22.0 

114 

104.1 

46.4 

174 

159.0 

70.8 

234 

213.8 

95.2 

294 

268.6 

119.6 

55 

50.2 

22.4 

115 

105.1 

46.8 

175 

159.9 

71.2 

235 

214.7 

95.6 

295 

269.5 

120.0 

56 

51.2 

22.8 

116 

106.0 

47.2 

176 

160.8 

71.6 

236 

215.6 

96.0 

296 

270.4 

120  4 

57 

52.1 

23.2 

117 

106.9 

47.6 

177 

161.7 

72.0 

237 

216.5 

96.4 

297 

271.3 

120  8 

53 

53.0 

23.6 

118 

107  8 

48.0 

178 

162.6 

72.4 

238 

217.4 

96.8 

298 

272.2 

121.2 

59 

53.9 

24.0 

119 

108  7 

48  4 

179 

163:5 

72.8 

239 

218.3 

97.2 

299 

273.2 

121  6 

GO 

54  8 

24.4 

120 

109.6 

48.8 

180 

164.4 

73.2 

240 

219.3 

97.6 

300 

274.1 

122.0 

[list. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Den 

Lat, 

For  GG  Degrees. 

228 

TABLE  IV. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  25  DEGREES. 

Dist, 

Lat. 

Dep 

Dist, 

Lat. 

Dep 

Dist. 

Lat.    Dep 

Dist, 

Lat. 

Dep.  i 

Dist, 

Lat. 

Dep. 

l 

00.9 

10.4 

61 

55.3 

25.8 

121 

109.751.1 

181 

164.0 

76.5 

241 

218.4 

101.9 

2 

01.8 

00.8 

62 

56  2 

26.2 

122 

110.651.6 

182 

164.9 

76.9' 

242 

219.3 

102.3 

3 

02.7 

01.3 

63 

57.1 

26.6 

123 

111.552.0 

183 

165.9 

77.3, 

243 

220.2 

102.7 

4 

03.6 

01.7 

64 

58.0 

27.0 

124 

112.452.4 

184 

166.8 

77.8 

244 

221.1 

103.1 

5 

04.5 

02.1 

65 

58.9 

27.5 

125 

113.352.8 

185 

167.7 

78.  2' 

245 

222.0 

103.5 

6 

05.4 

02.5 

66 

59.8 

27.9 

126 

114.2 

53.2 

186 

168.6 

78.6 

246 

223.0 

104  0 

7 

06.3 

03  0 

67 

60.7 

28.3 

127 

115  1 

53.7 

187 

169.5 

79.0 

247 

223.9 

104.4 

8 

07.3 

03.4 

68 

61.6 

28.7 

128 

116.0 

54.1 

188 

170.4 

79.  5i 

248 

224.8 

101.8 

9 

08.2 

03.8 

69 

62  5 

29.2 

129 

116.954.5 

189 

171.3 

79.9 

249 

225.7 

105  2 

10 

09.1 

04.2 

70 

63.4 

•29.6 

130 

117.854.9 

190 

172.2 

80.3, 

250 

226.6 

105.7 

11 

10.0J4.6 

71 

64.3 

30.0 

131 

118.7 

55.4 

191 

173.1 

80.7 

251 

227.5 

106.1 

12 

10.905.1 

72 

65.3 

30.4 

132 

119.6 

55.8 

192 

174.0 

81.1; 

252 

228.4 

106  5 

13 

11.805.5 

73 

66.2 

30  9 

133 

120.5 

56.2 

193 

174.9 

81.6 

253 

229.3 

106.9 

14 

12.705  9 

74 

67.1 

31.3 

134 

121.4 

56.6 

194 

175.8 

82.  0' 

254 

230.2 

107.3 

15 

13.606.3 

75 

68.0 

31.7 

135 

122.4 

57.1 

195 

176.7 

82.4 

255 

231.1 

107.8 

16 

14.5 

06.8 

76 

68.932.1 

136 

123.3 

57.5 

196 

177.6 

82.8 

256 

232.0 

108.2 

17 

15.4 

07.2 

77 

69.8 

32.5 

137 

124.2 

57.9 

197 

178.5 

83.3 

257 

232  9 

103.  6 

18 

16.307.6 

78 

70.733.0 

138 

125.1 

58.3 

198 

179.4 

83.  7] 

258 

233.8 

109  4 

19 

17.2 

08.0 

79 

71.633.4 

139 

126.0 

58.7 

199 

180.4 

84.1 

259 

234.7 

1C9.5 

20 

18.1 

08.5 

80 

72.533.8 

140 

126.9 

59.2 

200 

181.3 

84.  5 

260 

235.6 

101)  9, 

'21 

19.008.9 

81 

73.434.2 

141 

127.8 

59.6 

201 

182.2 

84.9, 

261 

236  .  5 

11U.3 

22 

19.909.3 

82 

74.334.7 

142 

128.7 

60.0 

202 

183.1 

85.  4! 

262 

237.5 

110.7 

23 

20.809.7 

83 

75.235.1 

143 

129.6 

60.4 

203 

184.0 

85.  8i 

263 

238.4 

111.1 

24 

21.810.1 

84 

76.135.5 

144 

130.5 

60.9 

204 

184.9 

86.  21 

264 

239.3 

111.6 

25 

22.7 

10.6 

85 

77.0 

35.9 

145 

131.4 

61.3 

205 

185.8 

86.6 

265 

240.2 

112.0 

26 

23.611.0 

86 

77.936.3 

146 

132.3 

G1.7 

206 

186.7 

87.  1! 

266 

241.1 

112.4 

27 

24.511.4 

87 

78.836.8 

147 

133.2 

62.1 

207 

187.6 

87.5! 

267 

242.0 

112.8: 

28 

25  4 

11.8 

88 

79.837.2 

148 

134.1 

62.5 

208 

188.5 

87.  9 

268 

242.9 

113.3 

29 

26.3 

12.3 

89 

80.737.6 

149 

135.0 

63.0 

209 

189.4 

88.3 

269 

243  8 

113.71 

30 

27.  If 

12.7 

90 

81.638.0 

150 

135.9 

63.4 

210 

190.3 

88.  7| 

270 

244.7 

114.  Ij 

31 

•28.1 

13.1 

91 

82.538.5 

151 

136.9 

63.8 

211 

191.2 

89.  2: 

271 

245.6 

114.5 

32 

29  013.5 

92 

83.438.9 

152 

137.8 

64.2 

212 

192.1 

89.6 

272 

246.5 

115.0 

33 

29.913.9 

93 

84.339.3 

153 

138.7 

64.7 

213 

193.0 

90.0 

273 

247.4 

115.4 

34 

30.814.4 

94 

85  239.7 

154 

139.6 

65.1 

214 

193.9 

90.4 

274 

248.3 

115.8 

35 

31.7 

14.8 

95 

86.1 

40.1 

155 

140.5 

65.5 

215 

194.9 

90.9 

275 

249.2 

116.2 

36 

32.615.2 

96 

87.040.6 

156 

141.4 

65.9 

216 

195.8 

91.3 

276 

250.1 

116.6 

37 

33.5 

15.  i; 

97 

87.941.0 

157 

142.3 

66.4 

217 

196.7 

91.1 

277 

251.0 

117.1 

38 

34.4 

16.1 

98 

88.841.4 

158 

143.2 

66.8 

218 

197.6 

92.  l' 

278 

252.0 

117.5 

39 

35.3 

16.5 

99 

89.741.8 

159 

144.1 

67.2 

219 

198.5 

92.6 

279 

252.9 

117.9 

40 

36.316.9 

100 

90.642.3 

160 

145.0 

67.6 

220 

199.4 

93.0 

280 

253.8 

118.3 

41 

37.  '217.  3 

10J 

91.542.7 

161 

145.9 

68.0 

221 

200.3 

93.4 

281 

254.7 

118.8, 

42 

38.1 

17.7 

102 

92.443.1 

162 

146.868.5 

222 

201.2 

93.  81 

282 

255.6 

119.21 

43 

39.0 

IS.  '2 

103 

93.343.5 

163 

147.768.9 

223 

202.1 

94.2' 

283 

256.5 

119.6 

44 

39.918.6 

104 

94.344.0 

164 

148.669.3 

224 

203.0 

94.7 

284 

257.4 

120.0 

45 

40.  819.0 

105 

95.244.4 

165 

149.569.7 

225 

203.9 

95.1 

285 

258.3 

120.4 

43 

41.7 

19.4 

106 

96.1 

44.8 

166 

150.4 

70.2 

228 

204.8 

95.5 

286 

259.2 

120.9 

47 

42.6 

19.9 

107 

97.045.2 

167 

151.4 

70  6 

227 

205.7 

95.9 

287 

260.1 

121.3 

48 

43.5 

20.3 

108 

97.945.6 

168 

152.3 

71.0 

228 

206.6 

96.4 

288 

261.0 

121.7 

49 

44.420.7 

109 

98.846.1 

169 

153.2 

71.4 

229 

207.5 

96.8; 

289 

261.9 

122.1 

50 

45  321.1 

110 

99.746.5 

170 

154.1 

71.8 

230 

208.5 

97.2 

290 

262.8 

122.6 

51 

46.221.6 

111 

100.646.9 

171 

155.0 

72.3 

231 

209.4 

97.6 

291 

263.7 

123.0 

52 

47.1 

22.0 

112 

101.547.3 

172 

155.9 

72.7 

232 

210.3 

98.0 

292 

264.6 

123.4 

53 

48.0 

22.4 

113 

102.447.8 

173 

156.8 

73.1 

233 

211.2 

98.5; 

293 

265.5 

123.8 

54 

48.922.8 

114 

103.348.2 

174 

157.7 

73.5 

234 

212.1 

98.9 

.294 

266.5 

124.2 

55 

49.823.2 

115 

104.248.6 

175 

158.6 

74.0 

235 

213.0 

99.3 

295 

267.4 

124.7 

56 

50.823.7 

116 

105.1 

49.0 

176 

159.5 

74.4 

236 

213.9 

99.7 

296 

268.3 

125.1 

57 

51.724.1 

117 

106.049.4 

177 

160.4 

74.8 

237 

214.8 

100.2 

297 

269.2 

125.5 

53 

52.6 

24.5 

118 

106.949  9 

178 

161.3 

75.2 

238 

215.7 

100.6 

298 

270.1 

125.9 

59 

53.5 

24.9 

119 

107.950.3 

179 

162.2 

75.6 

239 

216.6 

101.0 

299 

271.0 

126.4 

60 

54.4 

25.4 

120 

108.8 

50.7 

180 

163.1 

76.1 

240 

217.5 

101.4 

,  ,  „  ' 

300 

271.9 

126.8 

Dist. 

Dep 

Lat.  'Dist. 

Dep. 

Lat. 

Dist.  Dep." 

Lat, 

Dist. 

Dep. 

Lat.  iDist, 

Dep. 

Lat, 

For  65  Degrees. 

TABLE  IV.                                           229 

DIFFERENCE  OF  LATITUDE  ASD  DEPARTURE  FOR  26  DEGREES. 

[list. 

Lat. 

Dep 

Dist. 

Lat. 

Dep  Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

30.9 

00.4 

61 

54.8 

26.7 

121 

108.8 

53.0 

181 

162.7 

79.3 

241 

216.  G 

105.6 

2 

01.8 

00.9 

62 

55.7 

27.2 

122 

109.7 

53.5 

182 

163.6 

79.8 

242 

217.5 

106.1 

3 

02.7 

01.3 

63 

56.0 

27.6 

123 

110.  G 

53.9 

183 

164.5 

80.2 

243 

218.4 

106.5 

4 

03.  G 

01.8 

64 

57.5 

28.1 

124 

111.5 

54.4 

184 

165.4 

80.7 

244 

219.3 

107.0 

5 

04.5 

02.2 

65 

58.4 

28.5 

125 

112.3 

54.8 

185 

166.3 

81.1 

245 

220.2 

107.4 

6 

05.4 

02.6 

66 

59.3 

28.9 

126 

113.2 

55.2 

186 

167.2 

81.5 

246 

221.1 

107.8 

7 

03.3 

03.1 

67 

60.2 

29  4 

127 

114.1 

55.7 

187 

168.1 

82.0 

247 

222.0 

108.3 

8 

07.2 

03.5 

68 

61.1 

29.8 

128 

115.0 

56.1 

188 

169.0 

82.4 

248 

222.9 

108.7 

9 

08.1 

03.9 

G9 

62.0 

30.2 

129 

115.9 

56.5 

189 

169.9 

82.9 

249 

223.8 

109.2 

10 

09.0 

04.4 

70 

62.9 

30.7 

130 

116.8 

57.0 

190 

170.8 

83.3 

250 

224.7 

109  6 

11 

09  9 

04.8 

71 

G3.6 

31.  Ill  131 

117.7 

•37.4 

191 

171  7 

83.7 

251 

225.6 

110.0 

12 

10.8 

05.3 

72 

64.7 

31.  G 

132 

118.6 

57.9 

192 

172.6 

84.2 

252 

226.5 

110.5 

13 

11.7 

05.7 

73 

65.6 

32.0 

133 

119.  C 

58.3 

193 

173.5 

84.6 

253 

227.4 

110.9 

14 

12.0 

06.1 

74 

66.5 

32.4 

134 

120.4 

58.7 

194 

174.4 

85  0 

254 

228.3 

111.3 

15 

13.5 

06.6 

75 

67.4 

32.9 

135 

121.3 

59.2 

195 

175.3 

85.5 

255 

229.2 

111.8 

1C 

14.4 

07.0 

76 

68  3 

33.3 

136 

122.2 

59.6 

196 

176.2 

85.9 

256 

230.1 

112.2 

17 

15  3 

07.5 

77 

69.2 

33.8 

137 

123.1 

60.1 

197 

177.1 

86.4 

257 

231.0 

112.7 

18 

16.2 

07.9 

78 

70.1 

34.2 

138 

124  0 

60.5 

198 

178.0 

86.8 

258 

231.9 

113.1 

19 

17  1 

08.3 

79 

71.0 

34.  G 

139 

124.9 

60  9 

199 

178.9 

87.2 

259 

232.8 

113.5 

20 

18.0 

08.8 

80 

71.9 

35.1 

140 

125.8 

61.4 

200 

179.8 

87.7 

260 

233.7 

114.0 

21 

18.9 

09.2 

81 

72.6 

35.5 

141 

126.7 

61.8 

201 

180.7 

88.1 

261 

234.6 

114.4 

22 

19  8 

09  G 

82 

73.7 

35.9 

142 

127.6 

62.2 

202 

181.6 

88.6 

262 

235.5 

114.9 

23 

20.7 

10.1 

83 

74.6 

36.4 

143 

128.5 

62.7 

203 

182.5 

89.0 

263 

236.4 

115.3 

24 

21.  C 

10.5 

84 

75.5 

36.8 

144 

129.4 

63.1 

204 

183.4 

89.4 

264 

237.3 

115.7 

25 

22.  C 

11.0 

85 

76.4 

37.3 

145 

130.3 

63.6 

205 

184.3 

89.9 

265 

238.2 

116.2 

26 

13.4 

11.4 

86 

77.3 

37.7 

146 

131.2 

64.0 

206 

185.2 

90.3 

266 

239.1 

116.6 

27 

24.3 

11.8 

87 

78.2 

38.1 

147 

132.1 

64.4 

207 

186.1 

90.7 

267 

240.0 

117.0 

28 

25.2 

12.3 

88 

79.1 

38.6 

148 

133.0 

64.9 

208 

186.9 

91.2 

268 

240.9 

117  5 

29 

:e.i 

12.7 

89 

80.0 

39.0 

149 

133.9 

65.3 

209 

187.8 

91.6 

269 

241.8 

117.9 

30 

27.0 

13.2 

90 

80.9 

39  5 

150 

134.8 

65.8 

210 

188.7 

92.1 

270 

242.7 

118.4 

31 

27.9 

13.6 

91 

81.8 

39.9 

151 

135.7 

66.2 

211 

189.6 

92.5 

271 

243.6 

118.8 

32 

28.8 

14.0 

92 

82.7 

40.3 

152 

136.6 

66.6 

212 

190.5 

92.9 

272 

244.5 

119.2 

3:3 

:9.7 

14.5 

93 

83.  C 

40.8 

153 

137.5 

67.1 

213 

191.4 

93.4 

273 

245.4 

119.7 

34 

30.0 

14.9 

94 

84.5 

41.2 

154 

138.4 

67.5 

214 

192.3 

93.8 

274 

246.3 

120.1 

35 

31.5 

15.3 

95 

85.4 

41.  C 

155 

139.3 

67.9 

215 

193.2 

94.2 

275 

247.2 

120.6 

36 

32.4 

15.8 

96 

86.3 

42.1 

150 

140.2 

68  4 

216 

194.1 

94.7 

276 

248.1 

121.0 

37 

33.3 

16.2 

97 

.  87.2 

42.5 

157 

1  11  .  1 

(?O     O 
DO.O 

217 

195.0 

95.1 

277 

249.0 

121.4 

33 

34.2 

16.7 

98 

88.1 

43.  C 

158 

142.0 

69.3 

218 

195.  9 

95.6 

278 

249.9 

121.9 

39 

35.1 

17.1 

99 

89.0 

43.4 

159 

142.9 

69.7 

219 

196.8 

96.0 

279 

250.8 

122.3 

40 

36  0 

17.5 

100 

89.9 

43.8 

1GO 

143.8 

70.1 

220 

197.7 

96.4 

280 

251.7 

122.7 

TT 

30.  t> 

18.0 

101 

90.  b 

44.3 

1G1 

144.7 

71.  (5 

221 

198.  G 

96.9 

281 

252.6 

123.2 

42 

37.7 

18  4 

102 

91.7 

44.7 

162 

145.6 

71.0 

222 

199.5 

97.3 

282 

253.5 

123.6 

43 

33.  C 

18.8 

103 

92.6 

45.2 

163 

146.5 

71.5 

223 

200.4 

97.8 

283 

254.4 

124.1 

44 

39.5 

19.3 

104 

93.5 

45.  G 

1G4 

147.4 

71.9 

224 

201.3 

98.2 

284 

255.3 

124.5 

45 

iO.4 

19.7 

105 

94.4 

46.0 

165 

148.3 

72.3 

225 

202.2 

98  G 

285 

256.2 

124.9 

46 

41.3 

20.2 

100 

95.3 

46.5 

1GG 

149.2 

72.8 

226 

203.1 

99.1 

286 

257.1 

125.4 

47 

42.2 

20.6 

107 

96.2 

46.9 

167 

150.1 

73.2 

227 

204.0 

99.5 

287 

258.0 

125.8 

48 

13.1 

21.0 

108 

97.1 

47.3 

168 

151.0 

73  6 

228 

204.9 

99.9 

288 

258.9 

126.3 

49 

44.0 

21.5 

109 

93.0 

47.8 

169 

151.9 

74.1 

229 

205.8 

100.4 

289 

259.8 

126.7 

50 

44.9 

21.9 

110 

93.9 

48.2 

170 

152.8 

74  5 

230 

206.7 

100.8 

290 

260.7 

127.1 

51 

45.8 

22.4 

111 

99.8 

48.7 

171 

153.7 

75.0 

231 

207.  G 

101.3 

291 

2G1.5 

127.6 

52 

46.7 

22.8 

112 

100.7 

49.1 

172 

154.6 

75.4 

232 

208.5 

101.7 

292 

262.4 

128.0 

53 

47.  C 

23.2 

113 

101.  G 

49.5 

173 

155.5 

75.8 

233 

209.4 

102.1 

293 

263.3 

128.4 

61 

48.5 

23.7 

114 

102.5 

50.0 

174 

156.4 

76.3 

234 

210.3 

102.6 

294 

264.2 

128.9 

55 

19.4 

24  1 

115 

103.4 

50.4 

175 

157.3 

76.7 

235 

211.2 

103.0 

295 

265.1 

129.3 

56 

50.3 

24.5 

116 

104.3 

50.9 

176 

158.277.2 

236 

212.1 

103.5 

296 

266.0 

129.8 

57 

31  2 

25.0 

117 

105.2 

51.3 

177 

159.1 

77.6 

237 

213.0 

103.9 

297 

266.9 

130.2 

58 

52.1 

25.4 

118 

10G.1 

51.7 

178 

160.  0 

78.0 

238 

213.9 

104.3 

298 

267.8 

130.  G 

59 

53.0 

25.9 

119 

107.0 

52.2 

179 

1G0.9 

78.5 

239 

214.8 

104.8 

299 

268.7 

131.1 

GO 

53.9 

26.3 

120 

107.9 

52.  G 

180 

1G1.8 

78.9 

240 

215.7 

105.2 

300 

269.6 

131.5 

list, 

Dep 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

LatJDist. 

Dep. 

Lat. 

Dist. 

Dep. 

Liit. 

For  64  Degrees. 

230                                          TABLE  IV. 

DIFFERENCE  OF   LATITUDE  AND 

DEPARTURE  FOR  27  DEGREES. 

[list. 

Lat. 

Dep 

Hist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.5 

61 

54.4 

27.7 

121 

107.8 

54.9 

181 

161.3 

82.2 

241 

214.7 

109.4 

2 

01.8 

00.9 

62 

55.2 

•28.1 

122 

108.755.4 

182 

162.2 

82.6 

242 

215.  C 

109.9 

3 

02.7 

01.4 

63 

56  1 

28.6 

123 

109.655.8 

183 

163.] 

83.1 

243 

216.5 

110.3 

4 

03.6 

01.8 

64 

57.029.1 

124 

110.556  3 

184 

163.9 

83.5 

244 

217.4 

110.8 

5 

04.5 

02.3 

65 

57.9 

29.5 

125 

111.456.7 

185 

164.8 

84.0 

245 

218.3 

111.2 

6 

05.3 

02.7 

66 

58.8 

30.0 

126 

112.357.2 

186 

165.7 

84.4 

24G 

219.2 

111.7 

7 

)6.2 

03.2 

67 

59.7 

30.4 

127 

113.257.7 

187 

166.6 

84.9 

247 

220.1 

112.1 

8 

07.1 

03.6 

68 

60.6 

30.9 

128 

114.058.1 

188 

167.5 

85.4 

248 

221.0 

112.6 

9 

08  0 

04.1 

69 

61.5 

31.3 

129 

114.958.6 

189 

168.4 

85.8 

249 

221.9 

113.0 

10 

08.9 

04.5 

70 

62.431.8 

130 

115.859.0 

190 

169.3 

86.3 

250 

222.8 

113.5 

11 

09.8 

05.0 

71 

63.3 

32.2 

131 

116.759.5 

191 

170.2 

86.7 

251 

223.6 

114.0 

12 

10.7 

05.4 

72 

64.2 

32.7 

132 

117.659.9 

192 

171.1 

87.2 

252 

224.5 

114.4 

13 

11  6 

05.9 

73 

65.0 

33.1 

133 

118.560.4 

193 

172.0 

87.6 

253 

225.4 

114.9 

14 

12.5 

06.4 

74 

65.9 

33.6 

134 

119.460.8 

194 

172.9 

88  1 

254 

226.3 

115.3 

15 

13.4 

06.8 

75 

66.8 

34.0 

135 

120.3 

61.3 

195 

173.7 

88.5 

255 

227.2 

115.8 

16 

14.3 

07.3 

76 

67.7 

34.5 

136 

121.2 

61.7 

196 

174.6 

89.0 

256 

228.1 

116.2 

17 

15.1 

J7.7 

77 

68.6 

35.0 

137 

122.162.2 

19? 

175.5 

89.4 

257 

229.0 

116.7 

18 

16.0 

08.2 

78 

69.5 

35.4 

138 

123.062.7 

198 

176.4 

89.9 

258 

229.9 

117.  1! 

19 

16.9 

08.  6 

79 

70  4 

35.9 

139 

123.863.1 

199 

177.3 

90.3 

259 

230.8 

117.6 

20 

17.8 

09.1 

80 

71  3 

36.3 

140 

124.763.6 

200 

178.2 

90.8    260 

231.7 

118.0 

21 

18.7 

09.5 

81 

72.2 

36.8 

14i 

125.  U  64.0 

201 

179.1 

91.3 

26  1 

232.6 

118.51 

22 

19.6 

10.0 

82 

73.1 

37.2 

142 

126.564.5 

202 

180.0 

91.7 

262 

233.4 

118.9 

23 

20.5 

10.4 

83 

74.0 

37.7 

143 

127.464.9 

203 

180.9 

92.2 

263 

234.3 

119.4 

24 

21.4 

10.9 

84 

74.8 

38.1 

144 

128.3 

65.4 

204 

181.8 

92.6 

264 

235.2 

119.9 

25 

22.3 

11.3 

85 

75.7 

38.6 

145 

129.2 

65.8 

205 

182.7 

93.1 

265 

236.1 

120.3 

2G 

23.2 

11.8 

86 

76.6 

39.0 

146 

130  1 

66.3 

206 

183.5 

93.5 

266 

237.0 

120.8 

27 

24.1 

12.3 

87 

77.5 

J9.5 

147 

131.066.7 

207 

184.4 

94.0 

267 

237.9 

121.2 

28 

24  C 

12.7 

88 

78.4 

40.0 

148 

131.967.2 

208 

185.3 

94.4 

268 

238.8 

121.7 

29 

25.8 

13.2 

89 

79.3 

40.4 

149 

132.867.6 

209 

186.2 

94.9 

269 

239.7 

122.1 

30 

26.7 

13.6 

90 

80.2 

40.9 

150 

133.7|G8.1 

210 

187.1 

95.3 

270 

240.  G 

122.6 

31 

27.  G 

14.1 

91 

81.1 

41.3 

151 

134.568.6 

211 

188.0 

95.8 

271 

241.5 

123.0 

32 

28.5 

14.5 

92 

82.0 

41.8 

152 

135.469.0 

212 

188.9 

96.2 

272 

242.4 

123.5 

33 

.9.4 

15.0 

93 

82.9 

42.2 

153 

136.369.5 

213 

189.8 

96.7 

273 

243.2 

123.9 

3i 

30.3 

15.4 

91 

83.8 

42.7 

154 

137.269.9 

214 

190  7 

97.2 

274 

244.1 

124.4 

35 

31.2 

15.9 

95 

84.6 

43.1 

155 

138.1 

70.4 

215 

191  6 

97.6 

275 

245.0 

124.8 

36 

32.1 

16.3 

96 

85.5 

43.6 

156 

133.070.8 

216 

192.5 

98.1 

276 

245.9 

125.3 

37 

33.0 

16.8 

97 

86.4 

44.0 

157 

139.971.3 

217 

193.3 

98.5 

277 

246.8 

125.8 

38 

33.0 

17.3 

98 

87.3 

44.5 

158 

140.871.7 

218 

194.2 

99.0 

278 

247.7 

126.2 

39 

34.7 

17.7 

99 

88.2 

44.9 

159 

141.7 

72.2 

219 

195.1 

99.4 

279 

248.6 

12G.7 

40 

35.6 

18.2 

100 

89.1 

45.4 

160 

142.6 

72.6 

220 

196.0 

99.9 

280 

249.5 

127.1 

41 

3(3.5 

18.6 

101 

90.0 

45.9 

161 

143.5 

73  J 

221 

196  9 

100.3 

281 

250.4 

127.6 

42 

37.4 

19.1 

102 

90.9 

46.3 

162 

144.3 

73.5 

222 

197.8 

100.8 

282 

251.3 

128.0 

43 

38.3 

19.5 

103 

91.8 

46  8 

163 

145.2 

74.0 

223 

198.7 

101.2 

283 

252.2 

128.5 

44 

39.2 

20.0 

104 

92  7 

47.2 

164 

146  1 

74.5 

224 

199.6 

101.7 

284 

253.0 

128.9 

45 

40.1 

20.4 

105 

93.6 

47.7 

165 

147.074.9 

225 

200.5 

102.1 

285 

253.9 

129.4 

46 

41.0 

20.9 

106 

94.448  1 

166 

147  9 

75.4 

226 

201.4 

102.6 

286 

254.8 

129.8 

47 

41.9 

21.3 

107 

95.348.6 

167 

148.8 

75.8 

227 

202.3 

103.1 

287 

255.7 

130.3 

48 

42.  b 

21.8 

108 

96.2 

49.0 

168 

149.7 

76.3 

228 

203.1 

103.5 

288 

256.6 

130.7 

49 

43.7 

22.2 

109 

97.1 

49.5 

169 

150.676.7 

229 

204.0 

104.0 

289 

257.5 

131.2 

50 

14.6 

22.7 

110 

98.0 

49.9 

170 

151.5 

77.  £ 

230 

204.9 

104.4 

290 

258.4 

131.7 

51 

45.4 

23.2 

111 

93.9 

50.4 

171 

152.4 

77.6 

231 

205.8 

104.9 

291 

259.3 

132.1 

52 

46.3 

23.6 

112 

99.8 

50.8 

172 

153.378.1 

232 

206.7 

105.3 

292 

260.2 

132.6 

53 

47.2 

24.1 

113 

100.7 

51.3 

173 

154.1 

78.5 

233 

207.6 

105.8 

293 

261.1 

133.0 

54 

48.1 

24.5 

114 

101.6 

51.8 

174 

155.079.0 

234 

208.5 

106.2 

294 

262.0 

133.5 

55 

49.0 

25.0 

115 

102.5 

52.2 

175 

155.979.4 

235 

209.4 

106.7 

295 

262.8 

133.9 

56 

49.9 

25.4 

116 

103.4 

52.7 

176 

156.879.9 

236 

210.3 

107.1 

296 

263.7 

134.4 

57 

50.8 

25.9 

117 

104.253.1 

)77 

157.780.4 

237 

211.2 

107.6 

297 

264.6 

134.8 

58 

51.7 

26.3 

118 

105.153.6 

178 

158.680.8 

238 

212.1 

108.0 

298 

265.5 

135.3' 

59 

52.6 

26.8 

119 

106.054.0 

179 

159.581.3 

239 

213.0 

108.5 

299 

266.4 

135.7 

60 

53.5 

27.2 

120 

106.9 

54.5 

180 

160.4 

81.7 

240 

213.8 

109.0 

300 

267.3 

136.2 

Hist. 

Dcp 

Lat.  Dist. 

Den. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  63  Degrees. 

TABLE  IV.                                           231 

DIFFERENCE  OF    LATITUDE    AND  DEPARTURE    FOR  28  DEGREES. 

DistJLat. 

Dep  Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.5 

61 

53.9 

28.6 

121 

106.8 

56.8 

181 

159.8 

85.0 

241 

212.8 

113.1 

2 

01.8 

00.9 

62 

54.729.1 

122 

107.7 

57.3 

182 

160.7 

85.4 

242 

213.7 

113.6 

3 

02.  G 

01.4 

63 

55.629.6 

123 

108.6 

57.7 

183 

161.6 

85.9 

243 

214.6 

114.1 

4 

03.5 

01.9 

64 

56.530.0 

124 

109.5 

58.2 

184 

162.5 

86.4 

244 

215.4 

114.6 

5 

04.4 

02.3 

65 

57.430.5 

125 

110.4 

58.7 

185 

163.3 

86.9 

245 

216.3 

115.0 

6 

05.3 

02.8 

66 

58.331.0 

126 

111.3 

59.2 

186 

164.2 

87.3 

246 

217.2 

115.5 

7 

06.2 

03.3 

67 

59.231.5 

127 

112.1 

59.  G 

187 

165.1 

87.8 

247 

218.1 

116.0 

8 

07.1 

03.8 

68 

60.031.9 

128 

113.0 

60.1 

388 

166.0 

88.3 

248 

219.0 

116.4 

9 

07.9 

04.2 

69 

60.932.4 

129 

113.9 

60.6 

189 

166.9 

88.7 

249 

219.9 

116.9 

10 

08.8 

04.7 

70 

61.832.9 

130 

114.8 

61.0 

190 

167.8 

89.2 

250 

220.7 

117.4 

11 

09.7 

05.2 

71 

62.733.3 

131 

115.7 

61.5 

191 

168.6 

89.7 

251 

221.G 

117.9 

12 

10.  G 

05.  G 

72 

63.633.8 

132 

116.5 

62.0 

192 

169.5 

90.1 

252 

222.5 

118.3 

13 

11.5 

06.1 

73 

64.534.3 

133 

117  4 

62.4 

193 

170.4 

90.6 

253 

223.4 

118.8 

14 

12  4 

06.6 

74 

65.334.7 

134 

118.3 

62.9 

194 

171  3 

91.1 

254 

224.3 

119.2 

15 

13.2 

07.0 

75 

66.235.2 

135 

119.2 

G3.4 

195 

172.2 

91.5 

255 

225.2 

119.7 

1G 

14.1 

07.5 

76 

67.135.7, 

136 

120.1 

63.8 

196 

173.1 

92.0 

256 

226.0 

120.2 

17 

15.0 

08.0 

77 

63.036.1 

137 

121.0 

64.3 

197 

173.9 

92.5 

257 

226.9 

120.7 

18 

15.9 

08.  5 

78 

68.936.6 

138 

121.8 

64.8 

198 

174.8 

93.0 

258 

227.8 

121.1 

19 

1G.8 

08.9 

79 

69.837.1 

139 

122.7 

65.3 

199 

175.7 

93.4 

259 

228.7 

121.6 

20 

17.7 

09.4 

80 

70.637.6 

140 

123.6 

G5.7 

200 

176.6 

93.9 

2GO 

229.  G 

122.1 

21  J'8.5 

09.9 

81 

71.538.0 

141 

124.5 

GG.2 

201 

177.5 

94.4 

261 

230.4 

122.5 

22    19.4 

10.3 

82 

72.438.5 

142 

125.4 

CG  7 

202 

178.4 

94.8 

262 

231.3 

123.0 

23 

20.3 

10.8 

83 

73.339.0 

143 

126.3 

(37.1 

203 

179.2 

95.3 

263 

232.2 

123.5 

24 

21.2 

11.3 

84 

74.2 

39.4 

144 

127.1 

67.6 

204 

180.1 

95.8 

264 

233.1 

123.9 

25 

22.1 

11.7 

85 

75.1 

39.9 

145 

128.0 

68.1 

205 

181.0 

96  2 

265 

234.0 

124.4 

26 

23.0 

12.2 

86 

75.9 

40.4 

14G 

128.9 

68.5 

206 

181.9 

96.7 

266 

234.9 

124.9 

27 

23.8 

12.7 

87 

76.8 

40.8; 

147 

129.8 

69.0 

207 

182.8 

97.2 

267 

235  .7 

125.3 

28 

21.7 

13.1 

88 

77.7 

41.3 

148 

130.7 

69.5 

208 

183.7 

97.7 

268 

236.6 

125.8' 

29 

25.  G 

13.6 

89 

78.6 

41.8 

149 

131.6 

70.0 

209 

184.5 

98.1 

269 

237.5 

126.3 

30 

2G.5 

14.1 

90 

79.542.3i 

150 

132.470.4 

210 

185.4 

98.6 

270 

238.4 

126.8 

31 

27.4 

14.6 

91 

80.3 

42.7 

151 

133.3 

70.9 

211 

18G.3 

99.1 

27J 

239.3 

127.2 

32 

28.3 

15.0 

92 

81.2 

43.2 

152 

134.2 

71.4 

212 

187.2 

99.5 

272 

240.2 

127.7 

33 

29.1 

15.5 

93 

82.1 

43.7 

153 

135.1 

71.8 

213 

188.1 

100.0 

273 

241.0 

128.2 

34 

30.0 

16.0 

94 

83.0 

44.1 

154 

136.0 

72.3 

214 

189.0 

100.5 

274 

241.9 

128.6 

35 

30.9 

16.4 

95 

83.944.6! 

155 

136.9 

72  8 

215 

189.8 

100.9 

275 

242.8 

129.1 

36 

31.8 

16.9 

96 

84.845.1 

156 

137.7 

73.2 

216 

190.7 

101.4 

276 

243.7 

129.  G 

37 

32.7 

17.4 

97 

85.645.5 

157 

138.  G 

73.7 

217 

191.6 

101.9 

277 

244.6 

130.0 

38 

33.6 

17.8 

98 

86.546.0 

158 

139.5 

74.21  218 

192.5 

102.3 

278 

245.5 

130.5 

39 

34.4 

18.3 

99 

87.446.5 

159 

140.4 

74.6 

219 

193.4 

102.8 

279 

246.3 

131  0 

40 

3>.3 

18.8 

100 

88.346.9 

160 

111.375.1 

220 

194.2 

103.3 

280 

247.2 

131.5 

41 

36.2 

19.fc 

101 

69.247.4 

101 

142.  2  75.  G 

221 

195.1 

103.8 

281 

248.1 

131.9 

42 

.i7.1 

19.7 

102 

90.147.9 

162 

143.0 

76.1 

222 

196.0 

104.2 

282 

249.0 

132.4 

43 

38.0 

20.2 

103 

90.948.4 

1G3 

143.9 

76.5 

223 

196.9 

104.7 

283 

249.9 

132.9 

44 

33.8 

20.7 

104 

91.848.8 

1G4 

144.8 

77.0 

224 

197.8 

105.2 

284 

250.8 

133.3 

45 

39.7 

21.1 

105 

92.749.3 

165 

145.7 

77.5 

225 

198.7 

105.6 

285 

251.  G 

133.8 

4G 

40.6 

21  .-G 

106 

93.G49.8 

166 

146.6 

77.9 

226 

199.5 

106.1 

286 

252.5 

134.3 

47 

41.6 

22.1 

107 

94.550.2 

167 

147.5 

78.4 

227 

200.4 

10G.6 

287 

253.4 

134.7 

48 

42.4 

22.5 

108 

95.4 

50.7 

168 

148.3 

78.9 

228 

201.3 

107.0 

288 

254.3 

135.2 

49 

43.3 

23.0 

109 

96.251.2 

169 

149.2 

79.3 

229 

202.2 

107.5 

289 

255.2 

135.7 

50 

44.1 

23.5 

110 

97.1 

51.6 

170 

150.1 

79.8 

230 

203.1 

108.0 

290 

256.1 

136.1 

51 

15.  U 

23.9 

111 

98.052.1 

171 

151.0 

80.3 

231 

204.0 

1U8.4 

291 

256.9 

13G.G 

52 

45.9 

24.4 

112 

98.9 

52.  C 

172 

151.9 

80.7 

232 

204.8 

108.9 

292 

257.8 

137.1 

53 

46.8 

24.9 

113 

99.8 

53.1 

173 

152.7 

HI.  2 

233 

205.7 

109.4 

293 

258.7 

137.6 

54 

47.7 

25.4 

114 

100.7 

53.5 

174 

153.6 

81.7 

234 

206.6 

109.9 

294 

259.6 

138.0 

55 

48.6 

25.8 

115 

.101.5 

54.0 

175 

154.5 

82.2 

235 

207.5 

110.3 

295 

260.5 

138.5 

5G 

19.4 

26.3 

11G 

102.4 

54.6 

176 

155.4 

82.6 

236 

208.4 

110.8 

296 

261.3 

139.0 

57 

50.3 

26.8 

117 

103.3 

54.9 

177 

156.3 

83.1 

237 

209.3 

111.3 

297 

262.2 

139.4 

58 

51.2 

27.2 

118 

104.2 

55.4 

178 

157.2 

83.6 

238 

210.1 

111.7 

298 

263.1 

139.9 

59 

52.1 

27.7 

119 

105.1 

55.9 

179 

158.0 

84.0 

239 

211.0 

112.2 

299 

264.0 

140.4 

GO 

53.0 

28.2 

120 

106.0 

56.3 

180 

158.9 

84.5 

240 

211.9 

112.7 

300 

264.9 

140.8 

Dixt.  Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

l.at. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  G2  Degrees. 

232                                          TABLE  IV. 

DIFFERENCE    OF   LATITUDE  AND  DEPARTURE  FOR  29    DEGREES. 

Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.5 

61 

53.4 

29.6 

121 

105.8 

58.7 

181 

158.3 

87.8 

241 

210.8 

116.8 

2 

01.7 

01.0 

62 

54.2 

30.1 

122 

106.7 

59.1 

182 

159.2 

88.2 

242 

211.7 

117.3 

3 

02.6 

01.5 

63 

55.1 

30.5 

123 

107.6 

59.6 

183 

160.1 

88.7 

243 

212.5 

117.8 

4 

03.5 

01.9 

64 

56.0 

31.0 

124 

108.5 

60.1 

184 

160.9 

89.2 

244 

213.4 

118.3 

5 

01.4 

02.4 

65 

56.9 

31.5 

125 

109.3 

60.6 

185 

161.8 

89.7 

245 

214.3 

118  8 

6 

05.2 

02.9 

66 

57.7 

32.0 

126 

110.2 

61.1 

186 

162.7 

90.2 

246 

2l5.L> 

119.3 

7 

06.1 

03.4 

67 

58.6 

32.5 

127 

111.1 

61.6 

187 

163.6 

90.7 

247 

216.0 

119.7 

8 

07.0 

03.9 

68 

59.5 

33.0 

128 

112.0 

62.1 

188 

164.4 

91.1 

248 

216.9 

120.2 

9 

07.9 

04.4 

69 

60.3 

33.5 

129 

112.8 

62.5 

189 

165.3 

91.6 

249 

217.8 

120.7 

10 

08.7 

04.8 

70 

61.2 

33.9 

130 

113.7 

63.0 

190 

166.2 

92.1 

250 

218.7 

121.2 

11 

09.6 

05.3 

71 

62.1 

34.4 

131 

114  6 

63.5 

191 

167.1 

92.6 

251 

219.5 

121.7 

W 

10.5 

05.8 

72 

63.0 

34.9 

132 

115.4 

64.0 

192 

167.9 

93.1 

252 

220.4 

122.2 

13 

11.4 

06.3 

73 

63.8 

35.4 

133 

116.3 

64.5 

193 

168.8 

93.6 

253 

221.3 

122.7 

14 

12.2 

06.8 

74 

64.7 

35.9 

134 

117.2 

65.0 

194 

169.7 

94.1 

254 

222.2 

123J 

15 

13.1 

07.3 

75 

65.6 

36.4 

135 

118.1 

65.4 

195 

170.6 

94.5 

255 

223  0 

123.6 

16 

14.0 

07.8 

76 

66.5 

36.8 

136 

118.9 

65.9 

196 

171.4 

95.0 

256 

223.9 

124.1 

17 

14.9 

08.2 

77     67.3 

37.3 

137 

119.8 

66.4 

197 

172.3 

95.5 

257 

224.8 

124.6 

18 

15.7 

08.7 

78     68.2 

37.8 

138 

120.7 

66.9 

198 

173.2 

96.0 

258 

225.7 

125.1 

19 

16.6 

09.2 

79     69.1 

38.3 

139 

121.6 

67.4 

199 

174.0 

96.5 

259 

226.5 

125  6 

20 

17.5 

09.7 

80     70.0 

38.8 

140 

122.4 

67.9 

200 

174.9 

97.0 

260 

227.4 

126.1 

21 

18.4 

10.2 

81 

70.8 

39.3 

141 

123.3 

68.4 

201 

175.8 

97.4 

261 

228.3 

126.5 

22 

19  2 

10.7 

82 

71.7 

39.8 

142 

124.2 

68.8 

202 

176.7 

97.9 

262 

229.2 

127.0 

23 

20.1 

11.2 

83 

72.6 

40.2 

143 

125.1 

69.3 

203 

177.5 

98.4 

263 

230.0 

127.5 

24 

21.0 

11.6 

84 

73.5 

40.7 

144 

125.9 

69.8 

204 

178.4 

98.9 

264 

230.9 

128.0 

25 

21.9 

12.1 

85 

74.3 

41.2 

145 

126.8 

70.3 

205 

179.3 

99.4 

265 

231.8 

128.5 

26 

22.7 

12.6 

86 

75.2 

41.7 

146 

127.7 

70.8 

206 

180.2 

99.9 

266 

232.6 

129.0 

27 

23.6 

13.1 

87 

76.1 

42.2 

147 

128.6 

71.3 

207 

181.0 

100.4 

267 

233.5 

129.4 

28 

24.5 

13.6 

88 

77.0 

42.7 

148 

129.4 

71.8 

208 

181.9 

100.8 

268 

234.4 

129  9 

29 

25.4 

14.1 

89     77.8 

43.1 

149 

130.3 

72.2 

209 

182.8 

101.3 

269 

235.3 

130.4 

30 

26.2 

14.5 

90     78.7 

43.6 

150 

131.2 

72.7 

210 

183.7 

101.8 

270 

236.1 

130.9 

31 

27.1 

15.0 

91 

79.6 

44.1 

151 

132.1 

73.2 

211 

184.5 

102.3 

271 

237.0 

131.4 

32 

28.0 

15.5 

92 

80.5 

44.6 

152 

132.9 

73.7 

212 

185.4 

102.8 

272 

237.9 

131.9 

33 

28.9 

16.0 

93 

81.3 

45.1 

153 

133.8 

74.2 

213 

186.3 

103.3 

273 

238.8 

132  4 

34 

29.7 

16.5 

94 

82.2 

45.6 

154 

134.7 

74.7 

214 

187.2 

103.7 

274 

239.6 

132.8 

35 

30.6 

17.0 

95 

83.1 

46.1 

155 

135.6 

75.1 

215 

188.0 

104.2 

275 

240.5 

133.3 

36 

31.5 

17.5 

96 

84.0 

46.5 

156 

136.4 

75.6 

216 

188.9 

104.7 

276 

241.4 

133.8 

37 

32.4 

17.9 

97 

84.8 

47.0 

157 

137.3 

76  1 

217 

189.8 

105.2 

277 

242.3 

134  3 

38 

33.2 

18.4 

98 

85.7 

47.5 

158 

138.2 

76.6 

218 

190.7 

105.7 

278 

243.1 

134.8 

39 

34.1 

18.9 

99 

86.6 

48.0 

159 

139.1 

77.1 

219 

191.5 

106.2 

279 

244.0 

135.3 

40 

35.0 

19.4 

100 

87.5 

48.5 

160 

139.9 

77.6 

220 

192.4 

106.7 

280 

244.9 

135.7 

41 

35.9 

19.9 

101 

88.3 

49.0 

161 

140.8 

78.1 

221 

193.3 

107.1 

281 

245.8 

136.2 

42 

36.7 

20.4 

102 

89.2 

49.5 

162 

141.7 

78.5 

222 

194.2 

107.6 

282 

246.6 

136.7 

43 

37.6 

20  8 

103 

90.1 

49.9 

163 

142.6 

79.0 

223 

195.0 

108.1 

283 

247.5 

137.2 

44 

38.5 

21.3 

104 

91.0 

50.4 

164 

143.4 

79.5 

224 

195.9 

108.5 

284 

248.4 

137.7 

45 

39.4 

21.8 

105 

91.8 

50.9 

165 

144.3 

80.0 

225 

196.8 

109.1 

285 

249.3 

138.2 

40 

40.2 

22.3 

106 

92.7 

51.4 

166 

145.2 

80  5 

226 

197.7 

109.6 

286 

250.1 

138.7 

47 

41.1 

22.8 

107 

93.6 

51.9 

167 

146  1 

81.0 

227 

198.5 

110.1 

287 

251.0 

139.1 

48 

42.0 

23.3 

108 

94.5 

52.4 

168 

146.9 

81.4 

228 

199.4 

110.5 

288 

251.9 

139.6 

49 

42.9 

23.8 

109 

95.3 

52.8 

169 

147.8 

81.9 

229 

200.3 

111.0 

289 

252.8 

140.1 

50 

13.7 

24.2 

110 

96.2 

53.3 

170 

148.7 

82.4 

230 

201.2 

111.5 

290 

253.6 

140  6 

51 

44.6 

24  7 

111 

97.1 

53.8 

171 

149.6 

82.9 

231 

202.0 

112.0 

291 

254  5 

141.1 

52 

45.5 

25.2 

112 

98.0 

54.3 

172 

150.4 

83.4 

232 

202.9 

112.5 

292 

255  4 

141.6 

53 

16.4 

25.7 

113 

98.8 

54.8 

173 

151.3 

83.9 

233 

203.8 

113.0 

293 

256.3 

142.0 

54 

47.2 

26.2 

114 

99.7 

55.3 

174 

152.2 

84.4 

234 

204.7 

113.4 

294 

257.1 

142.5 

55 

48.1 

26.7 

115 

100.6 

55.8 

175 

153.1 

84.8 

235 

205.5 

113.9 

295 

258  0 

143.0 

56 

49.0 

27.1 

116 

101.5 

56.2 

176 

153.9 

85.3 

236 

206.4 

114.4 

296 

258.9 

143  5 

57 

49.927.6 

117 

102.3 

56.7 

177 

154.8 

85.8 

237 

207.3 

114.9 

297 

259.8 

144  0 

58 

50.7 

28.1 

118 

103  2 

57.2 

178 

155.7 

86.3 

238 

208.2 

115.4 

298 

260  6 

144.5 

59 

51.6 

28.6 

119 

104  1 

57  7 

179 

156.6 

86.8 

239 

209.0 

115.9 

299 

261.5 

145  0 

60 

52.5 

29  1 

120 

105.0 

58.2 

180 

157.4 

87.3 

240 

209.9 

116.4 

300 

262.4 

145.4 

Dist. 

Dep 

Lat. 

Hist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

For  61  Degrees. 

TABLE  IV.                                           233 

DIFFERENCE  OF   LATITUDE  AXD  DEPARTURE   FOR  30  DEGREES. 

Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.  S 

00.5 

61 

52.8 

30.5 

121 

104.8 

60.5 

181 

156.8 

90.5 

241 

208.7 

120.5 

2 

01.7 

01.  C 

62 

53.7 

31.0 

122 

105.7 

61.0 

182 

157.6 

91.0 

242 

209.6 

121.0 

3 

02.6 

01.5 

63 

54.6 

31.5 

123 

106.5 

61.5 

183 

158.5 

91.5 

243 

210.4 

121.5 

4 

03.5 

02.0 

64 

55.4 

:^2.0 

124 

107.4 

62.0 

184 

159.3 

92.0 

244 

211.3 

122.0 

5 

04.3 

02.5 

65 

56.3 

32.5 

125 

108.3 

62.5 

185 

160.2 

92.5 

245 

212.2 

122.5 

6 

05.2 

03.0 

66 

57.2 

33.0 

126 

109.1 

63.0 

186 

161.1 

93.0 

246 

213.0 

123.0 

7 

06.1 

03.5 

67 

58.0 

33.5 

127 

110.0 

63.5 

187 

161.9 

93.5 

247 

213.9 

123.5 

8 

06.9 

04.0 

68 

58.9 

34.0 

128 

110.9 

64.0 

188 

162.8 

94.0 

248 

214.8 

124.0 

9 

07.8 

04.5 

69 

59.8 

34.5 

129 

111.7 

64.5 

189 

163.7 

94.5 

249 

215.6 

124.5 

10 

08.7 

05.0 

70 

60.6 

35.0 

130 

112.6 

65.0 

190 

164.5 

95.0 

250 

216.5 

125.0 

11 

09.5 

05.5 

71 

61.5 

35.5 

131 

113.4 

65.  5 

191 

165.4 

95.5 

251 

217.4 

125.5 

12 

10.4 

06.0 

72 

62.4 

36.0 

132 

114.3 

66  0 

192 

166.3 

96.0 

252 

218.2 

126.0 

13 

11.3 

06.5 

73 

63.2 

36.5 

133 

115.2 

66.5 

193 

167.1 

96.5 

253 

219.1 

126.5 

14 

12.1 

07.0 

74 

64.1 

37.0 

134 

116.0 

67.0 

194 

168.0 

97.0 

254 

220.0 

127.0 

15 

13.0 

07.5 

75 

65.0 

37.5 

135 

116.9 

67.5 

195 

168.9 

97.5 

255 

220.8 

127.5 

16 

13.9 

08.0 

76 

65.8 

38.0 

136 

117.8 

G8.0 

196 

169.7 

98.0 

256 

221.7 

1-28.0 

17 

14.7 

08.5 

77 

66.7 

38.5 

137 

118.6 

68.5 

197 

170.6 

98.5 

257 

222.6 

128.5 

18 

15.6 

09.0 

78 

67.5 

39.0 

138 

119.5 

69.0 

198 

171.5 

99.0 

258 

223.4 

129.0 

19 

16.5 

09.5 

79 

68.4 

39.5 

139 

120.4 

69.5 

199 

172.3 

99.5 

259 

224.3 

129.5 

20 

17.3 

10.0 

80 

69.3 

40.0 

140 

121.2 

70.0 

200 

173.2 

100.0 

260 

225.2 

130.0 

21 

18.  '2 

10.5 

81 

70.1 

40.5 

141 

122.1 

70.5 

201 

174.1 

100.5 

261 

226.0 

130.5 

22 

19.1 

11.0 

82 

71.0 

41.0 

142 

123.0 

71.0 

202 

174.9 

101.0 

•262 

226.9 

131.0 

23 

19.9 

11.5 

83 

71.9 

41.5 

143 

123.8 

71.5 

203 

175.8 

101.5 

263 

227.8 

131.5 

24 

20.8 

12.0 

84 

72.7 

42.0 

144 

124.7 

72.0 

204 

176.7 

102.0 

264 

228.6 

132.0 

25 

•21.7 

12.5 

85 

73.6 

42.5 

145 

125.6 

72.5 

205 

177.5 

102.5 

265 

229.5 

132.5 

26 

22.5 

13.0 

86 

74.5 

43.0 

146 

126.4 

73.0 

206 

178.4 

103.0 

266 

230.4 

133.0 

27 

23.4 

13.5 

87 

75.3 

43.5 

147 

127.3 

73.5 

207 

179.3 

103.5 

267 

231.2 

133.5 

28 

24.2 

14.0 

88 

76.2 

44.0 

148 

128.2 

74.0 

208 

180.1 

104.0 

268 

232.1 

134.0 

29 

25.1 

14.5 

89 

77.1 

44.5 

149 

129.0 

74.5 

209 

181.0 

104.5 

269 

233.0 

134.5 

30 

26.0 

15.0 

90 

77.9 

45.0 

150 

129.9 

75.0 

210 

181.9 

105.0 

270 

233.8 

135.0 

31 

26.8 

15.5 

91 

78.8 

45.5 

151 

130.8 

75.5 

211 

182.7 

105.5 

271 

234.7 

135.5 

32 

27.7 

16.0 

92 

79.7 

46.0 

152 

131.6 

76.0 

212 

183.6 

106.0 

272 

235.6 

136.0 

33 

28.6 

16.5 

93 

80.5 

46.5 

153 

132.5 

76.5 

213 

184.5 

106.5 

273 

236.4 

136.5 

34 

29.4 

17.0 

94 

81.4 

47.0 

154 

133.4 

77.0 

214 

185.3 

107.0 

274 

237.3 

137.0 

35 

30.3 

17.5 

95 

82.3 

47.5 

155 

134.2 

77.5 

215 

186.2 

107.5 

275 

238.2 

137.5 

36 

31.2 

18.0 

96 

83.1 

48.0 

156 

135.1 

78.0 

216 

187.1 

108.0 

276 

239.0 

138.0 

37 

32.0 

18.5 

97 

84.0 

48.5 

157 

136.0 

78.5 

217 

187.9 

108.5 

277 

239.9 

138.5 

38 

32.9 

19.0 

98 

84.9 

49.0 

158 

136.8 

79.0 

218 

188.8 

109.0 

278 

240.8 

139.0 

39 

33.8 

19.5 

99 

85.7 

49.5 

159 

137.7 

79.5 

219 

189.7 

109.5 

279 

241.6 

139.5 

40 

34.6 

20.0 

100 

86.6 

50.0 

160 

138.6 

80.0 

220 

190.5 

110.0 

280 

242.5 

140.0 

41 

35.5 

20.5 

101 

87.5 

50.5 

161 

139.4 

80.5 

221 

191.4 

110.5 

281 

243.4 

140.5 

42 

36.4 

21.0 

102 

88.3 

51.0 

162 

140.3 

81.0 

222 

192.3 

111.0 

282 

244.2 

141.0 

43 

37.2 

21.5 

103 

89.2 

51.5 

163 

141.2 

81.5 

223 

193.1 

111.5 

283 

245.1 

141.5 

44 

38.1 

22.0 

104 

90.1 

52.0 

164 

142.0 

82.0 

224 

194.0 

112.0 

284 

246.0 

142.0 

45 

39.0 

22.5 

105 

90.9 

52.5 

165 

142.9 

82.5 

225 

194.9 

112.5 

285 

246.8 

142.5 

46 

39.8 

23.0 

106 

91.8 

53.0 

166 

143.8 

83.0 

22G 

195.7 

113.0 

286 

247.7 

143.0 

47 

40.7 

23.5 

107 

92.7 

53.5 

167 

144.6 

83.5 

227 

196  6 

113.5 

287 

248.5 

143  5 

48 

41.6 

24.0 

108 

93.5 

54  0 

168 

145  5 

84.0 

228 

197.5 

114  0 

288 

249.4 

144.0 

49 

42.4 

24.5 

109 

94.4 

54.5 

169 

146.4 

84.5 

229 

198  3 

114.5 

289 

250.3 

144.5 

50 

43.3 

25  0 

110 

95.3 

55.0 

170 

147  2 

85.0 

230 

199.2 

115.0 

290 

251.1 

145.0 

51 

44.2 

25.5 

111 

96.1 

55.5 

171 

148.1 

85.5 

231 

200.1 

115.5 

291 

252.0 

145.5 

52 

45.0 

26.0 

112 

97.0 

56.0 

172 

149.0 

86.0 

232 

200.9 

116.0 

292 

252.9 

146.0 

53 

45.9 

26.5 

113 

97.9 

56.5 

173 

149.8 

86.5 

233 

201.8 

116.5 

293 

253.7 

146.5 

54 

46.8 

27.0 

114 

98.7 

57.0 

174 

150.7 

87.0 

234 

202.6 

117.0 

294 

254.6 

147.0 

55 

47.6 

27.5 

115 

99.6 

57.5 

175 

151.6 

87.5 

235 

203.5 

117.5 

295 

255.5 

147.5 

56 

48.5 

28.0 

116 

100.5 

58.0 

176 

152.4 

88.0 

236 

204.4 

118.0 

296 

256.3 

148.0 

57 

49.4 

28.5 

117 

101.3 

58.5 

177 

153.3 

88.5 

237 

205.2 

118.5 

297 

257.2 

148.5 

58 

50.2 

29.0 

118 

102.2 

59  0 

178 

154.2 

89.0 

238 

206.1 

119.0 

298 

258.1 

149.0 

59 

51.1 

29.5 

119 

103.1 

59.5 

179 

155.0 

89.5 

239 

207.0 

119.5 

299 

258.9 

149.5 

60 

52.0 

30.0 

120 

103.9 

60.0 

18b 

155.9 

90.0 

240 

207.8 

120.0 

300 

259.8 

150.0 

Dist, 

Dep 

Lat. 

Dist, 

Dep. 

Lat, 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  60  Degrees. 

234                                          TAJBLE  IV. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  31  DEGREES. 

Dist. 

Lat.  Dep 

Dist. 

Lat. 

3ep 

is!. 

Lat. 

[)0]I 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

30.900.5! 

61 

52.3 

31.4 

121 

103.7 

52.3 

181 

155.1 

93.2 

241 

206.6 

124.1 

2 

31.  701.0, 

62 

53  1 

31.9 

122 

104.662.8 

182 

156.0 

93.7 

242 

207.4 

124.6 

3 

32.6 

31.5 

63 

54.0 

32.4 

123 

105.4 

33.3 

183 

156.9 

94.3 

243 

208.3 

125.2 

4 

33.4 

32.  i; 

64 

54.9 

33.0 

124 

106.3 

33.9 

184 

157.7 

94.8 

244 

209.1 

125.7 

5 

84.302.6 

65 

55.7 

33.5! 

125 

107.1 

34.4 

185 

158.6 

95.3 

245 

210.0 

126.2 

6 

05.103.1 

66 

56.6 

34.0 

126 

108.0 

>4.9 

186 

159.4 

95.8 

246 

210.9 

126.7 

7 

06.003.6 

67 

57.4 

34.5 

127 

108  9 

35.4 

187 

160.3 

96.3 

247 

211.7 

127.2 

8 

06.9 

34.1 

68 

58.3 

35.0 

128 

109.7 

55.9 

188 

161.1 

96.8 

248 

212.6 

127.7 

9 

>7.7 

34.6: 

69 

59.1 

35.5 

129 

110.6 

56.4 

189 

162.0 

97.3 

249 

213.4 

128  2 

10 

08.6 

35.  '2 

70 

60.  U 

36.1 

130 

111.4 

57.0 

190 

162.9 

97.9 

250 

214.3 

128.8 

11 

ljy.405.7| 

71 

60.9 

36.  Gj 

131 

112.3 

S7.5 

191 

163.7 

98.  4! 

251 

215.1 

129.3 

12 

10.306.2 

72 

61.7 

37.1 

132 

113.1 

68.0 

192 

164.6 

98.9 

252 

216.0 

129.8 

13 

11.1 

06.7 

73 

62.  C 

37.6 

133 

114.0 

68.5 

193 

165.4 

99.4 

253 

216.9 

130.3 

14 

12.0 

)7.2 

74 

63.4 

38.1 

134 

114.969.0 

194 

166.3 

99.9 

254 

217.7 

130.8 

15 

12.9 

07.7 

75 

64.3 

38.  6! 

135 

115.7 

69.5 

195 

167.1 

100.4 

255 

218.6 

131.3 

16 

13.7 

08.2 

76 

65.1 

39.1 

136 

116.6 

70.0 

196 

168.0 

100.9! 

256 

219.4 

131.8 

17 

14.  C 

08.8 

77 

66.  (,. 

39.7 

137 

117.470.6 

197 

168.9 

101.  5| 

257 

220.3 

132.4 

18 

15.4 

09.3 

78 

66.9 

40.2 

138 

118.371.1 

198 

169.7 

102.0 

258 

221.1 

132.9 

19 

16.3 

09.8 

79 

67.7 

40.7 

139 

119.171.6 

199 

170.6 

102.5 

259 

222.0 

133.4 

20 

17.1 

10   'A 

80 

68.  ( 

41.2 

140 

120.072.1 

200 

171.4 

103.0 

260 

222.9 

133.9 

•<il 

itt.ojio.b 

81 

69.  4 

41.7, 

141 

120.  972.  G 

201 

172.3 

103.5 

261 

223.7 

134.4 

22 

18.9 

11.3 

82 

70.3 

42.2 

142 

121.773  1 

202 

173.1 

104.0 

262 

224.  G 

134.9 

23 

19.7 

11.8 

83 

71.1 

42.7 

143 

122.673.7 

203 

174.0 

104.6 

263 

225.4 

135.5 

24 

20.  C 

12.4 

81 

72.  ( 

43.3 

144 

123.4 

74.2 

204 

174.9 

105.1 

264 

226.3 

136.0 

25 

21.4 

12.9 

85 

72.9 

43.8 

145 

124.3 

74.7 

205 

175.7 

105.6 

265 

227.1 

136.5 

26 

22  3 

13.4 

86 

73.7 

44  3, 

146 

125.1 

75.2 

206 

176.6 

106.1 

266 

228.0 

137.0 

27 

23.1 

13.9 

87 

74.  G 

44.8 

147 

126.0 

75.7 

207 

177.4 

106.6 

267 

228.9 

137.5 

23 

24.0 

14.4 

8S 

75.4 

45.3 

148 

126  9 

76.2 

208 

178.3 

107.1 

268 

229.7 

138.0 

29 

24.9 

14.9 

89 

76.3 

45.8 

149 

127.7 

76.7 

209 

179.1 

107.6 

269 

230.6 

138.5 

30 

25.7 

15.5 

90 

77.1 

43.  4 

150 

128.6 

77.3 

21( 

180.0 

108.2 

270 

231.4 

139.1 

31 

2o.O 

16.0 

91 

70.0 

43.9 

151 

T29.4 

77.8 

211 

180.9 

108.  7 

271 

232.3 

139.6 

32 

27.4 

16.5 

92 

78.9 

47.4 

152 

130.3 

78.3 

212 

181.7 

109.2 

272 

233.1 

140.1 

33 

2S.3 

17.0 

93 

79.7 

47.9 

153 

131.1 

78.8 

213 

182.6 

109.7 

273 

234.0 

140.6 

34 

29.1 

17.5 

94 

80.  C 

48.4 

154 

132.0 

79.3 

214 

183.4 

110.2 

274 

234.9 

141.1 

35 

30.  C 

18.0 

95 

81.4 

48.9 

155 

132.9 

79.8 

215 

184.3 

110.7 

275 

235.7 

141.6 

33 

30.9 

18.5 

9b 

82.3 

49.4 

150 

133.7 

80.3 

216 

185.1 

111.2 

276 

236.6 

142.2 

37 

31.7 

19.1 

97 

83.1 

50.0 

157 

134.6 

80.9 

217 

186.0 

111.8 

277 

237.4 

142.7 

38 

32.6 

19.6 

98 

84.  ( 

50.5 

158 

135.4 

81.4 

2LS 

186.9 

112.3 

278 

238.3 

143  2 

39 

33.4 

20.1 

99 

84.9 

51.  (, 

159 

136.3 

81.9 

219 

187.7 

112.8 

279 

239  1 

143.7 

40 

34.3 

20.6 

100 

85.7 

51.5 

160 

137.1 

82.4 

220 

188.6 

113.3 

280 

240.  ( 

144.2 

41 

35.1 

21.1 

101 

8G.G 

5J.O 

161 

138.082.9 

221 

1S9.4 

113.8 

281 

240.9 

144.7 

42 

36.0 

21.6 

10L 

87.4 

52.5 

162 

138.9 

83.4 

22'- 

190.3 

114.3 

282 

241." 

145.2 

43 

33.9 

22.1 

103 

88.3 

53.0 

163 

139.7 

84.0 

223 

191.1 

114.9 

283 

242.6 

145.8 

4i 

37.7 

22.7 

10 

89.1 

53.6 

164 

140.6 

84.5 

224 

192.0 

115.4 

284 

243.4 

146.3 

45 

33.6 

23.  V! 

105 

90.0 

54.1 

165 

141.4 

85.0 

22f 

192.9 

115.9 

285 

244.3 

146.8 

46 

39.4 

23.7 

106 

90.9 

54.6 

166 

142.3 

85.5 

226 

193.7 

116.4 

286 

245.1 

147.3 

47 

43.3 

24.2 

10" 

91.7 

55  ] 

167 

143.1 

86  0 

22" 

194.6 

116.9 

287 

246.0 

147.8 

48 

41.1 

24.7 

108 

92.6 

55.  (3 

168 

144.0 

86.5 

228 

195.4 

117.4 

288 

246.9 

148.3 

49 

42.0 

25.2 

109 

93.4 

56.1 

169 

144.9 

87.0 

229 

196.3 

117.9 

289 

247.7 

148.8 

50 

42.9 

25  8 

IK 

94.3 

56.7 

170 

145.7 

87.6 

230 

197.1 

118.5 

290 

248.  G 

149.4 

61 

43.7 

26.0 

111 

95.1 

57.  fc 

171 

146.  b 

88.1 

231 

198.  (J 

119  0 

291 

249.4 

149.9 

52 

44.6 

26.8 

112 

96.0 

57.7 

172 

147.4 

88.6 

232 

198  9 

119.5 

292 

250  3 

150  4 

53 

45.4 

27.3 

113 

96.9 

58.2 

173 

148.3 

89.1 

233 

199.7 

120.0 

293 

251.2 

150.9 

54 

46.3 

27.8 

114 

97.7 

58.7 

174 

149.1 

89  6 

234 

200.  G 

120.5 

294 

252.  C 

151.4 

55 

47.1 

28.3 

115 

98.6 

59.2 

175 

150.0 

90.1 

235 

201.4 

121.0 

295 

252.9 

151.9 

5G 

48.0 

28.8 

11C 

99.4 

59.7 

176 

150.9 

90.6 

236 

202.  a 

121.5 

296 

253.7 

152.5 

57 

48.9 

29  4 

117 

100.3 

60.3 

17" 

151.7 

91.2 

23" 

203.1 

122.1 

297 

254.  fc 

153.0 

58 

49.729.9 

llfi 

101.1 

60.8 

17* 

152.  C 

91.7 

238 

204.  C 

122.6 

298 

255.4 

153.5 

59 

50.630  4 

118 

102.  (] 

61.3 

17£ 

153.4 

92.2 

23 

204.  £ 

123  .  1 

299 

256.3 

154.0 

60 

51.4 

30.9 

12t 

102.  S 

61.8 

18C 

154.  S 

92.7 

24C 

205.7 

123.6 

300 

257.1 

154.5 

Dist, 

Dep 

Lat. 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

'Dist 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

For  59  Degrees. 

TABLE  IV.                                           235 

DIFFERENCE  OF    LATITUDE   AND  DEPARTURE   FOR  32  DEGREES. 

Mat 

Lat. 

Dep 

Dist. 

Lat. 

DeplDist. 

II 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

i 

JO.  8 

00.5 

61 

51.7 

32.3 

121 

102.6 

64.1 

181 

153.5 

95.9 

241 

204.4 

127.7 

2 

01.7 

01.1 

62 

52.632.9: 

122 

103.5 

C4.7 

182 

154.3 

96.4 

242 

205.2 

128.2 

3 

02.5 

01.  ( 

63 

53.433.4i 

123 

104.3 

65.2 

183 

155.2 

97.0 

243 

200.1 

128.8 

4 

03.4 

02.1 

64 

54.  333.9, 

124 

105.2 

65.7 

184 

156.0 

97.5 

244 

206.9 

129.3 

5 

04.2 

02.6 

65 

55.131.4 

125 

106.0 

66.2 

185 

156.9 

98.0 

245 

207.8 

129.8 

6 

05.1 

03.2 

66 

56.035.0 

126 

106.9 

66.8 

186 

157.7 

98.6 

246 

208.6 

130.4 

7 

05.9 

03.7 

67 

56.835.5; 

127 

107.7 

67.3 

187 

158.6 

99.1 

247 

209.5 

130.9 

8 

06.  8 

04.2 

68 

57.7 

36.0 

128 

108.6 

67.8 

188 

159.4 

99.6, 

248 

210.3 

131.4 

9 

J7.6 

04.8 

69 

58.5 

36.6 

129 

109.4 

68.4 

189 

160.3 

100.2 

249 

211.2 

131.9 

10 

08.5 

05.3 

70 

59.437.li 

130 

110.2 

68.9 

19d 

161.1 

100.7 

250 

212.0 

132.5 

11 

09.3 

05.8 

71 

60.237.6 

131 

lll.l 

69.4 

191 

162.0 

101.2 

251 

212.9 

133.0 

12 

10.2 

06.4 

72 

61.138.2 

132 

111.9 

69.9 

192 

162.8 

101.7 

252 

213.7 

133.5 

13 

11.  0 

06.9 

73 

61.9 

38.7 

133 

112  8 

70.5 

193 

163.7 

102.3 

253 

214.  G 

134.1 

14 

11.9 

07  4 

74 

62.8 

39.2 

134 

113.6 

71.0 

194 

164.5 

102.8 

254 

215.4 

134.6 

15 

12.7 

07.9 

75 

63.6 

39.7 

135 

114.5 

71.5 

195 

165.4 

103.3 

255 

216.3 

135.1 

16 

13.6 

08  5 

7G 

6i.5 

40.3 

136 

115.3 

72.1 

196 

166.2 

103.9 

256 

217.1 

135.7 

17 

14.4 

09.0 

77 

65.3 

40.8 

137 

116.2 

72.6 

197 

167.1 

104.4 

257 

217.9 

136.2 

18 

15.3 

09.5 

78 

66.1 

41.3 

138 

117.0 

73.1 

198 

167.9 

104.9 

258 

218.8 

136.7 

19 

16.1 

10.1 

W 

67.0 

41.9 

139 

117.9 

73.7 

199 

168.8 

105.5 

259 

219.6 

137.2 

20 

17.0 

10.  G 

80 

67.8 

42.4 

140 

118.7 

74.2 

200 

169.6 

106.0 

260 

220.5 

137  8 

21 

17.8 

11.1 

81 

63.7 

42.9 

141 

119.6 

74.7 

201 

170.5 

106.5 

261 

221.3 

138.3 

22 

18.7 

11.7 

82 

69.5 

43.5 

142 

120.4 

75  2 

202 

171.3 

107.0 

26'2 

222.2 

138.8 

23 

19.5 

12.2 

83 

70.4 

44.0 

143 

121.3 

75.8 

203 

172.2 

107.6 

263 

223.0 

139.4 

24 

20.4 

12.7 

84 

71.2 

44.5 

144 

122.1 

76.3 

204 

173.0 

108.1 

264 

223.9 

139.9 

25 

21.2 

13.2 

85 

72.1 

45.0 

145 

123.0 

76.8 

205 

173.8 

108  6 

265 

224.7 

140.4 

2G 

•22.0 

13.8 

86 

72.9 

45.6 

146 

123.8 

77.4 

206 

174.7 

109.2 

266 

225.6 

141.0 

27 

22.9 

14.3 

87 

73.8 

46.1 

147 

124.7 

77.9 

207 

175.5 

109.7 

267 

226  4 

141.5 

23 

23.7 

14.8 

88 

74.6 

46.6 

148 

125.5 

78.4 

208 

176.4 

110.2 

268 

227.3 

142.0 

29 

24.6 

15.4 

89 

75.5 

47.2 

149 

126.4 

79.0 

209 

177.2 

110.8 

269 

228.1 

142.5 

30 

25.4 

15.9 

90 

76.3 

47.7 

150 

127.2 

79.5 

210 

178.1 

111.3 

270 

229.0 

143.1 

31 

2G.3 

16.4 

91 

77.2 

48.2 

151 

128.1 

80.0 

211 

178.9 

111.8 

271 

229.8 

143.6 

32 

27.1 

17.0 

92 

78.0 

48.8 

152 

128.9 

80.5 

212 

179.8 

112.3 

272 

230.7 

144.1 

33 

28.0 

17.5 

93 

78.9 

49.3 

153 

129.8 

81.1 

213 

180.6 

112.9 

273 

231.5 

144.7 

34 

28.8 

18.0 

94 

79.7 

49.8 

154 

130.6 

81.6 

214 

181.5 

113.4 

274 

232.4 

145.2 

35 

29.7 

18.5 

95 

80.6 

50.3 

155 

131.4 

82.1 

215 

182.3 

113.9 

275 

233.2 

145.7 

33 

30.5 

19.1 

96 

81.4 

50.9 

156 

132.3 

82.7 

216 

183.2 

114.5 

276 

234.1 

146.3 

37 

31.4 

19.6 

97 

82.3 

51.4 

157 

133.1 

83.2 

217 

184.0 

115.0 

277 

234.9 

146.8 

38 

32.2 

20.1 

98 

83.1 

51.9 

158 

134.0 

83.7 

218 

184.9 

115.5 

278 

235.8 

147.3 

39 

33.1 

20.7 

99 

81.0 

52.5 

159 

134.8 

84.3 

219 

185.7 

116.1 

279 

236.6 

147  8 

40 

33.9 

21.2 

100 

84.8 

53.0 

160 

135.7 

84.8 

220 

186.6 

116.6 

280 

237.5 

148.4 

41 

34.8 

21.7 

101 

85.7 

53.5 

1G1 

136.5 

85.3 

221 

187.4 

117.1 

281 

238.3 

148.9 

42 

35.6 

22.3 

102 

86.5 

54.1 

162 

137.4 

85.8 

222 

188.3 

117.6 

282 

239.1 

149.4 

43 

3G.5 

22.8 

103 

87.3 

,4.6 

163 

138.2 

86.4 

223 

189.1 

118.2 

283 

240.0 

150.0 

44 

37.3 

23.3 

104 

88.2 

55.1 

1G4 

139.1 

86.9 

224 

190.0 

118.7 

284 

240.8 

150.5 

45 

38.2 

23.8 

105 

89.0155.6 

165 

139.9 

87.4 

225 

190.8 

119.2 

285 

241.7 

151.0 

4(5 

39.0 

24.4 

106 

89.956.2 

166 

140.8 

88.0 

226 

191.7 

119.8 

286 

242.5 

151.6 

47 

39.9 

24.9 

107 

90.756.7 

167 

141.6 

88.5 

227 

192.5 

120.3 

287 

243.4 

152.1 

48 

40.7 

25.4 

108 

91.657.2 

168 

142.5 

89.0 

228 

193.4 

120.8 

288 

244.2 

152.6 

49 

41.  C 

26.0 

109 

92.457.8 

169 

143.3 

89.  G 

229 

194.2 

121.4 

289 

245.1 

153.1 

50 

42.4 

26.5 

110 

93.358.3 

170 

144.2 

90.1 

230 

195.1 

121.9 

290 

245.9 

153.7 

51 

13.3 

27.0 

111 

94.158.8 

171 

145.0 

90.6 

231 

195.9 

122.4 

291 

246.8 

154.2 

52 

44.1 

27.6 

112 

95.059.4 

172 

145.9 

91.1 

232 

196.7 

122.9 

292 

247.6 

154.7 

53 

44.9 

28.1 

113 

95.859.9 

173 

146.7 

91.7 

233 

197.6 

123.5 

293 

248.5 

155.3 

54 

45.8 

28.  C 

114 

96.7G0.4 

174 

147.6 

92.2 

234 

198.4 

124.0 

294 

249.3 

155.8 

55 

46.6 

29.1 

115 

97.560.9 

175 

148.4 

92.7 

235 

199.3 

124.5 

295 

250.2 

156.3 

5G 

47.5 

29.7 

116 

98.461.5 

176 

149.3 

93.3 

236 

200.1 

125.1 

296 

251.0 

156.9 

57 

48.3 

30.2 

117 

99.262.0 

177 

150.1 

93.8 

237 

201.0 

125.6 

297 

251.9 

157.4 

58 

49.2 

30.7 

118 

100.162.5 

178 

151.0 

94.3 

238 

201.8 

126.1 

298 

252.7 

157.9 

59 

50.0 

31.3 

119 

100.963.1 

179 

151.8 

94.9 

239 

202.7 

126.7 

299 

253.6 

158.4 

GO 

50.9 

31  8 

120 

101.8 

63.6 

180 

152.6 

95.4 

240 

203.5 

127.2 

300 

254.4 

159.0 

Dist.  'Dep 

Lat, 

Dist, 

Dcp. 

Lat. 

Dist. 

Dcp.  [Lat. 

Dist. 

Dcp. 

Lat. 

Dist. 

Dcp.     Lat, 

For  58  Degrees. 

236                                          TABLE  IV. 

DIFFERENCE  OF   LATITUDE  AND 

DEPARTURE  FOR  33  DEGREES. 

Dist. 

Lat. 

Dep  'Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat, 

Dep. 

1 

00.800.5 

61 

51.2 

33.2 

121 

101.5 

65.9 

181 

151.8 

98.6 

241 

202.1 

131.3 

2 

01  701.1 

62 

52.033.8 

122 

102.366.4 

182 

152.6 

99.1 

242 

203.0 

131.8 

3 

02.501.6 

63 

52  834.3 

123 

103  267.0 

183 

153.5 

99.7 

243 

203.8 

132.3 

4 

03.402.2 

64 

53.734.9 

124 

104.067  5 

184 

154.3 

100.2 

244 

204.6 

132.9 

5 

04.202.7 

65 

54.535.4 

125 

104.868.1 

185 

155.2 

100.8 

245 

205. 

133.4 

6 

05.003.3 

66 

55.435.9 

126 

105.768.6 

186 

156.0 

101.3 

246 

206. 

134.0 

7 

05.903  8 

67 

56.236.5 

127 

106.569.2 

187 

156.8 

101.8 

247 

207. 

134.5 

8 

06.701.4 

68 

57.037.0 

128 

107.369.7 

188 

157.7 

102.4 

248 

208. 

135.1 

9 

07.504  9 

69 

57.937.6 

129 

108.2|70.3 

189 

158.5 

102.9 

249 

208. 

135.6 

10 

08.405.4 

70 

58.738.1 

130 

109.0,70.8 

190 

159.3 

103.5 

250 

209. 

136.2 

11 

09.  206.0 

71 

59.5*38.7 

131 

109.971.3 

191 

160.2 

104.0 

251 

210. 

136.7 

12 

10.106.5 

72 

60.439.2 

132 

110.7J71.9 

192 

161.0 

104.6 

252 

211. 

137.2 

13 

10.907  1 

73 

61.239.8 

133 

111.572.4 

193 

161.9 

105.1 

253 

212. 

137.8 

14 

11.7 

07.6 

74 

62.140.3 

134 

112.473.0 

194 

162.7 

105  7 

254 

213. 

138.3 

15 

12.6 

08.2 

75 

62.9 

40.8 

135 

113.273.5 

195 

163.5 

106.2 

255 

213. 

138.9 

1G 

13.4 

08.7 

76 

63.7 

41.4 

136 

114.1 

74.1 

196 

164.4 

106.7 

256 

214. 

139.4 

17 

14.3 

09.3 

77 

64.6 

41.9 

137 

114.974.6 

19? 

165.2 

107.3 

257 

215. 

140.0 

18 

15.1 

09.8 

78 

65.4 

42.5 

138 

115.775.2 

198 

166.1 

107.8 

258 

216. 

140.5 

19 

15.910.3 

79 

66  3 

43.0 

139 

116.675.7 

199 

166.9 

108.4 

259 

217. 

141.1 

20 

16.  fc 

10.9 

80 

67  1 

43.6 

140 

117.4 

76.2 

200 

167.7 

108.9 

260 

218. 

141.6 

21 

17.6 

11.4 

81 

67.9 

44.1 

141 

118.3 

76.8 

201 

168.6 

109.5 

261 

218. 

142.2 

22 

18.5 

12.0 

82 

68.8 

44.7 

142 

119.1 

77.3 

202 

169.4 

110.0 

262 

219.7 

142.7 

23 

19.3 

12.5 

83 

69.6 

45.2 

143 

119.9 

77.9 

203 

170.3 

110.6 

263 

220.6 

143.2 

24 

20.1 

13.1 

84 

70.4 

45.7 

144 

120.8 

78.4 

204 

171.1 

111.1 

264 

221.4 

143.8 

25 

21.0 

13.6 

85 

71.3 

46.3 

145 

121.6 

79.0 

205 

171.9 

111.7 

265 

222.2 

144.3 

26 

21.  8 

14.2 

86 

72.1 

46.8 

146 

122.4 

79.5 

206 

172.8 

112.2 

266 

223.1 

144.9 

27 

22.6 

14.7 

87 

73.047.4 

147 

123.3 

80.1 

207 

173.6 

112.7 

267 

223.9 

145.4 

28 

•23.5 

15.2 

88 

73.847.9 

148 

124.1 

80.6 

208 

174.4 

113.3 

268 

224.8 

146.0 

29 

24.3 

15.8 

89 

74.648.5 

149 

125.0 

81.2 

209 

175.3 

113.8 

269 

225  6 

146.5 

3>> 

25.2 

16.3 

90 

75.549.0 

150 

125.8 

81.7 

210 

176.1 

114.4 

270 

226.4 

147.1 

31 

26.0 

16.9 

91 

76.3 

49.6 

151 

126.682.2 

211 

177.0 

114  9 

271 

227.3 

147.6 

32 

26.8 

17.4 

92 

77.250.1 

152 

127.582.8 

212 

177.8 

115.5 

272 

228.1 

148.1 

33 

-7.7 

18.0 

93 

78.050.7 

153 

128.383.3 

213 

178.6 

116.0 

273 

229.0 

148.7 

34 

28.5 

18.5 

94 

78.851.2 

154 

129.2 

83.9 

214 

179  5 

116.6 

274 

229.8 

149.2 

35 

29.4 

19.1 

95 

79.7 

51.7 

155 

130.0 

84.4 

215 

180.3 

117.1 

275 

230.6 

149.8 

36 

30.2 

19  6 

96 

80.5 

52.3 

156 

130.8185.0 

216 

181.2 

117.6 

276 

231.5 

150.3 

37 

31.0 

20.2 

97 

81.452.8 

157 

131.785.5 

217 

182.0 

118.2 

277 

232.3 

150.9 

38 

31.9 

20.7 

98 

82.253.4 

158 

132.586.1 

218 

182.8 

118  7 

278 

233.2 

151.4 

39 

32.7 

21.2 

99 

83.053.9 

159 

133.386.6 

219 

183.7 

119.3 

279 

234.0 

152.0 

40 

33.5 

21.8 

100 

83.954.5 

160 

134.287.1 

220 

184.5 

119.8 

280 

234.8 

152.5J 

41 

34  4 

22.3 

101 

84.755.0 

161 

135.0*7.7 

221 

185.3 

120.4 

281 

235.7 

153.0 

42 

35.2 

22.9 

102 

85.555.6 

162 

135.988.2 

222 

186  2 

120.9 

282 

236.5 

153.6 

43 

36.1!23.4 

103 

86.456.1 

163 

136.788.8 

223 

187.0 

121.5: 

283 

237.3 

154.1 

44 

36.924.0 

104 

87  256.6 

164 

137  589.3 

224 

187.9 

122.0 

284 

238.2 

154.7 

45 

37.724.5 

105 

88.157.2 

165 

138.489.9 

225 

188.7 

122.  5! 

285 

239.0 

155.2 

46 

38.6 

25.1 

106 

88.957  7 

166 

139  2!90.4 

226 

189.5 

123.1 

286 

239.9 

155.8 

47 

39.4 

25.6 

107 

89.7 

58.3 

167 

140.191.0 

227 

190.4 

123.6 

287 

240.7 

156.3 

48 

40.3 

26.1 

108 

90.6 

58.8 

168 

140.991.5 

228 

191.2 

124.2 

288 

241.5 

156.9 

49 

41.1 

26.7 

109 

91.4 

59.4 

169 

141.792.0 

229 

192.1 

124.7 

289 

242.4 

157.4 

50 

41.9 

27.2 

110 

92.3 

59.9 

170 

142.692.6 

230 

192.9 

125.3 

290 

243.2 

157.9 

51 

42.8 

27.8 

111 

93.1 

60.5 

171 

143.493.1 

231 

193.7 

125.81 

291 

244.1 

158.5 

52 

43.6'28.3 

112 

93.9 

61  0 

172 

144.393.7 

232 

194.6 

126.4 

292 

244.9 

159.0 

53 

44.428.9 

113 

94.8 

61.5 

173 

145.194.2 

233 

195.4 

126.9 

293 

245.7 

159.6 

54 

45.329.4 

114 

95.6 

62.1 

174 

145.994.8 

234 

196.2 

127.4! 

294 

246.6 

160.1 

55 

46.130.0 

115 

96.462.6 

175 

146.895.3 

235 

197.1 

128.  01 

295 

247.4 

160.7 

56 

47.030.5 

116 

97.363.2 

176 

147.695.9 

236 

197.9 

128.5 

296 

248.2 

161.2 

57 

47.831.0 

117 

98.1 

63.7 

177 

148.4196.4 

237 

198.8 

129.1 

297 

249.1 

161.8 

58 

48.631.6 

118 

99.0 

64.3 

178 

149.396.9 

238 

199.6 

129.6, 

298 

249.9 

162.3 

59 

49.532.1 

119 

99.8 

64.8 

179 

150.197.5 

239 

200.4 

130.2 

299 

250.8 

162.8 

60 

50.332.7 

120 

100.6 

65.4 

180 

151.0 

98.0 

240 

201.3 

130.7 

300 

251.6 

163.4 

Dist. 

Dep  Lat. 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

For  57  Degrees. 

TABLE  IV.                                           237 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  34  DEGREES. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

l 

00.8 

00.  C 

61 

50.  C 

34.1 

121 

100.3 

67.7 

181 

150.1 

101.2 

241 

199.8 

134.8 

2 

01.7 

01.1 

62 

51.4 

34  7 

122 

101.1 

68.2 

182 

150.9 

101.8 

242 

200.6 

135.3 

3 

02.5 

01.7 

63 

52.2 

35.2 

123 

102.0 

68.8 

183 

151.7 

102.3 

243 

201  5 

135.9 

4 

03.3 

00.2 

64 

53.1 

35.8 

124 

102.8 

69.3 

184 

152.5 

102.9 

244 

202.3 

136.4 

5 

04.1 

02.8 

65 

53.9 

36.3 

125 

103.6 

69.9 

185 

153.4 

103.5 

245 

203.1 

137.0 

G 

05.0 

03.4 

66 

54.7 

36.9 

126 

104.5 

70.5 

186 

154.2 

104.0 

246 

203.9 

137.6 

7 

05.8 

03.9 

67 

55.5 

37  5 

127 

105.3 

71.0 

187 

155.0 

104.6 

247 

204.8 

138.1 

8 

06.6 

04.5 

68 

56.4 

38.0 

128 

106.1 

71.6 

188 

155  9 

105.1 

248 

205.6 

138.7 

9 

07.5 

H5.0 

69 

57.2 

38.6 

1-29 

106.9 

72.1 

189 

156.7 

105.7 

249 

206.4 

139.2 

10 

08.3 

05.6 

70 

5K.O 

39.1 

130 

107  8 

72.7 

190 

157.5 

106.2 

250 

207.3 

139  8 

11 

09  1 

06.2 

71 

58  9 

39.7 

131 

108.6 

73.3 

191 

158.3 

106.8 

iS51 

208.1 

140.4 

12 

09.9 

06.7 

72 

59.7 

40.3 

132 

109.4 

73.8 

192 

159.2 

107.4 

252 

208.9 

140.9 

13 

10.8 

07.3 

73 

60.5 

40.8 

133 

110.3 

74.4 

193 

160.0 

107.9 

253 

209.7 

141.5 

14 

11.6 

07.8 

74 

61.3 

41.4 

134 

111.1 

74.9 

194 

160.8 

108  5 

254 

210.6 

142.0 

15 

12.4 

08.4 

75 

62  2 

41.9 

135 

111.9 

75.5 

195 

161.7 

109.0 

255 

211.4 

142.6 

16 

13.3 

08.9 

76 

63  0 

42.5 

136 

112.7 

76.1 

196 

162.5 

109.6 

256 

212.2 

143.2 

17 

14.1 

09.5 

77 

63.8 

43.1 

137 

113.6 

76.6 

197 

163.3 

110.2 

257 

213.1 

143.7 

18 

14.9 

10.1 

78 

64.7 

43.6 

138 

114.4 

77.2 

198 

164.1 

110.7 

258 

213.9 

144.3 

19 

15.8 

10  6 

79 

65.5 

44.2 

139 

115.2 

77  7 

199 

165.0 

111.3 

259 

214.7 

144.8 

20 

16.6 

11.2 

80 

66.3 

44.7 

140 

116.1 

78.3 

200 

165.8 

111.8 

260 

215.5 

145.4 

21 

17.4 

11.7 

81 

67.2 

45.3 

141 

116.9 

78.8 

201 

166.6 

112.4 

*61 

216.4 

145.9 

22 

18  2 

12.3 

82 

68  0 

45.9 

142 

117.7 

79.4 

202 

167.5 

113.0 

262 

217.2 

146.5 

23 

19.1 

12.9 

83 

88.8 

46.4 

143 

118.6 

80  0 

203 

168.3 

113.5 

263 

218.0 

147.1 

24 

19  9 

13.4 

84 

69.6 

47.0 

144 

119.4 

80.5 

204 

169.1 

114.1 

264 

218  9 

147.6 

25 

20.7 

14.0 

85 

70.5 

47.5 

145 

120.2 

81.1 

205 

170:0 

114.6 

265 

219.7 

148.2 

26 

21.6 

14.5 

86 

71.3 

48.1 

146 

121.0 

81.6 

206 

170.  & 

115.2 

266 

220.5 

148.7 

27 

22.4 

15.1 

87 

72.1 

48.6 

147 

121.9 

82.2 

2$>7 

171.6 

115.8 

267 

221.4 

149.3 

28 

•23.2 

15.7 

88 

73.0 

49.2 

148 

122.7 

82.8 

208 

172.4 

116.3 

268 

222.2 

149  9 

29 

24.0 

16.2 

89 

73.8 

49.8 

149 

123.5 

83.3 

209 

173.3 

116.9 

269 

223.0 

150.4 

30 

24.9 

16.8 

90 

74  6 

50.3 

150 

124.4 

83.9 

210 

174.1 

117.4 

270 

223.8 

151.0 

31 

23.7 

17.3 

91 

75.4 

50.9 

151 

l&i.  2 

84.4 

211 

1Y4.9 

118.  U 

ML 

224.7 

151.5 

32 

26.5 

17.9 

92 

76.3 

51.4 

152 

126.0 

85.0 

212 

175.8 

118.5 

272 

225.5 

152.1 

3.3 

27.4 

18.5 

93 

77.1 

52.0 

153 

126.8 

85.6 

213 

176.6 

119.1 

273 

226.3 

152.7 

34 

28.2 

19.0 

94 

77.9 

52.6 

154 

127.7 

86.1 

214 

177.4 

119.7 

274 

227.2 

153.2 

35 

29.0 

19.6 

95 

78.8 

53.1 

155 

128.5 

86.7 

215 

178.2 

120.2 

275 

228.0 

153.8 

36 

•29.8 

20.1 

96 

79.6 

53.7 

156 

129.3 

87  2 

216 

179.1 

120.8 

276 

228.8 

154.3 

37 

30.7 

20.7 

97 

80.4 

54.2 

157 

130.2 

87.8 

217 

179.9 

121.3 

277 

229  6 

154.9 

38 

31.  5 

21.2 

98 

81.2 

54.8 

158 

131.  C 

88.4 

218 

180.7 

121.9 

278 

230.5 

155.5 

39 

32.3 

21.8 

99 

82.1 

55.4 

159 

131.8 

88.9 

219 

181.6 

122.5 

279 

231.3 

156.0 

40 

33.2 

22.4 

100 

62.9 

55.9 

160 

132.6 

89.5 

220 

182.4 

123.0 

280 

232.1 

156  6 

41 

34.0 

22.9 

101 

83.7 

56.5 

101 

133.5 

90.0 

221 

183.2 

123.6 

H81 

V36.  0 

157.1 

42 

34.8 

23.5 

102 

34.6 

57.0 

162 

134.3 

90.6 

222 

184.0 

124.1 

282 

233.8 

157.7 

43 

35.6 

24.0 

103 

85.4 

57.6 

163 

135.1 

91.1 

223 

184.9 

124.7 

283 

234.6 

158.3 

44 

36.5 

24.6 

104 

86.2 

58.2 

164 

136.0 

91.7 

224 

185.7 

125.3 

284 

235.4 

158.8 

45 

37.3 

25.2 

105 

87.0 

58.7 

165 

136.8 

92.3 

225 

186.5 

125  8 

285 

236.3 

159.4 

46 

38.1 

25.7 

106 

87.9 

59.3 

166 

137.6 

92.8 

226 

187.4 

126.4 

286 

237.1 

159.9 

47 

39.0 

26.3 

107 

88.7 

59.8 

167 

138  4 

93.4 

227 

188.2 

126.9 

287 

237.9 

160.5 

48 

39.8 

26.8 

108 

89.5 

00.4 

168 

139.3 

93.9 

228 

189.0 

127.5 

288 

238.8 

161.0 

49 

10.6 

27.4 

109 

90.4 

61.0 

169 

140.1 

94.5 

229 

189.8 

128  1 

289 

239.6 

161.6 

50 

11.6 

28.0 

110 

91.2 

61.5 

170 

140.9 

95.1 

230 

190.7 

128.6 

290 

240.4 

162.2' 

61 

12.328.5 

111 

92.0 

62.1 

~m 

141.8 

95.6 

231 

191.5 

129.  -I 

291 

241.2 

102.  7i 

52 

43.1 

29.1 

112 

92.9 

62.6 

172 

142.6 

96.2 

232 

192  3 

129.7 

292 

242.1 

163  3 

53 

43.9 

29.6 

113 

93.7 

63.2 

173 

143.4 

96.7 

233 

193.2 

130.3 

293 

242.9 

163.8' 

51 

44.8 

30.2 

114 

94.5 

63.7 

174 

144.3 

97.8 

234 

194.0 

130.9 

294 

243.7 

164.4 

55 

15.6 

30.8 

115 

95.3 

64.3 

175 

145.1 

97.9 

235 

194.8 

131.4 

295 

244.6 

165.0 

56 

16.4 

31.3 

116 

96.2 

64.9 

176 

145.9 

98.4 

236 

195.7 

132.0 

296 

245.4 

165.5 

57 

17.3 

31.9 

117 

97.0 

65.4 

177 

146.7 

99.0 

237 

196.5 

132.5 

297 

246.2 

166.1 

58 

18.1 

32.4 

11897.8 

66.0 

178 

147.6 

99.5 

238 

197.3 

133.1 

298 

247.1 

166.6 

59 

18  9 

33.0 

11998.7 

66.5 

179 

148.4 

100.1 

239 

198.1 

133.6 

299 

247.9 

167.2 

60 

19.7 

33.6 

120 

99.5 

67.1 

180 

149.2 

100.7 

240 

199.0 

134.2 

300 

248.7 

167.8 

DisL 

Dcp 

Lat. 

Dist. 

Dcj) 

Lat. 

D~iZ 

Dcp. 

Lat. 

Dist. 

Dcp. 

Lat, 

Dist. 

Dcp. 

Lat. 

For  5G  Degrees. 

238                                          TABLE  IV. 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE  FOR  35  DEGREES. 

Hist. 

Lat. 

Dep  Dist.  LatJDepj  Dist.    Lat. 

Dep.    ftjst 

Lat. 

Dep. 

'Dist 

Lat. 

Dep. 

l 

00.8 

00.  C 

6150.0!35.0 

121 

9D.1 

69.4 

181 

148.3 

103.8 

241 

197.4 

138.2 

2 

01.6 

01.1 

6250.8*35.6 

122 

99.9 

70.0 

182 

149.1 

104.4 

242 

198.2 

138  8 

3 

02.5 

01.7 

6351.6:36.1 

123 

100.8 

70.5 

183 

149.9 

105.0 

243 

199.1 

139.4 

4 

03.302.3 

6452.4,36.7 

124 

101.6 

71.1 

184 

150.7 

105.5 

244 

199.9 

140.0 

5 

04.102.9 

6553.2!37.3 

125    102.4 

71.7 

185 

151.b 

106.1 

245 

200.7 

140.5 

6  104.903.  4 

60 

54.137.9 

126 

103.2 

72.3 

186 

152.4 

106.7 

246 

201.5 

141.1 

7 

05.704.0 

67 

54.938.4 

127 

104  0 

72.8 

187 

153.2 

107.3 

247 

202.3 

141.7 

8 

06.604.6 

6855.739.0 

128 

104.9 

73.4 

188 

154.0 

107.8 

248 

203.1 

142.2 

9 

07.405.2 

6956  539.6 

129 

105.7 

74.0 

189 

154.8 

108.4 

249 

204.0 

112  8 

10 

03.205.7 

70 

57.340.2 

130 

106.5 

74.6 

19( 

155.6 

109.0 

250 

204.8 

143.4 

11   09.0,06.3 

71 

58.  2J40.7 

131 

107.3 

75.1 

191 

156.5 

109.0 

251 

205.6 

144.  0; 

12 

09.806.9 

72 

59.041.3 

132 

103.1 

75.7 

192 

157.3 

110.1 

252 

206.4 

144.5 

13 

10.607.5 

73 

6Q.8I41  9 

133 

108.9 

76.3 

193 

158.1 

110.7 

253 

207.2 

145.1 

14 

11.508.0 

74 

60.642.4 

134 

109.8 

76.9 

194 

158.9 

111.3 

254 

208.1 

145.7 

15 

12.3 

08.6 

75 

61.443.0 

135 

110.6 

77.4 

195 

159.7 

111.8 

255 

208.9 

146.3 

10 

13.1 

09.2 

76 

62.343.6 

136 

111.4 

78.0 

196 

160.6 

112.4 

256 

209.7 

146.8 

17 

13  9 

09.8 

77 

63.144.2 

137 

112.2 

78.6 

197 

161.4 

113.0 

257 

210.5 

147.4 

18 

14.7 

10.3 

78 

63  944.7 

138 

113.0 

79.2 

198 

162.2 

113.6 

258 

211.3 

148.0 

19 

15.6 

10.9 

7964.715.3 

139 

113.9 

79.7 

199 

163.0 

114.1 

259 

212.2 

148.6 

20 

16  4 

11.5 

80 

65.5j45.9 

140 

114.7 

80.3 

200 

163.8 

114.7 

260 

213.0 

149.1 

21 

17.2 

12.0 

81 

66.4]46.5 

141    115.5 

80.9 

201 

164.0 

115.3 

261 

213.8 

149.7 

22 

18.0 

12.6 

82 

67.2147.0 

142 

116.3 

81.4 

202 

165.5 

115.9 

262 

214.6 

150.3 

23 

18.8 

13.2 

83 

68.0J47.6 

143 

117.1 

82.0 

203 

166.3 

116.4 

263 

215.4 

150.9 

24 

19.713.8 

81 

68.848.2 

144 

118.  ( 

82.6 

204 

167.1 

117.0 

264 

216.3 

151.4 

25 

20.5 

14.3 

85 

69.648.8 

145 

118.8 

83.2 

205 

167.9 

117.6 

265 

217.1 

152.0 

26 

•21.3 

14.9 

8G 

70  449.3 

146 

119.  ( 

83.7 

206 

168.7 

118. 

266 

217.9 

152.6 

27 

22.1 

15.5 

87 

71.349.9 

147 

120.4 

84.3 

207 

169.6 

118. 

267 

218.7 

153.1 

28 

22  9 

16.1 

88 

72.1:50.5 

148 

121  2 

84.9 

208 

170.4 

119. 

268 

219.5 

153.7 

29 

23.8 

16.6 

8972.9)61.0 

149 

122.1 

85.5 

209 

171.2 

119. 

269 

220  4 

154.3 

30 

24.6 

17.2 

90 

73.751  6 

150 

122.9 

86.0 

210 

172.0 

120. 

270 

221.2 

154.9: 

31 

25.4 

17.8 

91 

74.552.2 

151 

123.7 

86.6 

211 

172.8 

121. 

271 

222.  C 

155.4 

32 

26.2 

18.4 

92 

75.452.8 

152 

124  5 

87.2 

212 

173.7 

121. 

272 

222.8 

156.0 

33 

27.0J18.9 

93 

76.253.3 

153 

125.3 

87.8 

213 

174.5 

122. 

273 

223.6 

156.6 

34 

27.919.5 

94 

77  053.9 

154 

126.1 

88.3 

214 

175.3 

122. 

274 

224.4 

157.2 

35 

28.7120.1 

95 

77.854.5 

155 

127.0 

88.9 

215 

176.1 

123. 

275 

225.3 

157.7 

36 

29.5,20.6 

9(i 

78.C55.1 

156 

127.  b 

89.5 

216 

176.9 

123. 

276 

226.1 

158.3 

37 

30.321.2 

97 

79.555.6 

157 

128.6 

90  1 

217 

177.8 

124. 

277 

226  9 

158.9 

38 

31.121.8 

98 

SO.  356.  2 

158 

129.4 

90.6 

218 

178.6 

125.0 

278 

227.7 

159  5 

39 

31.922.4 

99 

81.156.8 

159 

130.2 

91.2 

219 

179.4 

125.6 

279 

228  5 

160  0 

40 

32.  £22.  9 

100 

81.957.4 

160    131.1 

91.8 

220 

180.2 

126.2 

280 

229.4 

160.6 

41 

33.6 

23.5 

101 

82.757.9 

101 

131.9 

92.3 

22i 

181.0 

126.8 

281 

230.2 

161.2 

42 

31.4 

24.1 

10283.658.5 

162    132.7 

92.9 

222 

181.9 

127.3 

282 

231.0 

161.7 

43 

33.2 

24.7 

10384.459.1 

163 

133.5 

93.5 

223 

182.7 

127.9 

283 

231.8 

162.3 

4i 

36.025.2 

10J85.259.7 

164 

134.3 

94.1 

224 

183.5 

128.5 

284 

232.6 

162.9 

45 

36.925.8, 

10586.060.2 

165 

135.2 

94.6 

225 

184.3 

129.1 

285 

233.5 

163.5 

46 

37.7i'26.4 

10686.860.8 

166 

136  0 

95.2 

226 

185.1 

129.6 

286 

234.3 

164.0 

47 

38.527.0 

107 

87  661  4 

167 

136.8 

95  8 

227 

185.9 

130.2 

287 

235.1 

164  6 

48 

39.327.5 

108 

88.561.9 

168 

137.  <i 

96.4 

228 

186.8 

130.8 

288 

235.9 

165.2 

49 

40.128.1 

109 

89.362.5 

109 

138.4 

96.9' 

229 

187.6 

131.3 

289 

236.7 

165.8 

50 

41  0 

28.7 

110 

90.163.1 

170 

139.3 

97.5 

230 

188.4 

131.9 

290 

237.6 

166.3 

51 

41.829.3 

111 

90.963.7 

171 

140.1 

98.1 

231 

189.2 

132.5 

291 

238.4 

167  J 

52 

42.629.8 

112 

91.764.2 

172 

140.9 

98.7! 

232 

190.0 

133.1 

292 

239.2 

167.5 

53 

43.430.4 

113 

92.664.8 

173 

141  7 

99.2 

233 

190.!) 

133.6 

293 

240.0 

168.1 

54 

44.231.0 

11493.465.4 

174 

142.5 

99.8 

234 

191.7 

134.2 

294 

240.8 

168.6 

55 

45.131.5 

11594.266.0 

175 

143.4 

100.4 

235 

192.5 

134.8 

295 

241.6 

169.2 

56 

45.932.2 

11695.066.5 

176 

144.2 

100.9 

236 

193.3 

135.4 

296 

242.5 

169.8 

57 

46.732.7 

117 

95.867.1 

177 

145.0 

101.5 

237 

194.1 

135.9 

297 

243.  i1 

170.4 

58 

47.533.3 

118 

96.767.7 

178 

145.8 

102.1 

238 

195.0 

136.5 

298 

244.1 

170.9 

59 

48.333.8 

11997.568.3 

179 

146.6 

102.7 

239 

195.8 

137.1 

299 

244.9 

171.5 

60 

49.1 

34.4 

120 

98.368.8 

180 

147.4 

103.2 

240 

196.6 

137.7 

300 

245.7 

172.1 

Dist.  Dep  Lat.  Dist. 

Dep  Lat. 

Wat. 

Den. 

Lat. 

list. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  55  Degrees. 

TABLE  IV.                                           239 

DIFFERENCE  OF    LATITUDE   AND  DEPARTURE   FOR  36  DEGREES. 

Dist.  Lat, 

Dep 

)ist.  Lat.  Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.8 

00.  C 

61 

49.4 

35.9 

121 

97.9 

71.1 

181 

140.4 

106.4 

241 

195.0 

141.7 

2 

01.6 

01.2 

6250.2 

36.4 

122 

98.7 

71.7! 

182 

147.2 

107.0 

242 

195.8 

142.2 

3 

02.4 

01.8 

6351.037.0 

123 

99.5 

72.3 

183 

148.1 

107.6 

213 

196.  G 

142.8 

4 

03.2 

02.4 

6451.837.6 

124 

100.3 

72.9 

184 

148.9 

108.2 

244 

197.4 

143.4 

5 

04.0 

02.9 

6552.638.2 

125 

101.1 

73.5 

185 

149.7 

103.7 

245 

198.2 

144.0 

G 

04.9 

03.5 

6653.438.8 

126 

101.9 

74.1 

186 

150.5 

109.  3t 

246 

199.0 

144.6 

-7 

05.7 

04.1 

6754.2;39.4 

127 

102.7 

74.6 

187 

151.3 

109.9 

247 

199.8 

145.2 

8 

06.5 

04.7 

6855.040.0 

128 

103.6 

75.2 

188 

152.1 

110.  f 

248 

200.  « 

145.8 

9 

07.3 

05.3 

6955.840.6 

129 

104.4 

75.8 

189 

152.9 

111.1 

249 

201.4 

146.4 

10 

08.1 

05.9 

7056.641.1 

130 

105.2 

76.4 

190 

153.7 

111.7 

250  202.3 

146.9; 

11 

08.9 

06.5 

71  57.  4  41.  V 

131 

lOo.O 

77.0 

191 

154.5 

112.3 

251 

203.1 

147.5 

12 

09.7 

07.1 

72-58.2142.3 

132 

106.8 

77.6; 

192 

155.3 

112.9 

252 

203.9 

148.1 

13 

10.5 

07.6 

7319.142.9 

133 

107  6 

78.2 

193 

156.1 

113.4' 

253 

204.7 

148.7 

14 

11.3 

08  2 

74 

53.9 

13.5 

134 

108.4 

78.8 

194 

156.9 

114.0 

254 

205.5 

149.3 

15 

12.1 

03.8 

75 

30.7 

41.1 

135 

109.2 

79.4 

195 

157.8 

114.6 

255 

208.3 

149.9 

16 

12.9 

09.4 

76 

31.5 

44.7 

136 

110.0 

79.9 

196 

158.6 

115.2 

256 

207.1 

150.5 

17 

13.8 

10.  0 

77 

62.345.3 

137 

110.8 

83.5 

197 

159.4 

115.8 

257 

207.9 

151.1 

18 

14.6 

10.6 

78 

33.145.8 

138 

111.6 

81.1 

198 

160.2 

116.4 

258 

208.7 

151.6 

19 

15.4 

11.2 

7963.943.4 

139 

112.5 

si.?: 

199 

161.0 

117.0 

259 

209.5 

152.2 

20 

16.2 

11.8 

8064.7 

47.0 

140 

113.3 

82.3 

200 

161.8 

117.6 

260 

210.3 

152.8 

21 

17.0 

12.3 

8165.5 

47.  01 

141 

114.1 

82.  1J 

201 

162.0 

118.111  261 

211.* 

153.4 

22 

17.8 

12.9 

8233.3 

48.  2! 

142 

114.9 

83  5 

202 

163.4 

118.7'  262 

212.0 

154.0 

23 

18.  G 

13.5 

83 

G7.1 

48.8 

143 

115.7 

84.1 

203 

164.2 

119.3 

263 

212.8 

154.  G 

24 

19.4 

14.1 

84 

63.0 

49.4 

114 

116.5 

84.6 

204 

165.0 

119.9 

264 

213.  G 

155.2 

25 

>0.2 

14.7 

8568.850.0 

145 

117.3 

85.2 

205 

165.8 

120  5 

265 

214.4 

155.8 

26 

21.0 

15.3 

8669.650.5 

146 

118.1 

85.8 

206 

166.7 

121.1 

266 

215.2 

156.4 

27 

22.8 

15.9 

8770.451.1 

147 

118.9 

86.  4| 

207 

167.5 

121.7 

267 

216.0 

156.9 

23 

22.7 

16.5 

8871.251.7 

148 

119.7 

87.0 

208 

168.3 

T22.3 

268 

216.8 

157.5 

29 

23  5 

17.0 

8972.0 

52.3 

149 

120.5 

87.  G; 

209 

169.1 

122.8 

2C9 

217.  G 

158.1 

33 

24.3 

17.  G 

90 

72.8 

52.9 

150 

121.4 

83.2 

210 

169.9 

123.4 

270 

218.4 

158.7 

31 

25.1 

18.2 

9i 

73.6 

53.5 

151 

122.2 

83.  «• 

211 

170.7 

124.0 

271 

219.2 

159.3 

32 

25.9 

18.8 

92 

74.4 

54.1 

152 

123.0 

89.3 

212 

171.5 

124.6 

272 

220.1 

159.9 

33 

26.7 

19.4 

93 

75.2 

54.7 

153 

123.8 

89.9 

213 

172.3 

125.2 

273 

220.9 

160.5 

34 

27.5 

20.0 

94 

76.0 

55.3 

154 

124.6 

90.5 

214 

173.1 

125.8 

274 

221.7 

161.1 

35 

23.3 

20.6 

95 

76.9'55.8 

155 

125.4 

91.  11 

215 

173.9 

126.4 

275 

222.5 

161.  G 

33 

29.1 

21.2 

90 

77.7156.4 

156 

123.2 

91.7, 

216 

174.7 

127.0 

276 

223.3 

162.2 

37 

29.9 

21.7 

9778.557.0 

157 

127.0 

92.3 

217 

175.  G 

127.5 

277 

224.1 

162.8 

33 

3'J.7 

22.3 

98  79.  3  57.  C 

158 

127.8 

92.9 

218 

176.4 

128.1 

278 

224.9 

163.4 

33 

31.  G 

22.9 

9083.158.2 

159 

128.6 

93.5 

219 

177:2 

128.7 

279 

225.7 

164  0 

40 

32.4 

23.5 

100 

30.958.8 

160 

129.4 

94.0 

220 

178.0 

129.3 

280 

226.5 

164.6 

41 

33.  i! 

24.1 

101 

81.7159.4 

161 

130.3 

94.0 

221 

178.  b 

129.9 

281 

'227.3 

165.2 

42 

34.0 

24.7 

102 

32.560.0 

162 

131.1 

95.2 

222 

179.  C 

130.5 

282 

228.1 

165.8 

43 

34.8 

25.3 

103 

83.360.5 

163 

131.9 

95.8 

223 

180.4 

131.1 

283 

229.0 

166.3 

44 

35.6 

25.9 

104 

84.161.1 

164 

132.7 

96.4 

224 

181.2 

131.7 

284 

229.8 

166.9 

45 

36.4 

26.5 

105 

84.961.7 

165 

133.5 

97.0 

225 

182.0 

132.3 

285 

230.  C 

167.5 

43 

37.2 

27.0 

106 

85.862.3 

166 

134.3 

97.  C 

226 

182.8 

132.8 

286 

231.4 

168.] 

47 

33.0 

27.6 

107 

86.662.9 

167 

135.1 

98.2 

227 

183.  G 

133.4 

287 

232.2 

168.7 

48 

33.8 

28.2 

103 

87.463.5 

168 

135.9 

98.7 

228 

184.5 

134.0 

288 

233.0 

169.3 

49 

39.  G 

28.8 

109 

83.264.1 

169 

136.7 

99.3 

229 

185.3 

134.6 

289 

233.8 

169.9 

50 

40.5 

29.4 

110 

89.061.7 

170 

137.5 

99.9 

230 

186.1 

135.2 

290 

231.6 

170.5 

TT 

11.3 

30.0 

111 

89.865.2 

171 

138.3 

100.  b 

231 

186.9 

135.8 

291 

235.4 

171.0 

52 

12.1 

33.6 

112 

90.665.8 

172 

139.2 

101.1 

23* 

187.7 

136.4 

292 

236.2 

171.6 

53 

42.9 

31.2 

113 

91.466.4 

173 

140.0 

101.7 

233 

183.5 

137.0 

293 

237.0 

172.2 

54 

43.7 

31.7 

114 

92.267.0 

174 

140.8 

102.3 

234 

189.3 

137.5 

294 

237.9 

172.8 

55 

11.5 

32.3 

115 

93.  067.  C 

175 

141.6 

102.9 

235 

190.1 

133.1 

295 

238.7 

173.4 

56 

45.3 

32.9 

116 

93.868.2 

176 

142.4 

103.5 

236 

190.9 

138.7 

296 

239.5 

174.0 

57 

46.1 

33.5 

117 

94.768.8 

177 

143.2 

104.0 

237 

191.7 

139.3 

297 

240.3 

174.  G 

58 

46.9 

34.1 

118 

95.569.4 

178 

144.0 

104.6 

238 

192.5 

139.9 

298 

241.1 

175.2 

59 

47.7 

34.7 

11996.369.9 

179 

144.8 

105.2 

239 

193.4 

140.5 

299 

241.9 

175.7 

60 

48.5 

35.3 

12097.170.5 

180 

145.6 

105.8 

240 

194.2 

141.1 

300 

242,.  7 

176.3 

Lat. 

Dist. 

Dep 

Lat. 

DistJDep 

Dist. 

Dep. 

Lat.    Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  54  Degrees. 

240 

TABLE  IV. 

DIFFERENCE    OF   LATITUDE  AXD  DEPARTURE  FOR  37    DEGREES. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.800.6 

61 

48  7 

36.7 

121 

96.6 

72.8 

181 

144.6 

108.9 

241 

192.5 

145.0 

2 

01.601.2 

62 

49.5 

37.3 

122 

97.4 

73.4 

182 

145.4 

109.5 

242 

193.3 

145.6 

3 

)2.4'01.8 

63 

50.3 

37.9 

123 

98.2 

74.0 

183 

146.2 

110.1 

243 

194.1 

146.2 

4 

03.202.4 

64 

51.1 

38.5 

124 

99.0 

74.6 

184 

146.9 

110  7 

244 

194.9 

146.8 

5 

01  003  0 

65 

51.9 

39.1 

125 

99.8 

75.2 

185 

147.7 

111.3 

245 

195.7 

147  4 

6 

04.8 

03.6 

66 

52.7 

39.7 

126 

100.6 

75.8 

186 

148  5 

111.9 

246 

196.5 

148.0 

7 

05  6 

04.2 

67 

53.5 

10.3 

127 

101.4 

76.4 

187 

149.3 

112.5 

247 

197.3 

148.6 

8 

1)6.4 

01.8 

68 

54.3 

10.9 

128 

102.2 

77.0 

188 

150.1 

113.1 

248 

198.1 

149.3 

9 

07.2 

05.4 

6955.1 

41  5 

129 

103.0 

77.6 

189 

150.9 

113.7 

249 

198.9 

119.9 

10 

08.0 

06  0 

7055.9 

42.1 

130 

103.8 

78.2 

190 

151.7 

114.3 

250 

199.7 

150.5 

11 

U8.8 

OG.G 

7J  50.7 

42.7 

131 

Io4  G 

78.8 

191 

152.5 

114  9 

251 

200.5 

151.1 

12 

09.  G 

07.2 

7257.5 

43.3 

132 

105.4 

79.4 

192 

153.3 

115.5 

252 

201.3 

151.7 

13 

10.4 

07.8 

7358.3 

43.9 

133 

103.2 

80.0 

193 

154.1 

116  2 

253 

202.1 

152.3 

14 

11.  2 

08.4 

7459.1 

44.5 

134 

107.0 

80.6 

194 

154.9 

116.8 

254 

202.9 

152.9 

15 

12.0 

09.0 

7559.9 

45.1 

135 

107.8 

81.2 

195 

155  7 

117.4 

255 

203  7 

153.5 

1C 

12.8 

J9  6 

7660.7 

45.7 

136 

108.6 

81.8 

196 

156.5 

118.  (» 

256 

204.5 

154.1 

17 

13.6 

10.2 

7761.; 

46  3 

137 

109.4 

82.4 

197 

157.3 

118  6 

257 

205.2 

154.7 

18 

14.4 

10.8 

7862.3 

tG.9 

138 

110.2 

83.1 

198 

158.1 

119.2 

258 

206.0 

155.3 

19 

15.2 

11.4 

7963  1 

47.5 

139 

111.0 

83.7 

199 

158.9 

119.8 

259 

206.8 

155.9 

20 

16.  0 

12.0 

8063.9 

43.1 

140 

111.8 

84  3 

200 

159  7 

120.4 

260 

207.6 

156  5 

21 

10.8 

12.0 

8104  7 

48.7 

141 

H2.6 

84.9 

201 

160.5 

121.0 

261 

208.4 

157.1 

22 

17  G 

13  2 

8265.5 

49.3 

142 

113.4 

85.5 

202 

161.3 

121.6 

262 

209.2 

157.7 

23 

18.4 

13.8 

8366.3 

50  0 

143 

1J4.2 

86.1 

203 

1G2.1 

122.2 

263 

210  0 

158.3 

24 

19.2 

14.4 

8467  1 

50.  C 

144 

115.0 

86.7 

204 

162.9 

122.8 

264 

210.8 

158.9 

25 

20.0 

15.0 

8567.9 

51.2 

145 

115  8 

87.3 

205 

163.7 

123.4 

265 

211.6 

159.5 

20 

20.8 

15.  G 

866H.7 

51.8 

146 

116  6 

87.9 

206 

164.5 

124.0 

266 

212.4 

160.1 

27 

21.6 

16.2 

87169.5 

52.4 

147 

117.4 

88.5 

207 

165.3 

124.6 

267 

213.2 

160.7 

28 

22.4 

16.9 

8870.3 

53.0 

148 

118  2 

89.1 

208 

16G.1 

125.2 

268 

214.0 

161  3 

29 

23.2 

17.5 

89,71.1 

53  6 

149 

119  0 

89.7 

209 

163.9 

125.8 

269 

214.8 

161.9 

30 

24.0 

18.1 

9071.9 

54.2 

150 

119.8 

90.3 

210 

167.7 

126.4 

270 

215.6 

162.5 

31 

24.6 

18.7 

9172.7 

54.8 

151 

120.0 

90.9 

•211 

108.5 

127.0 

271 

216.4 

103.1 

32 

25.  C 

19.3 

92^73.5 

55.4 

152 

121.4 

91.5 

212 

169.3 

127.6 

272 

217.2 

163.7 

33 

26.4 

19.9 

93,74.3 

56.0 

153 

122.2 

92.1 

213 

170.1 

128.2 

273 

218.0 

164.3 

34 

27.2 

20.5 

9475  1 

56.  G 

154 

123  0 

92.7 

214 

170  9 

128.8 

274 

218.8 

164.9 

35 

28.0 

21.1 

9575.9 

57.2 

155 

123.8 

93  3 

215 

171.7 

129.4 

275 

219.6 

165.5 

3G 

28.8 

21.7 

9676.7 

57.8 

156 

124.6 

93.9 

216 

172.5 

130.0 

276 

220.4 

166.1 

37 

29.5 

22.3 

97,77.5 

58.4 

157 

125.4 

94  5 

217 

173.3 

130.6 

277 

221.2 

166.7 

38 

30.3 

22.9 

9878.3 

59.0 

158 

126.2 

95.1 

218 

174.1 

131.2 

278 

222.0 

107.3 

39 

31.1 

23.5 

9979.1 

59.6 

159 

127.0 

95.7 

219 

174.9 

131.8 

279 

222.8 

167.9 

40 

31.9 

24.1 

100'79.0 

60.2 

160 

127.8 

96.3 

220 

175  7 

132.4 

280 

223.6 

168.5 

41 

32.7 

24.7 

10180.7 

60.8 

161 

128.0 

90  9 

221 

176.5 

133.0 

281 

224.4 

109.1 

42 

33.5 

25.3 

10281.5 

61.4 

1G2 

129.4 

97.5 

222 

177  3 

133.6 

282 

225.2 

169.7 

43 

34  3 

25.9 

10382.3 

62.0 

16b 

130.2 

98.1 

223 

178.1 

134.2 

283 

226.0 

170.3 

44 

35.1 

26.5 

10483.1 

62  6 

164 

131.0 

98.7 

224 

178.9 

134  8 

284 

226.8 

170.9 

45 

35  9 

27.1 

10583.9 

63.2 

165 

131.8 

99.3 

225 

179.7 

135.4 

285 

227.6 

171.5 

46 

36.7 

27.7 

10G84.7 

G3.8 

160 

132.6 

99  9 

2-26 

180.5 

136.0 

286 

228.4 

172.1 

47 

37.5 

28.3 

10785.5 

64.4 

167 

133  4 

100.5 

227 

181.3 

136.6 

287 

229.2 

172.7 

48 

38.3 

28.9 

108  88.  3 

65.0 

168 

134.2 

101.1 

228 

182.1 

137.2 

288 

230.0 

173.3 

49 

39.1 

29.5 

10987.1 

65.  G 

169 

135.0 

101.7 

229 

182.9 

137.8 

289 

230.8 

173.7 

50 

39.9 

30.1 

11087.8 

66.2 

170 

135.8 

102.3 

230 

183.7 

138.4 

290 

231.  G 

174  5 

51 

40  7 

30.7 

11188.6 

60.8 

171 

130.0 

102.9 

'231 

1*4.5 

139.0 

291 

232.4 

175.1 

52 

11.5 

31.3 

11289.4 

67.4 

17-2 

137.4 

103.5 

232 

185.3 

139.6 

292 

233  2 

175.7 

53 

12.3 

31.9 

11390.2 

68.0 

173 

138.2 

104.1 

233 

186.1 

140.2 

293 

234.0 

176.3 

54 

43.1 

32.5 

11491.0 

68.6 

174 

139.0 

104.7 

234 

186.9 

140.8 

294 

234.8 

176.9 

55 

43.9 

33.1 

11591.8 

69.2 

175 

139.8 

105.3 

235 

187.7 

141.4 

295 

235.6 

177.5 

5G 

44.7 

33.7 

11692.6 

69.8 

17G 

140.6 

105.9 

236 

188.5 

142.0 

296 

236.4 

178  1 

57 

45.5 

34.3 

117 

93.4 

70.4 

177 

141.4 

106.5 

237 

189.3 

142.0 

297 

237.2 

178  7 

58 

46.3 

34.9 

118 

94  2 

71.0 

178 

142.2 

107.1 

238 

190.1 

143.2 

298 

238  0 

179.3 

59 

47.1 

35.5 

119 

95  0 

71  6 

179 

143.0 

107.7 

239 

190.9 

143.3 

299 

238.8 

179  9 

GO 

47  9 

36.1 

120 

95.8 

72.2 

180 

143.8 

108.  c 

240 

191.7 

144.4 

300 

239.6 

180.5 

Dist. 

Dep 

Lat. 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  53  Degrees. 

TABLE  IV.                                           241 

DIFFERENCE  OF   LATITUDE  A$D  DEPARTURE  FOR  38  DEGREES. 

Dist. 

Lat.  Dep|!Dist. 

Lat. 

Dep 

Dist, 

Lat.     Dep. 

Dist. 

Lat. 

Dep.  1 

Dist, 

Lat. 

Dep. 

l 

00.800.61 

61 

48.1 

37.6 

121 

95.3     74.5 

181 

142.6 

111.4    241 

189.9 

148.4 

2 

01  601.2 

62 

48.938.2 

122 

9J.1     75.1 

182 

143.4 

112.  1' 

24'2 

190.7 

149.0 

3 

02.401.8 

63 

49.638  8 

123 

96.9 

75  7 

183 

144.2 

112.7 

243 

191.5 

149.6 

4 

03.202.5 

64 

50.439.4 

124 

97.7 

76  3 

184 

145.0 

113.3 

244 

192  3 

150.2 

5 

03.903.1 

65 

51.240.0 

125 

98.5 

77.0 

185 

145.8 

113.9 

245 

193.1 

150.8 

6 

04.703.7 

66 

52.040.6 

126 

99.3 

77.  G 

186 

146.6 

214.5 

246 

193.9 

151.5 

7 

05.504.3 

67 

52.841.2 

127 

100.1 

78.2 

187 

147.4 

115.1 

247 

194.6 

152.1 

8 

06.304.9 

68 

53.6 

41.0 

128 

100.9 

78.8 

188 

148.1 

115.7 

248 

195.4 

152.7 

9 

07.105  5 

6954.4 

42.5 

129 

101.7     79.4 

189 

148.9 

116.4 

249 

196.2 

153.3 

10 

07.906.2 

70 

55.243.1 

130 

102.4     80.0 

190 

149.7 

117.0 

250 

197.0 

153.9 

11  108.7,00.8 

71 

55.9 

43.7 

131 

103.  2i     80.7 

191 

150.5 

117.6 

251 

197  > 

154.5 

12  09  507.4 

72 

56.7 

14.3 

132 

104.  (i 

81.3 

192 

151.3 

118.2 

252 

198.6 

155.1 

13 

10.2 

08.0 

73 

57.5 

44.9 

133 

104.8 

81.9 

193 

152.1 

118.8 

253 

199.4 

155.8 

14 

11.0 

08.6 

74 

58.3 

45.6 

134 

105.6 

82.5 

194 

152.9 

119  4 

254 

200.2 

156.4 

15 

11.8 

09.2 

75 

59.146.2 

135 

106.4 

83.1 

195 

153.7 

120.1 

255 

200.9 

157.0 

16 

12.6 

09.9 

76 

59.946.8 

136 

107.2 

83.7 

196 

154.5 

120.7 

256 

201.7 

157.6 

17 

13.4 

10.5; 

77 

60.747.4 

137 

108.0 

84.3 

197 

155.2 

121.3 

257 

202.5 

158.2 

18 

14.2 

11.1 

78 

61.548.0 

138 

108.7 

85.0 

198 

156.0 

121.9 

258 

203.3 

158.8 

19 

15.0 

11.7 

79 

62  348.6 

139 

109.5 

85.6 

199 

156.8 

122.5 

259 

204.1 

159.5' 

20 

15.8 

12.3 

80 

63.049  3 

140 

110.3 

86.2 

200 

157.6 

123.1 

260 

204.9 

160.1 

21 

16.5 

1279 

81 

63.849.9 

141 

111.1;     86.8 

201 

158.4 

123.7 

261 

205  7 

160.7' 

22 

17.3 

13.5 

82 

G4.G50.5 

142 

111.9     87.4 

202 

159.2 

124.4 

262 

206.5 

161.3 

23 

18.1 

14.2 

83 

65.451.1 

143 

112.7     8S.O 

203 

160.0 

125.  0: 

263 

207.2 

161.9 

24 

18.9 

14.8 

84 

66.2 

51.7 

144 

113.5 

88.7 

204 

160.8 

125.6 

264 

208.0 

162.5 

25 

19.7 

15.4 

85 

67.0 

52.3 

145 

114.3 

89.3 

205 

161.5 

126.2 

265 

208.8 

1G3.2 

26 

20.5 

1G.O 

8G 

67.852.9 

146 

115.0 

89.9 

206 

162.3 

126.8 

266 

209.6 

163.8 

27 

21  3 

16.6 

87 

68.6 

53.6 

147 

115.8 

90.5 

207 

163.1 

127.4 

267 

210.4 

164.4 

28 

22.1 

17.2 

88 

69.  b 

54.2 

148 

116.6 

91.1 

208 

163.9 

128.1 

268 

211.2 

1G5.0 

29 

22.9 

17.9 

89 

70.1 

54.8 

149 

117.4 

91.7    209 

164.7 

128.7 

269 

212  0 

165.6 

30 

23.6 

18.5 

90 

70.955.4 

150 

118.2 

92.3    210 

165.5 

129.3 

270 

212.8 

1GG.2 

31 

24.4J19.1 

91 

71.7 

56.0 

151 

119.0     93.01  211 

166.3 

129.9 

271 

213.6 

166.8 

32 

25.219.7 

92 

72.5 

56.6 

152 

119.8     93.6    212 

167.1 

130.5 

272 

214  3 

167.5 

33 

.6.020.3 

93 

73.3 

57.3 

153 

120.6 

94.2 

213 

167.8 

131.1 

273 

215.1 

1G8.1 

34 

26.820.9 

94 

74.1 

57.9 

154 

121.4 

94.8    214 

168  6 

131.8 

274 

215.9 

168.7 

35 

27.621.5 

95 

74.9 

58.5 

155 

122.1 

95.4    215 

169.4 

132.4 

275 

216.7 

169.3 

36 

28.4 

22.2 

96 

75.6 

59.1 

156 

122.9 

96.0 

216 

170.2 

133.0 

276 

217.5 

169.9 

37 

29.222.8 

97 

76.459.7 

157 

123.7 

96.7 

217 

171.0 

133.6 

277 

218.3 

170.5 

38 

29.923.4 

98 

77.260.3 

158 

124.5 

97.3 

218 

171.8 

134  2 

278 

219.1 

171.2 

39 

30.724.0 

99 

78.061.0 

159 

125.3 

97.9 

219 

172.6 

134.8 

279 

219.9 

171.8 

40 

31.524.6 

100 

78.861.6 

160 

126.1 

98.5 

220 

173.4 

135.4 

280 

220.6 

172.4 

41 

32.3 

25.2 

101 

79.662.2 

161 

126.9 

99  1 

221 

174  2 

136.1 

281 

221.4 

173.0 

42 

33.1 

25.9 

102 

80.462.8 

162 

127.7 

99.7 

222 

174.9 

136.7, 

282 

222.2 

173.6 

43 

33.9 

26.5 

103 

81.263.4 

163 

128.4 

100.4 

223 

175.7 

137.3 

283 

223.0 

174.2 

44 

34.727.1 

104 

82  064.0 

164 

129  2 

101.0 

224 

176.5 

137.9 

284 

223.8 

174.8 

45 

35.527.7 

105 

82.7G4.6 

165 

130.0 

101.6 

225 

177.3 

138.5 

285 

224.6 

175.5 

46  ;36.228.3 

106 

83  565.3 

166 

130  8 

102.2 

226 

178.1 

139.1 

286 

225.4 

176.1 

-17   37.028.9 

107 

84.365.9 

167 

131.6 

102.8 

227 

178.9 

138.8 

287 

226.2 

176.7 

48  37.829.6 

108 

85.166.5 

168 

132.4 

103.4 

228 

179.7 

140.4 

288 

226.9 

177.3 

49   38.630.2 

109 

85.967.1 

169 

133.2 

104.0 

229 

180.5 

141.0! 

289 

227.7 

177.9 

50   39.430.8    110 

86.767.7 

170 

134.0 

104.7 

230 

181.2 

141.6 

290 

228.5 

178.5 

51    10.231.4 

111 

87.568.3 

171 

131.7 

105.3 

231 

182.0 

142.2 

291 

229  .  3 

179.2 

52 

41.032.0 

112 

88.369  0 

172 

135.5 

105.9 

232 

182.8 

142.8 

292 

230.1 

179.8 

53 

41.8 

32.6 

113 

89.069.6 

173 

136.3 

106.5 

233 

183.6 

143.4 

293 

230.9 

180.4 

54 

42.6 

33.2 

114 

89.870.2 

174 

137.1 

107.1 

234 

184.4 

144.1 

294 

231.7 

181.0 

55 

43.3 

33.9 

115 

90.670.8 

175 

137.9 

107.7 

235 

185.2 

144.7 

295 

232.5 

181.6 

56 

11.  1 

34.5 

116 

91.471.4 

176 

138.7 

108.4 

236 

186.0 

145.3 

296 

233.3 

182.2 

57 

44.9 

35.1 

117 

92.272.0 

377 

133.5 

109.0 

237 

186.8 

145.9 

297 

234.0 

182.9 

58 

15.  7 

35.7 

118 

93.072.6 

178 

140.3 

109.6 

238 

187.5 

146.5 

298 

234.8 

183.5 

59 

46.5 

36.3 

119 

93.873.3 

179 

141.1 

110.2 

239 

188.3 

147.1 

299 

235.6 

184.1 

60  47.3 

36.9 

120 

94.  C 

73.9 

180 

141.8 

110.8 

240 

189.1 

147.8 

300 

236.4 

184.7 

Dist.!  Dep 

Lat. 

D~isl 

Dep 

Lat. 

iDist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat, 

For  52  Degrees. 

242                                          TABLE  IV. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  39  DEGREES. 

Dist, 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.8 

00.6 

61 

47.4 

38.4 

121 

94.0 

76.1 

181 

140.7 

113.9 

241 

187.3 

151.7 

2 

01.601.3 

62 

48  2 

39.0 

122 

94.8 

76.8 

182 

141.4 

114.5 

242 

188.1 

152.3 

3 

02.3 

01.9 

63 

49.0 

39.6 

123 

95.6 

77.4 

183 

142.2 

115.2' 

243 

188.8 

152.9 

4 

03.1 

02.5 

64 

49.7 

40.3 

124 

96.4 

78.0 

184 

143.0 

115.  8' 

244 

189.6 

153.6 

5 

03.903.1 

65 

50.5 

40.9 

125 

97.1 

78.7 

185 

143.8 

116.4 

245 

190.4 

154.2 

6 

04.703.8 

66 

51.3 

41.5 

126 

97.9 

79.3 

186 

144.5 

117.1 

246 

191.2 

154.8 

7 

03.404  4 

67 

52.1 

42.2 

127 

98  7 

79.9 

187 

145.3 

117.7 

247 

192.0 

155.4 

8 

06.2K)5.0 

68 

52.8 

42.8 

128 

99.5 

80.6 

188 

146.1 

118.3 

248 

192.7 

156.1 

9 

>7.0 

05.7 

69 

53  643.4 

129 

100.3 

81.2 

189 

146.9 

118.9 

249 

193.5 

156.7 

10 

07.8 

06.3 

70 

54.444.1 

130 

101.0 

81.8 

190 

147.7 

119.  6' 

250 

194.3 

157.3 

11 

08  5 

0(5.9 

71 

35.2 

44.7 

131 

101.8 

8^.4 

191 

148.4 

120.2 

251 

195.1 

158.0 

12 

J9.3 

07.6 

72 

56.0 

45.3 

132 

102.6 

83.1 

'192 

149.2 

120.8 

252 

195.8 

158.6 

13 

10.1 

08.2 

73 

56.7 

45.9 

133 

103.4 

83.7 

193 

150.0 

121.5, 

•553 

196.6 

159.2 

14 

Kh  9 

08.8 

74 

57.5 

46.6 

134 

104.1 

84.3 

194 

150.8 

122.1' 

254 

197.4 

159.8 

15 

11.7 

09.4 

75 

58.3 

17.2 

135 

104.9 

85.0 

195 

151.5 

122.  7, 

255 

198.2 

160.5 

16 

12.4 

10.1 

76 

59.1 

47.8 

136 

105.7 

85.6 

196 

152.3 

123.3 

256 

198.9 

161.1 

17 

13.2 

10.7 

77 

39.848.5 

137 

106.5 

86.2 

197 

153.1 

124.0 

257 

199.7 

161.7 

18 

14.0 

11.3 

78 

60  649.1 

138 

107.2 

86.8 

198 

153.9 

124.  6! 

258 

200.5 

162.4 

19 

14.8 

L2.0 

79 

61.4 

49.7 

139 

108.0 

87.5 

199 

154.7 

125.2 

259 

201.3 

163.0 

20 

15.5 

12.6 

80 

62.2 

50.3 

140 

108.8 

88.1 

200 

155.4 

125.9 

260 

202.1 

163.6 

•ZL 

10.  -3 

13/2 

81 

62.9 

51.0 

141 

109.6 

88.7 

201 

156.2 

126.5 

261 

202.8 

164.3 

22 

17.1 

13.8 

82 

63.7 

51.6 

142 

110.4 

89  4 

202 

157.0 

127.1 

262 

203.6 

164.9 

23 

17.9 

14.5 

83 

64.5 

52.2 

143 

111.1 

90.0 

203 

157.8 

127.8 

263 

204.4 

165.5 

24 

18.7 

15.1 

84 

65.3 

52.9 

144 

111.9 

90.6 

204 

158.5 

128.4 

264 

205.2 

166.1 

25 

19.4 

15.7 

85 

66.1 

53.5 

145 

112.7 

91.3 

205 

159.3 

129.0 

265 

205.9 

166.8 

26 

:o  2 

16.4 

86 

66  8 

54.1 

146 

113.5 

91.9 

206 

160.1 

129.6 

266 

206.7 

167  4 

27 

21.0 

17.0 

87 

67.6 

54.8 

147 

114.2 

92.5 

207 

160.9 

130.3 

267 

207.5 

168.0 

28 

21.8 

17.6 

88 

68.4 

55.4 

148 

115  0 

93.1 

208 

161.6 

130.9 

268 

208.3 

168.7 

29 

22.5 

18.3 

89 

G9.2 

56.0 

149 

115.8 

93.8 

209 

162.4 

131.5 

269 

209  1 

169.3 

30 

23.3 

18.9 

90 

69.9 

56.6 

150 

116.6 

94.4 

210 

163.2 

132.2 

270 

209.8 

169.9 

31 

24.1 

19.5 

91 

70.7 

57.3 

151 

117.3 

95.0 

211 

164  0 

132.8 

271 

210.6 

170.5 

32 

24.9 

20.1 

92 

71.5 

57.9 

152 

118.1 

95.7 

212 

164.8 

133.4 

272 

211.4 

171.2 

33 

25.6 

20.8 

93 

72.3 

58.5 

153 

118.9 

96.3 

213 

165.5 

134.0 

273 

212.2 

171.8 

34 

26.4 

21.4 

94 

73  1 

59.2 

154 

119.7 

96.9 

214 

166.3 

134.7 

274 

212.9 

172.4 

35 

27.2 

22.0 

95 

73.8 

59.8 

155 

120.5 

97.5 

215 

167.1 

135.3 

275 

213.7 

173.1 

36 

28.0 

22.7 

90 

74.660.4 

156 

121.2 

98.2 

216 

167.9 

135.9 

276 

214.5 

173.7 

37 

28.8 

23.3 

97 

75.461.0 

157 

122.0 

98.8 

217 

168.6 

136.6 

277 

215.3 

174.3 

38 

29.5 

23.9 

98 

76.261.7 

158 

122.8 

99.4 

218 

169.4 

137.2 

278 

216.0 

175  0 

39 

30.3 

24.5 

99 

76.962.3 

159 

123.6 

100.1 

219 

170.2 

137.8 

279 

216.8 

175  6 

40 

31.1 

25.2 

100 

77.762.9 

160 

124.3 

100.7 

220 

171.0 

138.5 

280 

217.6 

176.2 

41 

31.9 

25.  8 

101 

78.563.6 

161 

125  .  1 

101.3 

221 

171.7 

139.1 

281 

218.4 

176.8 

42 

32.6 

26.4 

102 

79.364.2 

162 

125.9 

101.9 

222 

172.5 

139.7 

282 

219.2 

177.5 

43 

33.4 

27.1 

103 

80.064.8 

163 

126.7 

102.6 

223 

173.3 

140.3 

283 

219.9 

178.1 

44 

34.2 

27.7 

104 

80.865.4 

164 

127.5 

103.2 

224 

174.1 

141.0 

284 

220.7 

178.7 

45 

35.0 

28.3 

105 

81.666.1 

165 

128.2 

103.8 

225 

174.9 

141.6 

285 

221.5 

179.4 

46 

35.7 

28.9 

106 

82.466.7 

166 

129.0 

104.5 

226 

175.6 

142.2 

286 

222.3 

180.0 

47 

36.5 

29.6 

107 

83.267.3 

167 

129.8 

105  1 

227 

176.4 

142.9 

287 

223.0 

180.6 

48 

37.3 

30.2 

108 

83.968.0 

168 

130.6 

105.7 

228 

177.2 

143.5 

288 

223.8 

181.2 

49 

33.1 

30.8 

109 

84.768.6 

169 

131.3 

106.4 

229 

178.0 

144.1 

289 

224.6 

181.9 

50 

38.9 

31  5 

110 

85.569.2 

170 

132.1 

107.0 

230 

178.7 

144.7 

290 

225.4 

182.5 

51 

39.6 

32.1 

111 

86.369.9 

171 

132.9 

107.6 

231 

179.5 

145.4 

291 

226  .  1 

183.1 

52 

JO.  4 

32.7 

112 

87.070.5 

172 

133.7 

108.2 

232 

180.3 

146.0 

292 

226.9 

183.8 

53 

il.2 

33.4 

113 

87.871.1 

173 

134.4 

108.9 

233 

181.1 

146.6 

293 

227.7 

184.4 

54 

42.0 

34.0 

114 

88.671.7 

174 

135.2 

109.5 

234 

181.9 

147.3 

294 

228.5 

185.0 

55 

42.7 

34.6 

115 

89.472.4 

175 

136.0 

110.1 

235 

182.6 

147.9 

295 

229.3 

185.6 

56 

43.5 

35.2 

116 

90.173.0 

176 

136.8 

110.8 

236 

183.4 

148.5 

296 

230.0 

186.3 

57 

44.3 

35.9 

117 

90.9 

73.6 

177 

137.6 

111.4 

237 

184.2 

149.1 

297 

230.8 

186.9 

58 

45.1 

36.5 

118 

91.7 

74  3 

178 

138.3 

112.0 

238 

185.0 

149.8 

298 

231.6 

187.5 

59 

45.9 

37.1 

11992.5 

74.9 

179 

139.1 

112.6 

239 

185.7 

150.4 

299 

232.4 

188.2 

60 

46.6 

37.8 

120 

93.3 

75.5 

180 

139.9 

113.3 

240 

186,5 

151.0 

300 

233.1 

188.8 

Dist. 

Dep 

Lat. 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

For  51  Degrees. 

TABLE  IV.                                           243 

DIFFERENCE  OF    LATITUDE   AND  DEPARTTTBE    FOR  40  DEGREES. 

Dist. 

Lat. 

[)ep 

list.  Lat.!  Dep  Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

DO.  8 

00.  C 

61 

40.739.2 

121 

92.7 

77.8 

181 

138.7 

116.3 

241 

184.6 

154.9 

2 

01.5 

01.3 

62  47.  5:39.9' 

122 

93.5 

78.4 

182 

139.4 

117.0 

242 

185.4 

155.6 

3 

[)2.3 

01.9 

6348.340.5 

123 

94.2 

79.1 

183 

140.2 

117.6 

243 

186.1 

156.2 

4 

03.1 

02.0 

64  49.  dil.l 

124 

95.0 

79.7 

184 

141.0 

118.3 

244 

186.9 

156.8 

5 

13.8 

03.2 

6549.8.41.8 

125 

95.8 

80.3 

185 

141.7 

118.9 

245 

187.7 

157.5 

6 

)4.6 

03.  y 

6650.642.4 

126 

96.5 

81.0 

180 

142.5 

119.6 

246 

188.4 

158.1 

7 

05.4 

04.5 

67 

31.343.1 

127 

97.3 

81.6 

187 

143.3 

120.2 

247 

189.2 

158.8 

8  06.1 

05.1 

68 

52.143.7 

128 

98.1 

82.3 

188 

144.0 

120.  8| 

248 

190.0 

159.4 

9 

06.9 

05.8 

6952.944.4 

129 

98.8 

82.9 

189 

144.8 

121.5 

249 

190.7 

100.1 

10 

37.7 

06.4 

7053.645.0 

130 

99.6 

83.  C 

190 

145.5 

122.1 

250 

191.5 

160.7 

11 

U8.4 

07.1 

71 

34.4i45.6 

131 

1U0.4 

84.2 

191 

146.3 

122.8 

251 

192.3 

161.3 

12 

09.2 

07.7 

72 

55.246.3 

132 

101.1 

84.8 

192 

147.1 

123.4 

252 

193.0 

162.0 

13 

10.  0 

08.4 

73 

55.946.9 

133 

101  9 

85.5 

193 

147.8 

124.1 

253 

193.8 

162.6 

14 

10.7 

09.0 

74 

56.747.6 

134 

102.6 

86.1 

194 

148.0 

124.7 

254 

194.6 

163.3 

15 

11.5 

09.6 

75 

57.548.2 

135 

103.4 

86.8 

195 

149.4 

125.3 

255 

195.3 

163.9 

16 

12.3 

10.3 

76 

58.248.9 

136 

104.2 

87.4 

196 

150.1 

126.0 

256 

196.1 

164.6 

17 

13.0 

10.9 

77 

39.049.5 

137 

104.9 

88.1 

197 

150.9 

126.6 

257 

196.9 

165.2 

18 

13.8 

11.6 

78 

59.850.1 

138 

105.7 

88.7 

198 

151.7 

127.3 

258 

197.6 

165.8 

19 

14.6 

12.2 

79 

GO.550.81 

139 

106.5 

89.3 

199 

152.4 

127.9 

259 

198.4 

166.5 

20 

15.3 

12.9 

80 

61.351.4 

140 

107.2 

90.0 

200 

153.2 

128.6 

260 

199.2 

167.1 

21 

16.1 

13.5 

81 

62.  0,52.  1| 

141 

108.0 

90.6 

201 

154.0 

129.2 

261 

199.9 

167.8 

22 

16.9 

14.1 

82 

62.852.7 

142 

108.8 

91  3 

202 

154.7 

129.8 

26'2 

200.7 

168.4 

23 

17.6 

14.8 

83 

63.653.4 

143 

109.5 

91.9 

203 

155.5 

130.5 

263 

201.5 

169.1 

24 

18.4 

15.4 

84 

64.354.0 

144 

110.3 

92.6 

204 

156.3 

131.1 

264 

202.2 

169.7 

25 

19.2 

16.1 

85 

65.154.6 

145 

111.1 

93.2 

205 

157.0 

131  8 

265 

203.0 

170.3 

26 

19.9 

16.7 

86 

65.955.3 

146 

111.8 

93.8 

206 

157.8 

132.4 

266 

203.8 

171.0 

27 

20.7 

17.4 

87 

G6.655.9 

147 

112.6 

94.5 

207 

158.6 

133.1 

267 

204  5 

171.6 

28 

21.4 

18.0 

88 

G7.4'56.6 

148 

113.4 

95.1 

208 

159.3 

133.7 

268 

205.3 

172.3 

29 

22.2 

18.6 

89 

63.257.2 

149 

114.1 

95.8 

209 

160.1 

134.3 

269 

208.1 

172.9 

30 

23.0 

19.3 

90 

68.957.9 

150 

114.9 

96.4 

210 

160.9 

135.0 

270 

206.8 

173.6 

31 

23.7 

19.9 

91 

69.758.5 

151 

115.7 

97.1 

211 

101.6 

135.6 

271 

207.6 

174.2 

32 

24.5 

20.6 

9270.559.1 

152 

116.4 

97.7 

212 

162.4 

136.3 

272 

208.4 

174.8 

33 

25,3 

•21.2 

9371.259.8 

153 

117.2 

98.3 

213 

163.2 

136.9 

273 

209.1 

175.5 

34 

26.0 

21.9 

9472.060.4 

154 

118.0 

99.0 

214 

163.9 

137.6 

274 

209.9 

176.1 

33 

26.8 

22.5 

9572.961.1 

155 

118.7 

99.0 

215 

164.7 

138.2 

275 

210.7 

176.8 

33 

27.6 

23.1 

9073.561.7 

156 

119.5 

100.3 

216 

165.5 

138.8 

276 

211.4 

177  .4 

37 

28.3 

23.8 

9774.372.4 

157 

120.3 

100.9 

217 

166.2 

139.5 

277 

212.2 

178.1 

38 

•29.1 

24.4 

9875.163.0 

158 

121.0 

101.6 

218 

167.0 

140.1 

278 

213.0 

178.7 

39 

29.9 

25.1 

9975.863.0 

159 

121.8 

102.2 

219 

107.8 

140.8 

27.9 

213.7 

179  3 

40 

30.6 

25  .  7 

10076.664.3 

160 

122.6 

102.8 

220 

108.5 

141.4 

280 

214.5 

180.0 

41 

31.4 

•26.4 

10177.404.9 

161 

123.3 

103.5 

221 

169.3 

142.1 

281 

215.3 

180.6 

42 

32.2 

27.0 

10278.165.6 

162 

124.1 

104.1 

222 

170.1 

142.7 

282 

216.0 

181.3 

43 

32.9 

•27.6 

10378.966.2 

163 

124.9 

104.8 

223 

170.8 

143.3 

283 

216.8 

181.9 

44 

33.7 

28.3 

10479.7G6.8 

164 

125.6 

105.4 

224 

171.6 

144.0 

284 

217.0 

182.6 

43 

34.5 

28.9 

10580.467.5 

165 

126.4 

106.1 

225 

172.4 

144.6 

285 

218.3 

183.2 

46 

35.2 

29.6 

10681.268.1 

166 

127.2 

106.7 

226 

173.1 

145.3 

286 

219.1 

183.8 

47 

36.0 

30.2 

107  82.  068.  8 

167 

127.9 

107.3 

227 

173.9 

145.9 

287 

219.9 

184.5 

48 

36.8 

30.9 

10882.769.4 

168 

128.7 

108.0 

228 

174.7 

146.6 

288 

220.6 

185.1 

49 

37.5 

31.5 

10983.5,70.1 

109 

129.5 

108.6 

229 

175.4 

147.2 

28!) 

221.4 

185.8 

50 

38.3 

32.1 

11084.370.7 

170 

130.2 

109.3 

230 

176.2 

147.8 

290 

222.2 

186.4 

~sT 

39.1 

32.8 

11185.071.3 

171 

131.0 

109.9 

231 

177.0 

148.5 

291 

222.9 

187.1 

52 

39.8 

33.4 

11285.872.0 

172 

131.8 

110.0 

232 

177.7 

149.1 

292 

223.7 

187.7 

53 

40.6 

34.1 

11386.  C72.G 

173 

132.5 

111.2 

233 

178.5 

149.8 

293 

224.5 

188.3 

54 

41.4 

34.7 

11487.373.3 

174 

133.3 

111.8 

234 

179.3 

150.4 

294 

225.2 

189.0 

55 

42.1 

35.4 

11588.173.9 

175 

134.1 

112.5 

235 

180.0 

151.1 

295 

226.0 

189.6 

56 

12.9 

36.0 

11688.974.6 

176 

134.8 

113.1 

236 

180.8 

151.7 

290 

226.7 

190.3 

57 

43.1 

36.6 

1  17  89.  r,  75.  2 

177 

135.6 

113.8 

237 

181.6 

152.3 

297 

227.5 

190.9 

58 

44.4 

37.3 

11890.475.8 

178 

136.4 

114.4 

238 

182.3 

153.0 

298 

228.3 

191.6 

59 

45.2 

37.9 

11991.276.5 

179 

137.1 

115.1 

239 

183.1 

153.6 

299 

229.0 

192.2 

60 

46.0 

38  6 

12C 

91.977.1 

180 

137.9 

115.7 

240 

183.9 

154.3 

300 

229.8 

192.8 

Dist  Dep 

Lat 

Dist 

Dep  Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat.  !;Dist. 

Dep. 

Lat, 

For  50  Degrees. 

244                                         TABLE  IV. 

DIFFERENCE    OP   LATITUDE  AND  DEPARTURE  FOR  41  DEGREES. 

Dist, 

Lat. 

Dep 

Dist.  Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

l 

00.6 

00.7 

6116.0 

40.0 

121 

91.3 

79.4 

181 

136.6 

118.7 

241 

181.9 

158.1 

2 

01.5 

01.3 

6246.8 

40.7 

122 

92.1 

80.0 

182 

137.4 

119.4 

242 

182.6 

158.8 

3 

D2.3 

02.0 

6347.5 

41.3 

123 

92.8 

80.7 

183 

138.1 

120.1 

243 

183.4 

159.4 

4 

03.0 

02.6 

6448.3 

42.0 

124 

93.6 

81.4 

184 

138.9 

120.7 

244 

184.1 

160.1 

5 

03.8 

03.3 

6549.1 

42.  G 

125 

94.3 

82.0 

185 

139.6 

121.4 

245 

184.9 

160  7 

6 

04.5 

03.9 

6649.8 

43.3 

126 

95.1 

82.7 

186 

140.4 

122.0 

246 

185.7 

161.4 

7 

05.3 

04.6 

6750.6 

44.0 

127 

95.8 

83.3 

187 

141.1 

122.7 

247 

186.4 

162.0 

8 

06.005.2 

6851.3 

44.6 

128 

96.6 

84.0 

188 

141.9 

123.3 

248 

187.2 

162.7 

9 

06.  & 

05.9 

6952.1 

45.3 

129 

97.4 

84.6 

189 

142.6 

124.0 

249 

187.9 

163.4 

10 

07.5 

06.6 

7052.8 

45.9 

130 

98.1 

85.3 

190 

143  4 

124.7 

250 

188.7 

164.0 

11 

08.3 

07.2 

7153.6 

46.6 

131 

98  9 

85.9 

191 

144.1 

125  3 

251 

189.4 

104.7 

12 

09.1 

07.9 

7254.3 

47.2 

132 

99.6 

86.6 

192 

144.9 

126.0 

252 

190.2 

165.3 

13 

09.8 

08.5 

7355.1 

47.9 

133 

100.4 

87.3 

193 

145.7 

126.6 

253 

190.9 

166.0 

14 

10.  C 

09.2 

7455.8 

48.5 

134 

101.1 

87.9 

194 

146.4 

127.3 

254 

191.7 

166.6 

15 

13.3 

09.8 

7556.  G 

49.2 

135 

101.9 

88.6 

195 

147.2 

127.9 

255 

192  5 

167.3 

16 

12.1 

10  5 

7657.4 

49.9 

136 

102.6 

89.2 

19G 

147.9 

128.6 

256 

193.  i 

168.0 

17 

12.8 

11.2 

7758.1 

0.5 

137 

103  4 

89.9 

197 

148.7 

129  2 

257 

194.0 

168.6 

18 

13.6 

11.8 

7858.9 

51.2 

138 

104.1 

90.5 

198 

149.4 

129.9 

258 

194.7 

169.3 

19 

14.3 

12.5 

7959  6 

51.8 

139 

104.9 

91.2 

199 

150.2 

130.6 

259 

195.5 

1G9  9 

20 

15.1 

13.1 

8060.4 

52.5 

140 

105.7 

91.8 

200 

150  9 

131.2 

260 

196.1 

170  6 

21 

15> 

13.8 

8161.1 

53.1 

141 

10JJ.4 

92.5 

201 

151.7 

131.9 

'261 

197.0 

171.2! 

22 

16  6 

14.4 

8261.9 

53.8 

142 

107.2 

93.2 

202 

152.5 

132.5 

262 

197.7 

171.9' 

23 

17.4 

15.1 

8362.6 

54.5 

143 

107.9 

93.8 

203 

153.2 

133.2 

263 

198  5 

172  5 

24 

18  1 

15.7 

8463  4 

55.1 

144 

108.7 

94.5 

204 

154.  ( 

133.8 

264 

199.2 

173.2 

25 

18.9 

16.4 

8564.2 

55.8 

145 

109.4 

95.1 

205 

154.7 

134.5 

265 

200.0 

173.9 

26 

19.  G 

17.1 

8664.9 

56.4 

146 

110  2 

95.8 

206 

155.5 

135.1 

266 

200.8 

174.5 

27 

•20.4 

17.7 

8765.7 

57.1 

147 

110.9 

96.4 

207 

156.2 

135.8 

267 

201.5 

175.2 

28 

21.1 

18.4 

8866.4 

57.7 

148 

111  7 

97.1 

208 

157.0 

136.5 

268 

202.3 

175  8 

29 

21.9 

19.0 

8967.2 

58  4 

149 

112  5 

97.8 

209 

157.7 

137.1 

269 

203.0 

176.5 

30 

22.6 

19.7 

9067.9 

59.0 

150 

113.2 

98.4 

210 

158.5 

137.8 

270 

203.8 

177.1 

~3T 

23.4 

•20.3 

916N.7 

59.7 

151 

114.0 

99.1 

211 

159.2 

138.4 

271 

204.5 

177.8 

32 

24.2 

21.0 

9269.4 

60.4 

152 

114.7 

99.7 

212 

160.0 

139.1 

272 

205.3 

178.4 

33 

24.9 

21.6 

9370.2 

61.0 

153 

115.5 

100.4 

213 

1G0.8 

139.7 

273 

206  0 

179.1 

34 

25.7 

22.3 

9470.9 

61.7 

154 

116  2 

101.0 

214 

161  5 

140.4 

274 

206.8 

179.8 

35 

26.4 

23.0 

9571.7 

62.3 

155 

117.0 

101.7 

215 

162.3 

141.1 

275 

207.5 

180.4 

36 

27.2 

23.6 

9672.5 

63.0 

156 

117.7 

102.3 

216 

163.0 

141.7 

276 

208.3 

181.1 

37 

27.9 

24.3 

9773.2 

63.6 

157 

118.5 

103  0 

217 

163.8 

142.4 

277 

209.1 

181.7 

38 

28.7 

24.9 

9874.0 

64.3 

158 

119.2 

103.7 

218 

164.5 

143.0 

278 

209.8 

182.4 

39 

29.4 

25.6 

9974.7 

64.9 

159 

120.0 

104.3 

219 

165.3 

143.7 

279 

210.6 

183.0' 

40 

30.2 

26.2 

10075.5 

65.6 

160 

120.8 

105.0 

220 

166.0 

144.3 

280 

211.3 

183.7 

41 

30.9 

26.9 

10176.2 

66.3 

161 

121.5 

105.  G 

221 

166.8 

145.0 

281 

212.1 

184.4 

42 

31.7 

27.6 

10277.0 

66.9 

162 

122.3 

106.  3 

222 

167.5 

145.6 

282 

212.8 

185.0 

43 

32.5 

28  2 

10377.7 

67.6 

163 

123.0 

106.9 

223 

168.3 

146.3 

283 

213.  G 

185.7 

44 

33.2 

28.9 

10478.5 

68.2 

164 

123.8 

107.6 

224 

169.1 

147.0 

284 

214.3 

186.3 

45 

34.0 

29  5 

10579.2 

68.9 

165 

124.5 

108.2 

225 

1G9.8 

147.6 

285 

215.1 

187.0 

40 

34.7 

30.2 

10680.0 

69.5 

16G 

125.3 

108  9 

226 

170.6 

148.3 

286 

215.8 

187.6 

47 

35.5 

30,8 

10780.8 

70.2 

167 

126  0 

109.6 

227 

171.3 

148.9 

287 

216.6 

188.3 

48 

36.2 

31.5 

10881.5 

70.9 

168 

126.8 

110.2 

228 

172.1 

149.6 

288 

217.4 

188.9 

49 

37.0 

32.1 

10982.3 

71.5 

169 

127.5 

110.9 

229 

172.8 

150.2 

289 

218.1 

189.6 

50 

37.7 

32.8 

11083.0 

72.2 

170 

128.3 

111.5 

230 

173.6 

150.9 

290 

218.9 

190.3 

51 

38.5 

33  5 

11183.8 

72.8 

171 

129.1 

112.2 

231 

174.3 

151.5 

291 

219.6 

190.9 

52 

39.2 

34.1 

11284.5 

73.5 

172 

129.8 

112.8 

232 

175.1 

152.2 

292 

220  4 

191.6, 

53 

40.0 

34.8 

11385.3 

74.1 

173 

130.6 

113.5 

233 

175.8 

152.9 

293 

221J 

192  2 

54 

40.8 

35.4 

11486.0 

74.8 

174 

131.3 

114.2 

234 

176.6 

153.5 

294 

221.9 

192.9 

55 

41.5 

36.1 

11586.8 

75.4 

175 

132.1 

114.8 

235 

177.4 

154.2 

295 

222.6 

193.5 

56 

42.3 

36.7 

11687.5 

76.1 

176 

132.8 

115.5 

236 

178.1 

154.8 

296 

223.4 

194  2 

57 

43.0 

37.4 

11788.3 

76.8 

177 

133.6 

116.1 

237 

178.9 

155.5 

297 

224.1 

194  8 

58 

43.8 

38.1 

11889  1 

77.4 

178 

134.3 

116.8 

238 

179.6 

156.1 

298 

224  9 

195.5; 

59 

44.5 

38.7 

11989  8 

78  I 

179 

135.1 

117.4 

239 

180.4 

156.8 

299 

225.7 

196  2 

60 

45.3 

39  4 

12090.6 

78.7 

180 

135.8 

118.1 

240 

181.1 

157.5 

300 

226.4 

196.8 

Oist. 

Dep 

Lat. 

Dist.  Dep 

Lat. 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

Dist, 

Dep. 

Lat. 

For  49  Degrees. 

TABLE  IV.                                          245 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE  FOR  42  DEGREES. 

Dist.  Lat.  Pep  Dist. 

Lat.  Pep  IMst. 

Lat. 

Pep. 

Dist. 

Lat. 

Pep. 

Dist. 

Lat. 

Pep. 

\     '0.700.7' 

61 

15.8*0:8 

121 

89.9 

81.0 

181 

134.5 

121.  1! 

241 

179.1 

161.3 

2   01  501.3 

62 

16.141.5 

122 

90.7 

81.6 

182 

135.3 

121.8! 

242 

179.8 

161.9 

3   02.202.0 

63 

46.8,42  2 

123 

91.4 

82.3 

183 

136.0 

122.5 

243 

180.6 

162.6 

4  03.002.7 

64 

17.642.8 

124 

92.1 

83  0 

184 

136.7 

123  .  1 

244 

181  3 

163.3 

5 

13.703.3 

65 

18.343.5 

125 

92.9 

83.6 

185 

137.5 

123.8 

245 

182.1 

163.9 

6 

04.5  >4.0 

66 

49.044.2 

126 

93.6 

84.3 

186 

138.2 

124.5 

246 

182.8 

164.6 

7 

•5.204.7 

67 

19  844.8 

127 

94.4 

85.0 

187 

139.0 

125.1 

247 

183.6 

165.3 

8 

05.905.4 

68  50  .  5  15  .  5 

128 

95.1 

85.6 

188 

139.7 

125.8 

248 

184.3 

165.9 

9 

06.706.0 

69 

31.346.2 

12!) 

95.9 

86.3 

189 

140.5 

126.5 

249   185.0 

166.6 

10 

07.4-06.7; 

70 

32.046.8 

130 

96.6 

87.0 

190 

141.2 

127.1 

250  185.8 

167.3 

11 

08.207.4 

71 

V2.847.5 

131 

97.4 

87.7 

191 

141.9 

127.8 

251 

186.5 

168.0 

12 

08.9  >8  0 

72 

53.5 

48.2 

132 

98.1 

88.3 

192 

142.7 

128.5 

252 

187.3 

168.6 

13 

09  708.7 

73 

54.2 

48.8 

133 

98.8 

89.0 

193 

143.4 

129.1 

253 

188.0 

169.3 

14 

10.409.4 

74 

55  0 

49.5 

134 

99.6 

89.7 

194 

144.2 

129  8 

254 

188.8 

170.  (i 

15 

11.1  10.  0 

75 

55.7 

50.2 

135 

100  3 

90.3 

195 

144.9 

130.5 

255 

189.5 

170.6 

16 

11.910.7 

76 

56.5 

50.9 

136 

101.1 

91.0 

196 

145.7 

131.1 

256 

190.2 

171.3 

17 

12.6,11.4 

77 

57.2 

51.5 

137 

101.8 

91.7 

197 

146.4 

131.8 

257 

191.0 

172.0 

18 

13.412.0: 

78 

58.0 

52.2 

138 

102.6 

92.3 

198 

147.1 

132.5 

258 

191.7 

172.6 

19 

14.1  12.  7j 

79 

58  7 

52.9 

139 

103.3 

93.0 

199 

147.9 

133.2 

259 

192.5 

173.3 

20 

U.913.4 

80 

59.5 

53  5 

140 

104.0 

93.7 

200 

148.6 

133.8 

260 

193.2 

174.0 

~2T 

15.614.1 

81 

30  254.2 

141 

104.8 

94.3 

201 

149.4 

134.5 

261 

194.0 

174.6 

22 

16.314.7 

82 

30  .  9  54  .  9 

142 

105.5 

95.0 

202 

150.1 

135.2 

262 

194.7 

175.3 

23 

17.1  15.4 

83 

61.755.5 

143 

106.3 

95.7 

203 

150.9 

135.8 

263 

195.4 

176.0 

24 

17.816.1 

84 

62.456.2 

144 

107.0 

96.4 

204 

151.6 

136.5 

264 

196.2 

176.7 

25 

18.616.7 

85 

63.256.9 

145 

107.8 

97.0 

205 

152.3 

137.2 

265 

196.9 

177.3 

2C> 

19.317.4 

86 

63.957.5 

146 

108  5 

97.7 

206 

153.1 

137.8 

266 

197.7 

178.0 

27 

20  1  18.1 

87 

34.7 

58.2 

147 

109.2 

98.4 

207 

153.8 

138  5 

267 

198.4 

178.7 

•js 

20.818.7 

88 

65.4 

58  9 

148 

110.0 

99.0 

208 

154.6 

139.2 

268 

199.2 

179.3 

29 

21.619.4 

89 

66.1 

59.6 

149 

110.7 

99.7 

209 

155.3 

139.8 

269 

199  9 

180.0 

30 

2-2.320.1 

90 

36.9 

60.2 

150 

111.5 

100.4 

210 

156.1 

140.5 

270 

200.6 

180.7 

~3T 

23.0:20.7. 

91 

87.  6]60.9 

151 

112.2   101.0 

211 

156.8 

141  2 

271   201.4 

181.  3j 

32 

23.  8  21.  41 

92 

<58.4'61.6 

152 

113.0 

101.7 

212 

157.5 

141.9 

272  202.1 

182.0! 

33 

.'4.5,22.1 

93 

69.162.2 

153 

113.7 

102.4 

213 

158.3 

142.5 

273 

202.9 

182.7, 

34 

25.322.8 

94 

69.962.9 

154 

114.4 

103.0 

214 

159  0 

143.2 

274 

203.6 

183.3 

35 

26.0'23.4 

95 

70.663.6 

155 

115.2 

103.7 

215 

159  8 

143.9 

275 

204.  4 

184.0 

30  126.824  1 

9(J 

71.364.2 

156 

115.9 

104.4 

216 

160.5 

144.5 

276 

205.1 

X184.7 

37 

27.524.8 

97 

72.164.9 

157 

116  7 

105.1 

217 

161.3 

145.2 

277 

205.9 

185.3 

38 

28.225.4 

98 

72.865.6 

158 

117.4 

105.7 

218 

162.0 

145.9 

278 

206.6 

186.0 

39 

29.026.1 

99 

73.666.2 

159 

118.2 

106.4 

219 

162.7 

146.5 

279 

207.3 

186.7 

40 

29.726.8 

100 

74.3;66.9 

160 

118.9 

107.1 

220 

163.5 

147.2 

280 

208.1 

187.4 

41  J30  5,27.4 

101 

75.1;67.6 

161 

119.6 

107.7 

221 

164.2 

147.9 

2811  208.8 

188.0 

42   31.228.1 

102 

75.868  3 

162 

120.4 

108.4 

222 

165.0 

148.5 

282 

209.6 

188.7 

43   32.0:28.8 

103 

76.568.9 

163 

121.1 

109  .  1 

223 

165.7 

149.2 

283 

210.3 

189.4 

44  32.729.4 

104 

77  369  6 

164 

121  9 

109.7 

224 

166.5 

149.9 

284 

211.1 

190.0 

45   33  4;30.1 

105 

78.070.3 

165 

122.6 

110.4 

225 

167.2 

150.6 

285 

211.8 

190.7 

46   34.230.8 

106 

78  870.9 

166 

123  4 

111.1 

226 

168.0 

151.2 

286 

212.5 

191.4 

47  St.  931.  4 

107 

79.5 

71.6 

167 

124.1 

111.7 

227 

168.7 

151.9 

287 

213.3 

192.0 

48  35.73-2.1 

108 

80.3 

72.3 

168 

124.8 

112.4 

228 

169.4 

152.6 

288 

214.0 

192.7 

49  36.432.8 

109 

81.072.9 

169 

125.6 

113.1 

229 

170.2 

153.2 

289 

214.8 

193.4 

50  37.233.5 

110 

81.7 

73.6 

170 

126.3 

113  8 

230 

170.9 

153.9 

290 

215.5 

194.0 

51 

37.934.1 

111 

82.5 

74.3 

171 

127  .  1 

114.4 

231 

171.7 

154.6 

291 

216.3 

194.7 

52 

38.634.8 

112 

83.2 

74  9 

172 

127.8 

115.1 

232 

172.4 

155.2 

292 

217.0 

195.4 

53 

39.435.5 

113 

84.0 

75.6 

173 

128.6 

115.8 

233 

173.2 

155.9 

293 

217.7 

196.1 

.'.I    10.136.1 

114 

84.7 

76.3 

174 

129.3 

116.4 

234 

173.9 

156.61  294 

218.5 

196.7 

55  40.936.8 

115 

85.5 

77.0 

175 

130.1 

117.1 

235 

174.6 

157.2    295 

219.2 

197.4 

56  41.6,37.6 

116 

86.2 

77.6 

176 

130.8 

117.8 

236 

175.4 

157.9]  296 

220.0 

198.1 

.',7    12.438.1 

117 

86.9 

78.3 

J77 

131.5 

118.4 

237 

176.1 

158.6,  297 

220.7 

198.7 

58 

43.1138.8 

118 

87.7 

79.0 

178 

132.3 

119.1 

238 

176.9 

159.3*  298 

221.5 

199.4 

59 

l;i.  *:!'.»  r, 

119 

88.4 

79.6 

179 

133.0 

119.8 

239 

177.6 

159.91  299 

222.2 

200.1 

60 

44.640.1 

120 

89.2 

80.3 

1HI 

133.8 

120.4 

240 

178.4 

160.6 

300 

222.9 

200.7 

Dist.  Pep  Lat.  Dist. 

Pei> 

Lilt. 

Dist. 

Pep. 

Lat. 

Dist. 

Pep. 

Lat. 

Dist. 

Pep. 

Lat 

For  48  Degrees. 

246                                         TABLE  IV. 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE  FOR  43  DEGREES. 

iDist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat, 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.7 

00.7 

61 

44.6 

41.  6 

121 

88.5 

82.  5' 

181 

132.4 

123.4 

241 

176.3 

164.4 

2 

01.5 

01.4 

62 

45.3 

42.3 

12'2 

89  2 

83.2 

182 

133.1 

1-24.1 

242 

177.0 

165.0 

3 

02.2 

02.0 

63 

46.1 

43.0 

123 

90.0 

83.  91 

183 

133.8 

124.8 

243 

177.7 

165.7 

4 

02.9 

02.7 

64 

46.8 

43.6 

124 

90.7 

84.6 

184 

134.6 

125.5 

244 

178.5 

166.4 

5 

03.7 

03.4 

65 

47.5 

44.3 

125 

91.4 

85.  2i 

185 

135.3 

126.2 

245 

179.2 

167.1 

6 

04.4 

04.1 

66 

48.3 

45.0 

126 

92.2 

85.9 

186 

136.0 

126.9 

246 

179.9 

167.8 

7 

05.1 

04.8 

67 

49.0 

45.7 

127 

92.9 

86.6 

187 

136.8 

127.5 

247 

180.6 

168.5 

8 

05.9 

05.5 

68 

19.7 

46.4 

128 

93.6 

87.3; 

188 

137.5 

128.2 

248 

181.4 

169.1 

9 

06.6 

06.1 

69 

50.5 

47.1 

129 

94.3 

88.0; 

189 

138.2 

128.9 

249 

182.1 

169.8 

10 

07.3 

06.8 

70 

51.2 

47.7 

130 

95  1 

88.  7| 

190   139.0 

129.6 

250 

182.8 

170  5 

11 

08.0 

07.5 

71 

51.9 

48.4 

131 

95.8 

b'9.3 

191 

139.7 

130.3 

251 

183.6 

171.2 

12 

08.8 

08.2 

72 

52.7 

49.1 

132 

96.5 

90.0 

192 

140.4 

130.9 

252 

184.3 

171.9 

13 

09.5 

08.9 

73 

53.4 

49.8 

133 

97.3 

90.  ?! 

193 

141.2 

131.6 

253 

185.0 

172.5 

14 

10.2 

09.5 

74 

o4.1 

50.5 

134 

98.0 

91.4 

194 

141.9 

132  3 

254 

185.8 

173.2 

15 

11.0 

10.2 

75 

54  9 

51.  ] 

135 

98.7 

92.1 

195 

142.6 

133  0 

255 

186.5 

173.9 

16 

11.7 

10.9 

76 

55  6 

51.8 

136 

99.5 

92.8 

196 

143.3 

133.7 

256 

187.2 

174.6 

17 

12  4 

11.6 

77 

56.3 

52.5 

137 

100.2 

93.4 

197 

144.1 

134.4 

257 

188.0 

175.3 

18 

13.2 

12  3 

78 

57.0 

53.2 

138 

100  9 

94.1 

198 

144.8 

135.0 

258 

188.7 

176.0 

19 

13  9 

13.0 

79 

57.8 

53.9 

139 

101.7 

94.8 

199 

145.5 

135.7 

259 

189.4 

176.6 

20 

14.6 

13.6 

80 

58.5 

54.6 

140 

102.4 

95.5 

200 

146.3 

136.4 

260 

190  2 

177.3 

21 

15.4 

14.3 

81 

59.2 

55.2 

141 

103.1 

96.2 

201 

147.0 

137.1 

261 

190.9 

178,0 

22 

16.1 

15  0 

82 

60  0 

55.9 

142 

103.9 

96.8 

202 

147.7 

137.8 

262 

191.6 

178.7 

23 

16.8 

15.7 

83 

60.7 

56.6 

143 

104.6 

97.5 

203 

148.5 

138.4 

263 

192.3 

179.4 

24 

17.6 

16.4 

84 

61.4 

57.3 

144 

105.3 

98.2 

204 

149.2 

139.1 

264 

193.1 

180.0 

25 

18.3 

17.0 

85 

62.2 

58.  (i 

145 

106.0 

98.9 

205 

149.9 

139.8 

265 

193.8 

180.7 

26 

19.0 

17.7 

86 

62.9 

58.7 

146 

106.8 

99.6 

206 

150.7 

140.5 

266 

194.5 

181.4 

27 

19.7 

18.4 

87 

63.6 

59.3 

147 

107.5 

100.3 

207 

151.4 

141.2 

267 

195.3 

182.1 

28 

•20.5 

19.1 

88 

64.4 

60.0 

148 

108.2 

100.9 

208 

152.1 

141.9 

268 

196.0 

182  8 

29 

21.2 

19.8 

89 

65'.  1 

60.7 

149 

109  0 

101.6 

209 

152.9 

142.5 

269 

196.7 

183.5 

30 

21.9 

•20.5 

90 

65.8 

61  4 

150 

109.7 

102.3 

210 

153.6 

143.2 

270 

197.5 

184.1 

31 

•22.7 

21.1 

91 

66.6 

62.1 

151 

110.4 

103.0 

211 

154.3 

143.9 

271 

198.2 

184.8 

32 

•23.4 

21.8 

92 

67.3 

62.7 

152 

111.2 

103.7 

212 

155.0 

144.6 

272 

198.9 

185.5 

33 

24.1 

22.5 

93 

68.0 

63.4 

153 

111.9 

104.3 

213 

155.8 

145  3 

273 

199.7 

186.2 

34 

24.9 

23.2 

94 

68.7 

64.1 

154 

112.6 

105.0 

214 

156.5 

145.9 

274 

200.4 

186.9 

35 

25.6 

•23.9 

95 

69.5 

64.8 

155 

113.4 

105.7 

215 

157.2 

146.6 

275 

201.1 

187.5 

36 

26.3 

24.6 

96 

70.2 

65.5 

156 

114.1 

106  4 

216 

158.0 

147.3 

276 

201.9 

188.2 

37 

27.1 

25.2 

97 

70.9 

66.2 

157 

114.8 

107.1 

217 

158.7 

148.0 

277 

202.  G 

188.9 

38 

27.8 

25.9 

98 

71.7 

66.8 

158 

115.6 

107.8 

218 

159.4 

148.7 

278 

203.3 

189.6 

39 

28.5 

26  6 

99 

72.4 

67.5 

159 

116.3 

108.4 

219 

160.2 

149.4 

279 

204.0 

190.3 

40 

29.3 

27.3 

100 

73.1 

68.2 

160 

117.0 

109.1 

220 

160.9 

150.0 

280 

204.8 

191.0 

41 

30.0 

•28.0 

101 

73.9 

68.9 

161 

117.7 

109.8 

2i!l 

161.6 

150.7 

281 

205.5 

191.6 

42 

30.7 

28.6 

102 

74.6 

69.6 

162 

118.5 

110.5 

222 

162.4 

151.4 

282 

206.2 

192.3 

43 

31.4 

29  3 

103 

75.3 

70.2 

163 

119.2 

111.2 

223 

163.1 

152.1 

283 

207.0 

193.0 

44 

32.2 

30.0 

104 

76.1 

70.9 

164 

119.9 

111.8 

224 

163.8 

152.8 

284 

207.7 

193.7 

45 

32.9 

30.7 

105 

76.8 

71.6 

165 

120.7 

112.5 

225 

164.0 

153  4 

285 

208.4 

194.4 

46 

33.6 

31.4 

106 

77.5 

72.3 

166 

121.4 

113.2 

226 

165.3 

154.1 

286 

209.2 

195.1 

47 

34.4 

32.1 

107 

78.3 

73.0 

167 

122  1 

113.9 

227 

166.0 

154.8 

287 

209.9 

195.7 

48 

35.1 

32.7 

108 

79.0 

73.7 

168 

122.9 

114  6 

22s 

166.7 

155.5 

288 

210.6 

196.4 

49 

35.8 

33.4 

109 

79.7 

74.3 

169 

123.6 

115.3 

2-29 

167.5 

156.2 

289 

211.4 

197.1 

50 

36.6 

34.1 

110 

80.4 

75.0 

170 

124  3 

115.9 

230 

168.2 

156.9 

290 

212.1 

197.8 

51 

37.3 

34.8 

111 

81.2 

75.7 

171 

1*5.1 

116.  6i 

231 

168  .  y 

157  5 

291 

212.8 

198.5 

52 

38.0 

35.5 

112 

81.9 

76.4 

172 

125.8 

117.  31 

232 

169.7 

158  2 

292 

213.6 

199  1 

53 

38.8 

36.1 

113 

82.6 

77.1 

173 

126.5 

118.0 

233 

170.4 

158.9 

293 

214.3 

199.8 

54 

39.5 

36.8 

114 

83.4 

77.7 

174 

127.3 

118.  7i 

234 

171.1 

159.6 

294 

215.0 

200.5 

55 

10  2 

37.5 

115 

84.1 

78  4 

175 

128.0 

119.3 

235 

171.9 

160.3 

295 

215.7 

201.2 

56 

41.0 

38.2 

116 

84.8 

79.1 

176 

128.7 

120.0 

236 

172.6 

161.0 

296 

216.5 

201.9 

57 

41.7 

38  9 

117 

85.6 

79.8 

177 

129.4 

120.7 

237 

173.3 

161.6 

297 

217.2 

202.6 

58 

42.4 

39.6 

11886.3 

80.5 

178 

130.2 

121.4! 

238 

174.1 

162.3 

298 

217.9 

203.2 

59 

43.140  2 

11987.0 

81.2 

179 

130.9 

122.1 

239 

174.8 

163.0 

299 

218.7 

203.9! 

60 

43.9 

40.9 

120 

87.8 

81.8 

180 

131.6 

122.8 

240 

175.5 

163.7 

300 

219.4 

204.6 

Dist. 

Dcp 

Lat. 

Dist. 

Dep 

Lat. 

Dist. 

Dep. 

Lat.    i 

Dist, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  47  Degrees. 

TABLE  IV.                                           247 

DIFFERENCE  OF   LATITUDE  AND  DEPARTURE   FOR  44  DEGREES. 

Dist, 

Lat. 

Dep 

Dist, 

Latfoep 

Dist. 

Lat. 

Dep.    Dist, 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.7 

00.7 

6143.942.4 

121 

87.0 

84.1 

181 

130.2 

125.7 

241 

173.4 

167.4 

2 

01.4 

01.4 

6244.643.1 

122 

87.8 

84.7 

182 

130.9 

126.4 

242 

174.1 

168.1 

3 

02.2 

02.1 

6345.343.8 

123 

88.5 

85.4 

183 

131.6 

127  1 

243 

174.8 

168.8 

4 

02.9 

02.8 

6446.044.5 

124 

89.2 

86.1 

184 

132.4 

127.8 

244 

175.5 

169.5 

5 

03.6 

03.5 

6546.845.2 

125 

89.9 

86.8 

185 

133.1 

128.5 

245 

176.2 

170.2 

6 

04.3 

04.2 

6647.545.8 

126 

90.6 

87.5 

186 

133.8 

129.2 

246 

177.0 

170.9 

7 

05.0 

04.9 

6748.246.5 

127 

91.4 

88.2 

187 

134.5 

129.9 

247 

177.7 

171.6 

8 

05.8 

05.6 

6848.947.2 

128 

92.1 

88.9 

188 

135.2 

130.6 

248 

178.4 

172.3 

9 

06.5 

06.3 

6949.647.9 

129 

92.8 

89.6 

189 

136.0 

131.3 

249 

179.1 

173.0 

10 

07.2 

06.9 

7050.448.6 

130 

93.5 

90.3 

190 

136.7 

132.0 

250 

179.8 

173.7 

11 

07.9 

07.6 

71151.149.3 

131 

94.2 

91.0 

191 

137.4 

132.7 

251 

180.0 

174.4 

12 

08.6 

08.3 

72,51.850.0 

132 

95.0 

91.7 

192 

138.1 

133.4 

252 

181.3 

175.1 

13 

09.4 

09.0 

73,52.550.7 

133 

95  7 

92.4 

193 

138.8 

134.1 

253 

182.0 

175.7 

14 

10.1 

09.7 

7453.251.4 

134 

96.4 

93.1 

194 

139.6 

134.8 

254 

182.7 

176.4 

15 

10.8 

10.4 

75 

54.052.1 

135 

97.1 

93.8 

195 

140.3 

135.5 

255 

183.4 

177.1 

16 

11.5 

11.1 

76 

54.752.8 

136 

97.8 

94.5 

196 

141.0 

136.2 

256 

184.2 

177.8 

17 

12.2 

11.8 

7755.453.5 

137 

98.5 

95.2 

197 

141.7 

136.8 

257 

184.9 

178.5 

18 

12.9 

12.5 

7856.154.2 

138 

99.3 

95.9 

198 

142.4 

137.5 

258 

185.6 

179.2 

19 

13.7 

13.2 

7956.854.9 

139 

100.0 

96.6 

199 

143.1 

138.2 

259 

186.3 

179.9 

20 

14.4 

13.9 

80 

57.555.6 

140 

100.7 

97.3 

200 

143.9 

138.9 

260 

187.0 

180.6 

21 

15.1 

14.6 

81 

58.3i56.3 

141 

101.4 

87.9 

201 

144.6 

139.6 

261 

187.7 

181.3 

22 

15.8 

15.3 

82 

59.057.0 

142 

102.1 

98  6 

202 

145.3 

140.3 

26-2 

188.5 

182.0 

23 

16.5 

16.0 

8359.7 

57.7 

143 

102.9 

99.3 

203 

146.0 

141.0 

263 

189.2 

182.7 

24 

17.3 

16.7 

8460.4 

58.4 

144 

103.6 

100.0 

204 

146.7 

141.7 

264 

189.9 

183.4 

25 

18.0 

17.4 

8561.1 

59.0 

145 

104.3 

100.7 

205 

147.5 

142  4 

265 

190.6 

184.1 

26 

18.7 

18.1 

8661.959.7 

146 

105.0 

101.4 

206 

148.2 

143.1 

266 

191.3 

184.8 

27 

19.4 

18.8 

8762.660.4 

147 

105.7 

102.1 

207 

148.9 

143.8 

267 

192.1 

185.5 

28 

20.1 

19.5 

8863.361.1 

148 

106.5 

102.8 

208 

149.6 

144.5 

268 

192.8 

186.2 

29 

20.9 

20.1 

8964.  061.  & 

149 

107.2 

103.5 

209 

150.3 

145.2 

269 

193.5 

186.9 

30 

21.6 

20.8 

9064.762.5 

150 

107.9 

104.2 

210 

151.1 

145.9 

270 

194.2 

187.  Gj 

31 

22.3 

21.5 

91G5.563.2 

151 

108.6 

104.9 

211 

151.8 

146.6 

271 

194.9 

188.3 

32 

23.0 

22.2 

9266.263.9 

152 

109.3 

105.6 

212 

152.5 

147.3 

272 

195.7 

188.9 

33 

23.7 

22.9 

9366.9,64.6 

153 

110.1 

106.3 

213 

153.2 

148.0 

273 

196.4 

189.6 

34 

24.5 

23.6 

9467.665.3 

154 

110.8 

107.0 

214 

153.9 

148.7 

274 

197.1 

190.3 

35 

25.2 

24.3 

9568.366.0 

155 

111.5 

107.7 

215 

154.7 

149.4 

275 

197.8 

191.0 

36 

25.9 

25.0 

9669.1 

66.7 

156 

112.2 

108.4 

216 

155.4 

150.0 

276 

198.5 

191.7 

37 

26.6 

25.7 

97  69.  8 

67.4 

157 

112.9 

109.1 

217 

156.1 

150.7 

277 

199.3 

192.4 

38 

27.3 

26.4 

9870.5 

68.1 

158 

113.7 

109.8 

218 

156.8 

151.4 

278 

200.0 

193.1 

39 

28.1 

27.1 

9971.268.8 

159 

114.4 

110.5 

219 

157.5 

152.1 

279 

200.7 

193  8 

40 

28.8 

27.8 

10071.  9,69.  5 

160 

115.1 

111  1 

220 

158.3 

152.8 

280 

201.4 

194.5 

41 

29.5 

28.5 

101 

72.7 

70.2 

161 

115.8 

111.8 

221 

159.0 

153.5 

281 

202.1 

195.2 

42 

30.2 

29.2 

102 

73.4 

70.9 

162 

116.5 

112.5 

222 

159.7 

154.2 

282 

202.9 

195.9 

43 

30.9 

29.9 

10374.1 

71.5 

163 

117.3 

113.2 

223 

160.4 

154.9 

283 

203.6 

196.6 

44 

31.7 

30.6 

104i74.8 

72.2 

164 

118.0 

113.9 

224 

161.1 

155.6 

284 

204.3 

197.3 

45 

32.4 

31.3 

10575.5 

72.9 

165 

118.7 

114.6 

225 

161.9 

156.3 

285 

205.0 

198.0 

46 

33.1 

32.0 

10676.3 

73.6 

166 

119.4 

115.3 

226 

162.6 

157.0 

286 

205.7 

198.7 

47 

33.8 

32.6 

10777.0 

74.3 

167 

120.1 

116:0 

227 

163.3 

157.7 

287 

206.5 

199.4 

48 

34.5 

33.3 

10877.7 

75.0 

168 

120.8 

116.7 

228 

164.0 

158.4 

288 

207.2 

200.1 

49 

35.2 

34.0 

10978.4 

75.7 

169 

121.6 

117.4 

229 

164.7 

159.1 

289 

207.9 

200.8 

50 

36.0 

34.7 

11079.176.4 

170 

122.3 

118.1 

230 

165.4 

159.8 

290 

208.6 

201.5 

51 

36.7 

35.4 

111 

79.877.1 

171 

123.0 

118.8 

231 

166.2 

160.5 

291 

209.3 

202.1 

52 

37.4 

36.1 

11280.677.8 

172 

123.7 

119.5 

232 

166.9 

161.2 

292 

210.0 

202.8 

53 

38.1 

36.8 

11381.378.5 

173 

124.4 

120.2 

233 

167.6 

161.9 

293 

210.8 

203.5 

54 

38.8 

37.5 

114 

82.079.2 

174 

125.2 

120.9 

234 

168.3 

162.6 

294 

211.5 

204.2 

55 

39.6 

38.2 

115 

82.7 

79.9 

175 

125.9 

121.6 

235 

169.0 

163.2 

295 

212.2 

204.9 

56 

40.3 

38.9 

116 

83.4 

80.6 

176 

126.6 

122.3 

236 

169.8 

163.9 

296 

212.9 

205.6 

57 

41.0 

39.6 

117 

84.2 

81.3 

177 

127.3 

123.0 

237 

170.5 

164.6 

297 

213.6 

206.3 

58 

41.7 

40  3 

118 

84.982.0 

178 

128.0 

123.6 

238 

171.2 

165.3 

298 

214.4 

207.0 

59 

42.4 

41.0 

119 

85.682.7 

179 

128.8 

124.3 

239 

171.9 

166.0 

299 

215.1 

207.7 

60 

43  2 

41.7 

120 

86.3 

83.4 

180 

129  5 

125.0 

240 

172.6 

166.7 

300 

215.8 

208.4 

Dist. 

Dep 

Lat. 

Dist, 

Dep 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dep. 

Lat, 

For  4G  Degrees. 

248                                         TABLE  IV. 

DIFFERENCE  OF    LATITUDE   AXD  DEPARTURE   FOR  45  DEGREES. 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.7 

00.7 

61 

43.1 

43.1 

121 

85.6 

85.6 

181 

128.0 

128.0 

241 

170.4 

170.4 

2 

01.4 

01.4 

62 

43.8 

43.8 

122 

86.3 

86.3 

182 

128.7 

128.7 

242 

171.1 

171.1 

3 

02.1 

02.1 

63 

44.5 

41.5 

123 

87.0 

87.0 

183 

129.4 

129.4 

243 

171.8 

171.8 

4 

02.8 

02.8 

64 

45.3 

45.3 

124 

87.7 

87.7 

184 

130.1 

130.1 

244 

172.5 

172.5 

5 

03.5 

03.5 

65 

46.0 

46.0 

125 

88.4 

88.4 

185 

130.8 

130.8 

245 

173.2 

]73.2 

6 

04.2 

04.2 

66 

16.746.7 

126 

89.1 

89.1 

186 

131.5 

131.5 

246 

173.9 

173.9 

7 

04.9 

04.9 

67 

47.4 

47.4 

127 

89.8 

89.8 

187 

132.2 

132.2 

247 

174.7 

174.7 

8 

05.7 

05.7 

68 

48.1 

48.1 

128 

90.5 

90.5 

188 

132.9 

132.9 

248 

175.4 

175.4 

9 

06.4 

06.4 

69 

48.8 

48.8 

129 

91.2 

91.2 

189 

133.6 

133.6 

249 

176.1 

176.1 

10 

07.1 

07.1 

70 

49.549.5 

130 

91.9 

91.9 

190 

134.3 

m.3 

250 

176.8 

176.8 

11 

U7.8 

07.8 

71 

50.250.2 

131 

92.6 

92.  ( 

191 

135.1 

135.1 

'251 

177.5 

177.5! 

12 

08.5 

08.5 

72 

50.950.9 

132 

93  3 

93.3 

192 

135.8 

135.8 

252 

178.2 

178.2 

13 

09.2 

09.2 

73 

51.651.6 

133 

94.0 

94.0 

193 

136.5 

136.5 

253 

178.9 

178.9 

14 

09.9 

09.9 

74 

52.352.3 

134 

94.8 

94.8 

194 

137.2 

137.2 

254 

179.6 

179.6 

15 

10.6 

10.6 

75 

53.053.0 

135 

95.5 

95.5 

195 

137.9 

137.9 

255 

180.3 

180.3 

16 

11.3 

11.3 

76 

53.753.7 

136 

96.2 

96.2 

196 

138.6 

138.6 

256 

181.0 

181.0 

17 

12.0 

12.0 

77 

54.454.4 

137 

96.9 

96.9 

197 

139.3 

139.3 

257 

181.7 

181.7 

18 

12.7 

12.7 

78 

55.255.2 

138 

97.6 

97.6 

198 

140.0 

140.0 

258 

182.4 

182.4 

19 

13.4 

13.4 

79 

55.955.9 

139 

98.3 

98.3 

199 

140.7 

140.7 

259 

183.1 

183.1 

20 

14.1 

14.1 

80 

56.656.6 

140 

99.0 

99  0 

200 

141.4 

141.4 

260 

183.8 

183.8 

21 

14.8 

14.8 

81 

57.357.3 

141 

99.7 

99.7 

201 

142.1!  142.1 

261 

184.0 

184.6 

22 

15  6 

15  6 

82 

58.058.0 

142 

100.4 

100.4 

202 

142.8 

142.8 

262 

185. 

185.3 

23 

16.3 

16.3 

83 

58.758.7 

143 

101.1 

101.1 

203 

143.5 

143.5 

263 

186 

186.0 

24 

17.0 

17.0 

84 

59  459.4 

144 

101.8 

101.8 

204 

144.2 

144.2 

264 

186. 

186.7 

25 

17.7 

17.7 

85 

60.160.1 

145 

102.5 

102.5 

205 

145.0 

145.0 

265 

187. 

187.4 

26 

18.4 

18.4 

86 

60.860.8 

146 

103.2 

103.2 

206 

145.7 

145.7 

266 

188. 

183.1 

27 

19.1 

19.1 

87 

61.561.5 

147 

103.9 

103.9 

207 

146.4 

146.4 

267 

188. 

188.8 

28 

19.8 

19.8 

88 

62.262.2 

148 

104.7 

104.7 

208 

147.1 

147.1 

268 

189. 

189  5 

29 

20.5 

20.5 

89 

62.962.9 

149 

105.4 

105.4 

209 

147.8 

147.8 

269 

190. 

190.2 

30 

•21.2 

21.2 

90 

63.6 

63.6 

150 

106.1 

106.1 

210 

148.5 

148.5 

270 

190. 

190  9 

31 

21.9 

21.9 

91 

64.3 

64.3 

151 

106.  b 

106.8 

211 

149.2 

149.2 

271 

191. 

191.0 

32 

22.6 

22.6 

92 

65.1 

65.1 

152 

107.5 

107.5 

212 

149.9 

149.9 

272 

192. 

192.3 

33 

23.3 

23.3 

93 

65.8 

65.8 

153 

108.2 

108.2 

213 

150.6 

150.6 

273 

193. 

193.0 

34 

24.0 

24.0 

94 

66.5 

66.5 

154 

108.9 

108.9 

214 

151.3 

151.3 

274 

193. 

193.7 

35 

24.7 

24.7 

95 

67.2 

67.2 

155 

109.6 

109.6 

215 

152.0 

152.0 

275 

194. 

194.5 

36 

25.5 

25.5 

96 

67.9 

67.9 

156 

110.3 

110.3 

216 

152.7 

152.7 

276 

195. 

195.2 

37 

26.2 

26.2 

97 

68.  6 

68.6 

157 

111.0 

111  0 

217 

153.4 

153.4 

277 

195. 

195.9 

38 

26.9 

26.9 

98 

69.3 

69.3 

158 

111.7 

111.7 

218 

154.1 

154.1 

278 

196. 

196.6 

39 

27.6 

27.6 

99 

70.0 

70.0 

159 

112.4 

112.4 

219 

154.9 

154.9 

279 

197. 

197.3 

40 

28.3 

28.3 

100 

70.7 

70.7 

160 

113.1 

113.1 

220 

155.6 

155.6 

280 

198.0 

198.0 

41 

29.0 

29.0 

101 

71.4 

71.4 

161 

113.8 

113.8 

221 

156.3 

156.3 

281 

198.7 

198.7 

42 

29.7 

29.7 

102 

72.1 

72.1 

162 

114.5 

]14.5 

222 

157.0 

157.0 

282 

199.4 

199.4 

43 

30.4 

30.4 

103 

72.8 

72.8 

163 

115.3 

115.3 

223 

157.7 

157.7 

283 

200.1 

200.1 

44 

31.1 

31.1 

104 

73.5 

73.5 

164 

116.0 

116.0 

224 

158.4 

158.4 

284 

200.8 

200.8 

45 

31.8 

31.8 

105 

74.2 

74.2 

165 

116.7 

116.7 

225 

159.1 

159.1 

285 

201.5 

201.5 

46 

32.5 

32.5 

106 

75.0 

75.0 

166 

117.4 

117  4 

226 

159.8 

159.8 

286 

202.2 

202.2 

47 

33.2 

33.2 

107 

75.7 

75.7 

167 

118  1 

118.1 

227 

160.5 

160.5 

287 

202.9 

202.9 

48 

33.9 

33.9 

108 

76.4 

76.4 

168 

118.8 

118.8 

228 

161.2 

161.2 

288 

203.6 

203.6 

49 

34.6 

34.6 

109 

77.1 

77.1 

169 

119.5 

119.5 

229 

161.9 

161.9 

289 

204.3 

204.3 

50 

35.4 

35.4 

110 

77.8 

77.8 

170 

120.2 

120.2 

230 

162.6 

162.6 

290 

205.1 

205.1 

51 

36.1 

36.1 

111 

78.5 

78.5 

171 

120.9 

120.9 

231 

163.3 

163.3 

291 

205.8 

'2U5  8 

52 

36.8 

36.8 

112 

79.2 

79.2 

172 

121.6 

121.6 

232 

164.0 

164.0 

292 

206  5 

206.5 

53 

37.5 

37.5 

113 

79.979.9 

173 

122.3 

122.3 

233 

164.8 

164.8 

293 

207.2 

207.2 

54 

38.2 

38.2 

114 

80.680.6 

174 

123.0 

123.0 

234 

165.5 

165.5 

294 

207.9 

207.9 

55 

38.9 

38.9 

115 

81.381.3 

175 

123.7 

123.7 

235 

166.2 

166.2 

295 

208.6 

208.6 

56 

39.6 

39.6 

116 

82.082.0 

176 

124.4 

124.4 

236 

166.9 

166.9 

296 

209.3 

209  3 

57 

10.3 

40.3 

117 

82.7 

82.7 

177 

125.2 

125.2 

237 

167.6 

167.6 

297 

210.0 

210  0 

58 

41.0 

41.0 

118 

83  4 

83.4 

178 

125.9 

125.9 

238 

168.3 

168.3 

298 

210.7 

210  7 

59 

41.7 

41.7 

119 

84.1 

84.1 

179 

126.6 

126.6 

239 

169.0 

169.0 

299 

211.4 

211  4 

60 

42  4 

42.4 

12084.9 

84.9 

180 

127.3 

127.3 

240 

169.7 

169.7 

300 

212.1 

212.1 

Dist. 

Dep 

Lat. 

DistJDep 

Lat. 

Dist, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

For  45  Degrees. 

TABLE  V.                 249 

MERIDIONAL  PARTS. 

M. 

0° 

1° 

2° 

3° 

40 

5° 

6° 

70 

8° 

9° 

10° 

11° 

12° 

13° 

14D 

15° 

1C. 

0 

0 

60 

120 

IbO 

240 

300 

361 

421 

482 

542 

003  064 

725 

787 

849 

910 

0 

1 

1 

61 

121 

181 

241 

301 

362 

422 

483 

543 

6041  665 

726 

788 

850 

912 

1 

2 

2 

62 

122 

182 

242 

302 

363 

423 

484 

544 

605 

666 

727 

789 

851 

913 

2 

3 

3 

63 

123 

183 

243 

303 

864 

424 

485 

545 

606 

667 

728 

790 

852 

914 

3 

4 

4 

G4 

124 

184 

244 

304 

365 

425 

486 

546 

607 

668 

729 

791 

853 

915 

4 

5 

5 

65 

125 

185 

245 

305 

366 

426 

487 

547 

608 

669 

730 

792 

854 

916 

5 

6 

6 

66 

126 

186 

246 

306 

367 

427 

488 

548 

609 

670 

731 

793 

855 

917 

6 

7 

7 

67 

127 

187 

247 

307 

368 

428 

489 

549 

610 

671 

732 

794 

856 

918 

7 

8 

8 

68 

128 

188 

248 

308 

369 

429 

490 

550 

611 

672 

734 

795 

857 

919 

8 

9 

9 

69 

129 

189 

249 

309 

370 

430 

491 

551 

612 

673 

735 

796 

858 

920 

9 

10 

10 

70 

130 

190 

250 

3iO 

371 

431 

492 

552 

613 

6V4 

V36 

797 

859 

9J4 

10 

11 

11 

71 

131 

191 

251 

311 

372 

432 

493 

553 

614 

675 

737 

798 

860 

922 

11 

12 

12 

72 

132 

192 

252 

312 

373 

433 

494 

554 

615 

676 

738 

799 

861 

923 

12 

13 

13 

73 

133 

193 

253 

313 

374 

434 

495 

555 

616 

677 

739 

800 

862 

924 

13 

14 

14 

74 

134 

194 

254 

314 

375 

435 

496 

556 

617 

678 

740 

801 

863 

925 

14 

15 

15 

75 

135 

195 

255 

315 

376 

436 

497 

557 

618 

679 

741 

802 

864 

926 

15 

16 

16 

76 

136 

196 

256 

316 

377 

437 

498 

558 

619 

680 

742 

833 

865 

927 

16 

17 

17 

77 

137 

197 

257 

317 

378 

438 

499 

559 

620 

681 

743 

804 

866 

928 

17 

18 

18 

78 

138 

198 

258 

318 

379 

439 

500 

560 

621 

682 

744 

805 

867 

92S 

18 

19 

19 

79 

139 

199 

259 

319 

380 

440 

501 

561 

622 

683 

745 

806 

868 

930 

19 

20 

20 

80 

140 

200 

260 

320 

381 

441 

502 

562 

623 

684 

746 

807 

869 

931 

20 

21 

21 

81 

141 

201 

261 

321 

382 

442 

503 

564 

624 

685 

747 

808 

870 

932 

21 

22 

22 

82 

142 

202 

262 

32-2 

383 

443 

504 

565 

625 

687 

748 

809 

871 

933 

22 

23 

23 

83 

143 

203 

263 

323 

384 

444 

505 

566 

626 

688 

749 

810 

872 

934 

23 

24 

24 

81 

144 

204 

264 

324 

385 

445 

506 

567 

627 

689 

750 

811 

873 

935 

24 

25 

25 

85 

145 

205 

265 

325 

386 

446 

507 

568 

628 

690 

751 

812 

874 

936 

25 

26 

26 

86 

14C 

200 

266 

326 

387 

447 

508 

569 

629 

691 

732 

813 

875 

937 

26 

27 

27 

87 

147 

207 

267 

327 

388 

448 

509 

570 

631 

692 

753 

815 

876 

938 

27 

28 

28 

8S 

148 

208 

268 

328 

389 

449 

510 

571 

632 

693 

754 

816 

877 

939 

28 

29 

29 

89 

149 

209 

269 

330 

390 

450 

511 

572 

633 

694 

755 

817 

878 

941 

29 

30 

30 

90 

150 

210 

270 

331 

391 

451 

512 

573 

634 

695 

756 

"818 

879 

942 

30 

31 

31 

91 

151 

211 

271 

332 

392 

452 

513 

574 

635 

696 

757 

819 

880 

943 

31 

32 

32 

92 

152 

212 

272 

333 

393 

453 

514 

575 

636 

697 

758 

820 

882 

944 

32 

33 

33 

93 

153 

213 

£73 

334 

394 

454 

515 

576 

637 

698 

759 

821 

883 

915 

33 

34 

34 

94 

154 

214 

274 

335 

395 

455 

516 

577 

638 

699 

760 

822 

884 

946 

34 

35 

35 

95 

155 

215 

275 

336 

396 

456 

517 

578 

639 

700 

761 

823 

885 

947 

35 

3G 

36 

96 

156 

216 

276 

337 

397 

457 

518 

579 

640 

701 

762 

824 

886 

948 

36 

37 

37 

97 

157 

217 

277 

338 

39$ 

,458 

519 

580 

641 

702 

763 

825 

887 

949 

37 

38 

38 

98 

158 

218 

278 

339 

399 

459 

520 

581 

642 

703 

764 

826 

888 

950 

38 

39 

39 

99 

159 

219 

279 

340 

400 

460 

521 

582 

643 

704 

765 

827 

889 

951 

39 

40 

40 

10U 

160 

"2M 

280 

341 

401 

461 

522 

583 

644 

705 

766 

8*8 

890 

952 

40 

41 

41 

101 

161 

221 

281 

342 

402 

462 

523 

584 

645 

706 

767 

829 

891 

953 

41 

42 

42 

102 

162 

222 

282 

343 

403 

463 

524 

585 

646 

707 

768 

830 

892 

954 

42 

43 

43 

103 

163 

223 

283 

344 

404 

464 

525 

586 

647 

708 

769 

831 

893 

955 

43 

44 

44 

104 

104 

224 

284 

345 

405 

465 

526 

587 

648 

709 

770 

832 

894 

956 

44 

45 

45 

105 

165 

225 

285 

346 

406 

466 

527 

588 

649 

710 

771 

833 

895 

957 

45 

46 

46 

lOb 

166 

226 

286 

347 

407 

467 

528 

589 

650 

711 

772 

834 

896 

958 

46 

47 

47 

107 

167 

227 

287 

348 

408 

468 

5'29 

590 

651 

712 

773 

835 

897 

959 

47 

48 

48 

108 

168 

228 

288 

349 

409 

469 

530 

591 

652 

713 

774 

836 

898 

960 

48 

49 

49 

10'J 

169 

229 

289 

350 

410 

470 

531 

592 

653 

714 

776 

837 

899 

961 

49 

50 

50 

110 

170 

230 

290 

361 

411 

471 

532 

593 

654 

715 

777 

838 

900 

962 

50 

51 

51 

111 

171 

231 

291 

352 

412 

472 

533 

594 

655 

716 

778 

839 

901 

963 

51 

52 

52 

112 

172 

232 

292 

353 

413 

473 

534 

595 

656 

717 

779 

840 

DOi 

964 

52 

53 

53 

113 

173 

233 

293 

354 

414 

474 

535 

596 

657 

718 

780 

811 

903 

965 

53 

54 

54 

114 

174 

234 

294 

355 

415 

476 

536 

597 

668 

719 

781 

842 

904 

966 

54 

55 

55 

115 

175 

235 

295 

356 

410 

477 

537 

598 

659 

720 

782 

843 

905 

968 

55 

56 

56 

116 

176 

236 

296 

357 

417 

478 

538 

599 

660 

721 

783 

844 

906 

96'. 

56 

57 

57 

117 

177 

237 

297 

358 

418 

479 

539 

600 

661 

722 

784 

845 

907 

970 

57 

58 

58 

118 

178 

238 

298 

359 

41i 

480 

510 

601 

662 

723 

785 

846 

908 

971 

58 

69 

59 

119 

179 

239 

299 

3GO 

4-20 

481 

541 

602 

G63 

724 

786 

847 

909 

972 

59 

M. 

0° 

1° 

2° 

3° 

4J 

5° 

G° 

70 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

ISO 

M. 

250                 TABLE  V. 

MERIDIONAL  PARTS. 

M. 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

M. 

0 

(,)7:i 

1035 

1098 

1161 

1225 

1289 

1354 

1419 

1484 

1550 

1616 

0 

1 

974 

1036 

1099 

1163 

1226 

1290 

1355 

1420 

1485 

1551 

1618 

1 

2 

975 

1037 

1100 

1164 

1227 

1291 

1356 

1421 

1486 

1552 

1619 

2 

3 

976 

1038 

1101 

1165 

1228 

1292 

1357 

1422 

1487 

1553 

1620 

3 

4 

977 

1039 

1102 

1166 

1229 

1293 

1358 

1423 

1488 

1554 

1621 

4 

5 

978 

1041 

1103 

1167 

1230 

1295 

1359 

1424 

1490 

1556 

1622 

5 

6 

979 

1042 

1105 

1168 

1232 

1290 

1360 

1425 

1491 

1557 

1623 

6 

7 

980 

1043 

1106 

1169 

1233 

1297 

1361 

1426 

1492 

1558 

1624 

7 

8 

981 

1044 

1107 

1170 

1234 

1298 

1362 

1427 

1493 

1559 

1625 

8 

9 

982 

1045 

1108 

1171 

1235 

1299 

1363 

1428 

1494 

1560 

1626 

9 

10 

983 

1046 

1109 

1172 

1236 

1300 

1364 

1430 

1495 

1561 

1628 

10 

11 

984 

1047 

1110 

1173 

1237 

1301 

1366 

1431 

1496 

1562 

1629 

11 

12 

985 

1048 

1111 

1174 

1238 

1302 

1367 

1432 

1497 

1563 

1630 

12 

13 

986 

1049 

1112 

1175 

1239 

1303 

1368 

1433 

1498 

1564 

1631 

13 

14 

987 

1050 

1113 

1176 

1240 

1304 

1369 

1434 

1499 

1565 

1632 

14 

15 

988 

1051 

1114 

1177 

1241 

1305 

1370 

1435 

1500 

1567 

1633 

15 

10 

989 

1052 

1115 

1178 

1242 

1306 

1371 

1436 

1502 

1568 

1634 

16 

17 

990 

1053 

1116 

1179 

1243 

1307 

1372 

1437 

1503 

1569 

1635 

17 

18 

991 

1054 

1117 

1181 

1244 

1308 

1373 

1438 

1504 

1570 

1637 

18 

19 

993 

10.35 

1118 

1182 

1245 

1310 

1374 

1439 

1505 

1571 

1638 

19 

20 

994 

1056 

1119 

1183 

1240 

1311 

1375 

1440 

1506 

1572 

1639 

20 

21 

995 

1057 

1120 

1184 

1248 

1312 

1376 

1441 

1507 

1573 

1640 

21 

22 

996 

1058 

1121 

1185 

1249 

1313 

1377 

1443 

1508 

1574 

1641 

22 

23 

997 

1059 

1122 

1186 

1250 

1314 

1379 

1444 

1509 

1575 

1642 

23 

24 

998 

1060 

1123 

1187 

1251 

1315 

1380 

1445 

1510 

1577 

1643 

24 

25 

999 

1061 

1125 

1188 

1252 

1316 

1381 

1446 

1511 

1578 

1644 

25 

2G 

1000 

1063 

1126 

1189 

1253 

1317 

1382 

1447 

1513 

1579 

1645 

26 

27 

1001 

1064 

1127 

1190 

1254 

1318 

1383 

1448 

1514 

1580 

1647 

27 

28 

1002 

1065 

1128 

1191 

1255 

1319 

1384 

1449 

1515 

1581 

1648 

28 

29 

1003 

1066 

1129 

1192 

1256 

1320 

1385 

1450 

1516 

1582 

1649 

29 

30 

1W04 

1067 

1130 

1193 

1257 

1321 

1386 

1451 

1517 

1583 

1650 

30 

31 

1005 

1068 

1131 

1194 

1258 

1322 

1387 

1452 

1518 

1584 

1651 

31 

32 

1006 

1069 

1132 

1195 

1259 

1324 

1388 

1453 

1519 

1585 

1652 

32 

33 

1007 

1070 

1133 

1196 

1260 

1325 

1389 

1455 

1520 

1586 

1653 

33 

34 

1008 

1071 

1134 

1198 

1261 

1326 

1390 

1456 

1521 

1588 

1654 

34 

35 

1009 

1072 

1135 

1199 

1262 

1327 

1392 

1457 

1522 

1589 

1656 

35 

36 

1010 

1073 

1136 

1200 

1264 

1328 

1393 

1458 

1524 

1590 

1657 

36 

37 

1011 

1074 

1137 

1201 

1265 

1329 

1394 

1459 

1525 

1591 

1658 

37 

38 

1012 

1075 

1138 

1202 

1266 

1330 

1395 

1460 

1526 

1592 

1659 

38 

39 

1013 

1076 

1)39 

1203 

1267 

1331 

1396 

1461 

1527 

1593 

1C60 

39 

40 

1014 

1077 

1140 

1204 

1268 

1332 

1397 

1462 

1528 

1594 

1661 

40 

41 

1015 

1078 

1141 

1205 

1269 

1333 

1398 

1463 

1529 

1595 

1662 

41 

42 

1016 

1079 

1142 

1206 

1270 

133i 

1399 

1464 

1530 

1596 

1G63 

42 

43 

1018 

1080 

1144 

1207 

1271 

1335 

1400 

1465 

1531 

1598 

1664 

43 

44 

1019 

1081 

1145 

1208 

1272 

1336 

1401 

1467 

1532 

1599 

1666 

44 

45 

1020 

1082 

1146 

1209 

1273 

1338 

1402 

1468 

1533 

1600 

1667 

45 

46 

1021 

1084 

1147 

1210 

1274 

1339 

1403 

1469 

1535 

1601 

1668 

46 

47 

1022 

1085 

1148 

1211 

1275 

1340 

1405 

1470 

1536 

1602 

1669 

47 

48 

1023 

1086 

1149 

1212 

1276 

1341 

1406 

1471 

1537 

1603 

1670 

48 

49 

1024 

1087 

1150 

1213 

1277 

1342 

1407 

1472 

1538 

1604 

1671 

49 

50 

1025 

1068 

1151 

1215 

1278 

1343 

1408 

1473 

1539 

1605 

1672 

50 

51 

1026 

1089 

1152 

1216 

1280 

1344 

1409 

1474 

1540 

1606 

1673 

51 

52 

1027 

1090 

1153 

1217 

1281 

1345 

1410 

1475 

1541 

1608 

1675 

52 

53 

1028 

1091 

1154 

1218 

1282 

1346 

1411 

1476 

1542 

1609 

1676 

53 

54 

1029 

1092 

1155 

1219 

1283 

1347 

1412 

1477 

1543 

1610 

1677 

54 

55 

1030 

1093 

1156 

1220 

1284 

1348 

1413 

1479 

1544 

1611 

1678 

55 

5G 

1031 

1094 

1157 

1221 

1285 

1340 

1414 

1480 

1546 

1612 

1679 

56 

57 

1032 

1095 

1158 

1222 

1286 

1350 

1415 

1481 

1547 

1613 

1680 

57 

58 

1033 

1096  1159 

1223 

1287 

1352 

1416 

1482 

1548 

1614 

1681 

58 

59 

1034 

1097  1160 

1224 

1288 

1353 

1418 

1483 

1549 

1615 

1682 

59 

M. 

1G3 

17° 

18J 

19° 

20° 

21° 

22 

23° 

24° 

25° 

2GU 

M. 

TABLE  V.                 251 

MERIDIONAL  PARTS. 

M, 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

M. 

0 

1684 

1751 

1819 

1888 

1958 

2028 

2100 

2171 

2244 

2318 

2393 

0 

1 

1685 

1752 

1821 

1890 

1959 

2030 

2101 

2173 

2246 

2319 

2394 

1 

2 

1686 

1753 

1822 

1891 

1960 

2031 

2102 

2174 

2247 

2320 

2395 

2 

3 

1687 

1755 

1823 

1892 

1962 

2032 

2103 

2175 

2248 

2322 

2396 

3 

4 

1688 

1756 

1824 

1893 

1963 

2033 

2104 

2176 

2249 

2323 

2398 

4 

5 

1689 

1757 

1825 

18J4 

1964 

2034 

2105 

2178 

2250 

2324 

2399 

5 

6 

1690 

1758 

1826 

1895 

1965 

2035 

2107 

2179 

2252 

2325 

2400 

6 

7 

1691 

1759 

1827 

1896 

1966 

2037 

2108 

2180 

2253 

2327 

2401 

7 

8 

1693 

1760 

1829 

1898 

1967 

2038 

2109 

2181 

2254 

2328 

2403 

8 

9 

1694 

1761 

1830 

1899 

1969 

2039 

2110 

2182 

2255 

2329 

2404 

9 

10 

1695 

1762 

1831 

1900 

1970 

2040 

2111 

2184 

2257 

2330 

2405 

10 

11 

1696 

1764 

1832 

1901 

1971 

2041 

2113 

2185 

2258 

2332 

2406 

11 

12 

1697 

1765 

1833 

1902 

.1972 

2043 

2114 

2186 

2259 

2333 

2408 

12 

13 

1698 

1766 

1834 

1903 

1973 

2044 

2115 

2187 

2260 

2334 

2409 

13 

14 

1699 

1767 

1835 

1905 

1974 

2045 

2116 

2188 

2261 

2335 

2410 

14 

15 

1700 

1768 

1837 

1906 

1976 

2046 

2117 

2190 

2263 

2337 

2411 

15 

16 

1701 

1769 

1838 

1907 

1977 

2047 

2119 

2191 

2264 

2338 

2413 

16 

17 

1703 

1770 

1839 

1908 

1978 

2048 

2120 

2192 

2265 

2339 

2414 

17 

18 

1704 

1772 

1840 

1909 

1979 

2050 

2121 

2193 

2266 

2340 

2415 

18 

19 

1705 

1773 

1841 

1910 

1980 

2051 

2122 

2194 

2268 

2342 

2416 

J9 

20 

1706 

1774 

1842 

1912 

1981 

2052 

2123 

2196 

2209 

2343 

2418 

20 

21 

1707 

1775 

1843 

1913 

1983 

2053 

2125 

2197 

2270 

2344 

2419 

21 

22 

1708 

1776 

1845 

1914 

1984 

2054 

2126 

2198 

2271 

2345 

2420 

22 

23 

1709 

1777 

1846 

1915 

1985 

2056 

2127 

2199 

2272 

2346 

2422 

23 

24 

1711 

1778 

1847 

1916 

1986 

2057 

2128 

2200 

2274 

2348 

2423 

24 

25 

1712 

1780 

1848 

1917 

1987 

2058 

2129 

2202 

2275 

2349 

2424 

25 

26 

1713 

1781 

1849 

1918 

1988 

2059 

2131 

2203 

2276 

2350 

2425 

26 

27 

1714 

1782 

1850 

1920 

1990 

2060 

2132 

2204 

2277 

2351 

2427 

27 

28 

1715 

1783 

1852 

1921 

1991 

2061 

2133 

2205 

2279 

2353 

2428 

28 

29 

1716 

1784 

1853 

1922 

1992 

2063 

2134 

2207 

2280 

2354 

2429 

29 

3u 

1717 

1785 

1854 

1923 

1993 

2064 

2135 

2208 

2*81 

2355 

2430 

30 

31 

1718 

1786 

1855 

1924 

1994 

2065 

2137 

2209 

2282 

2356 

2432 

31 

32 

1720 

1787 

1856 

1925 

1995 

2066 

2138 

2210 

2283 

2358 

2433 

32 

33 

1721 

1789 

1857 

1927 

1997 

2067 

2139 

2211 

2285 

2359 

2434 

33 

34 

1722 

1790 

1858 

1928 

1998 

2069 

2140 

2213 

2286 

2360 

2435 

34 

35 

1723 

1791 

1860 

1929 

1999 

2070 

2141 

2214 

2287 

2361 

2437 

35 

36 

1724 

1792 

1861 

1930 

2000 

2071 

2143 

2215 

2288 

2363 

2438 

36 

37 

1725 

1793 

1862 

1931 

2001 

2072 

2144 

2216 

2290 

2364 

2439 

37 

38 

1726 

1794 

1863 

1932 

2002 

2073 

2145 

2217 

2291 

2365 

2440 

38 

39 

1727 

1795 

1864 

1934 

2004 

2075 

2146 

2219 

2292 

2366 

2442 

39 

40 

1729 

1797 

1865 

1935 

2005 

2076 

2147 

2220 

2293 

2368 

2443 

40 

41 

1730 

1798 

1866 

1936 

2006 

2077 

2149 

2221 

2295 

2369 

2444 

41 

42 

1731 

1799 

1868 

1937 

2007 

2078 

2150 

2222 

2296 

2370 

2445 

42 

43 

1732 

1800 

1869 

1938 

2008 

'2079 

2151 

2224 

2297 

2371 

2447 

43 

44 

1733 

1801 

1870 

1939 

2010 

2080 

2152 

2225 

2298 

2373 

2448 

44 

45 

1734 

1802 

1871 

1941 

2011 

2082 

2153 

2226 

2293 

2374 

2449 

45 

46 

1735 

1803 

1872 

1942 

2012 

2083 

2155 

2227 

2301 

2375 

2451 

46 

47 

1736 

1805 

1873 

1943 

2013 

2084 

2156 

2228 

2302 

2376 

2452 

47 

48 

1738 

1806 

1875 

1944 

2014 

2085 

2157 

2230 

2303 

2378 

2453 

48 

49 

1739 

1807 

1876 

1945 

2015 

2086 

2158 

2231 

2304 

2379 

2454 

49 

50 

1740 

IbOS 

1877 

l'J4i> 

2017 

2088 

2109 

2232 

2306 

2380 

2456 

50 

51 

1741 

1809 

1878 

1948 

2018 

2089 

2161 

2233 

2307 

2381 

2457 

51 

52 

1742 

1810 

1879 

1949 

2019 

2090 

2162 

2235 

2308 

2383 

2458 

52 

53 

1743 

1811 

1880 

1950 

2020 

2091 

2163 

2236 

2309 

2384 

2459 

53 

54 

1744 

1813 

1881 

1951 

2021 

2092 

2164 

2237 

2311 

2385 

2461 

54 

55 

1746 

1814 

1883 

1952 

2022 

2094 

2165 

2238 

2312 

2386 

2462 

55 

56 

1747 

1815 

1884 

1953 

2024 

2095 

2167 

2239 

2313 

2388 

2463 

56 

57 

1748 

1816 

1885 

1955 

2025 

2096 

2168 

2241 

2314 

2389 

2464 

57 

58 

1749 

1817 

1886 

1956 

2026 

2097 

2169 

2242 

2316 

2390 

2466 

58 

59 

1750 

1818 

1887 

1957 

2027 

2098 

2170 

2243 

2317 

2391 

2467 

59 

M. 

27° 

28° 

21P 

30° 

31° 

32° 

33° 

34° 

35° 

3G° 

37° 

M. 

252                 TABLE  V. 

MERIDIONAL  PARTS. 

M.   38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

4G° 

47° 

48° 

M. 

0 

2408 

2545 

2023 

27u2 

2782 

2803 

2946 

3U30 

3116 

3203 

3292 

0 

1 

2470 

2546 

2624 

2703 

2783 

2864 

2947 

3031 

3117 

3204 

3293 

1 

2 

2471 

2548 

2625 

2704 

2784 

2866 

2949 

3033 

3118 

3206 

3295 

2 

3 

2472 

2549 

2627 

2706 

2786 

2867 

2950 

3034 

3120 

3207 

3296 

3 

4 

2473 

2550 

2628 

2707 

2787 

2869 

2951 

3036 

3121 

3209 

3298 

4 

5 

2475 

2551 

2629 

2708 

2788 

2870 

2953 

3037 

3123 

3210 

3299 

5 

6 

2476 

2553 

2G31 

2710 

2790 

2871 

2954 

3038 

3124 

3212 

3301 

6 

7 

2477 

2554 

2632 

2711 

2791 

2873 

2956 

3040 

3126 

3213 

3302 

7 

8 

2478 

2555 

2K33 

2712 

2792 

2874 

2957 

3041 

3127 

3214 

3303 

8 

9 

2480 

2557 

2634 

2714 

2794 

2875 

2958 

3043 

3129 

3216 

3305 

9 

10 

2481 

2558 

2606 

27  1  5 

2795 

2877 

2900 

3044 

3130 

3217 

3306 

10 

11 

2482 

2559 

2637 

2716 

2797 

2878 

2961 

3046 

3131 

3219 

3308 

11 

12 

2484 

2560 

2638 

2718 

2798 

2880 

2963 

3047 

3133 

3220 

3309 

12 

13 

2485 

2562 

2640 

2719 

2799 

2881 

2964 

3048 

3134 

3222 

3311 

13 

14 

2186 

2563 

2641 

2720 

2801 

2882 

2965 

3050 

3136 

3223 

3312 

14 

15 

2487 

2564 

2642 

2722 

2802 

2884 

2967 

3051 

3137 

3225 

3314 

15 

1G 

2489 

256G 

2G44 

2723 

2803 

2885 

2968 

3053 

3139 

3226 

3316 

16 

17 

2490 

25G7 

2645 

2724 

2805 

2886 

2970 

3054 

3140 

3228 

3317 

17 

18 

2491 

2568 

264G 

2726 

2806 

2888 

2971 

3055 

3142 

3229 

3319 

18 

19 

2492 

2569 

2648 

2727 

2807 

2889 

2972 

3057 

3143 

3231 

3320 

19 

20 

24U4 

2571 

2649 

2728 

2809 

2891 

2974 

3058 

3144 

3232 

3322 

20 

21 

2495 

2572 

2650 

2729 

2810 

2892 

2975 

3060 

3146 

3234 

3323 

21 

22 

2496 

2573 

2C51 

2731 

2811 

2893 

2976 

3061 

3147 

3235 

3325 

22 

23 

2498 

2575 

2653 

2732 

2813 

2895 

2978 

3063 

3149 

3237 

3326 

23 

2-4 

2499 

2576 

2G54 

2733 

2814 

2896 

2979 

3064 

3150 

3238 

3328 

24 

25 

2500 

2577 

2655 

2735 

2815 

2897 

2981 

3065 

3152 

3240 

3329 

25 

26 

2501 

2578 

2657 

2736 

2817 

2899 

2982 

3067 

3153 

3241 

3331 

26 

27 

2503 

2580 

2658 

2737 

2818 

2900 

2983 

3068 

3155 

3242 

3332 

27 

28 

2504 

2581 

2659 

2739 

2820 

2902 

2985 

3070 

3156 

3244 

3334 

28 

29 

2505 

2582 

2661 

2740 

2821 

2903 

2986 

3071 

3157 

3245 

3335 

29 

30 

25u6 

2584 

'2002 

2742 

2822 

2904 

2988 

30/3 

3159 

3247 

3337 

30 

31 

2*08 

2585 

26G3 

2743 

2824 

2906 

2989 

3074 

3160 

3248 

3338 

31 

32 

2509 

2586 

2665 

2744 

2825 

2907 

2991 

3075 

3162 

3250 

3340 

32 

33 

2510 

2588 

2666 

2746 

2826 

2908 

2992 

3077 

3163 

3251 

3341 

33 

34 

2512 

2589 

2667 

2747 

2828 

2910 

2993 

3078 

3165 

3253 

3343 

34 

35 

2513 

2590 

26G9 

2748 

2829 

2911 

2995 

3080 

3166 

3254 

3344 

35 

36 

2514 

2591 

2670 

2750 

2830 

2913 

2996 

3081 

3168 

3256 

3346 

36 

37 

2515 

2593 

2671 

2751 

2832 

2914 

2998 

3083 

3169 

3257 

3347 

37 

38 

2517 

2594 

2673 

2752 

2833 

2915 

2999 

3084 

3171 

3259 

3349 

38 

39 

2518 

2595 

2674 

2754 

2834 

2917 

3000 

3085 

3172 

3260 

3350 

39 

40 

2519 

2597 

20(5 

27o5 

2836 

2918 

3002 

3087 

3173 

3202 

3352 

40 

41 

2521 

2593 

2676 

2756 

2837 

2919 

3003 

3088 

3175 

3263 

3353 

41 

42 

2522 

2599 

2678 

2758 

2839 

2921 

3005 

3090 

3176 

3265 

3355 

42 

43 

2523 

2G01 

2679 

2759 

2840 

2922 

3006 

3091 

3178 

3266 

3356 

43 

44 

2524 

2602 

2680 

2760 

2841 

2924 

3007 

3093 

3i79 

3268 

3358 

44 

45 

2526 

2603 

2682 

2762 

2843 

2925 

3009 

3094 

3181 

3269 

3359 

45 

46 

2527 

2G04 

2683 

2763 

2844 

2926 

3010 

3095 

3182 

3271 

3361 

46 

47 

2528 

2606 

2684 

2764 

2845 

2928 

3012 

3097 

3184 

3272 

3362 

47 

48 

2530 

2607 

2686 

2766 

2847 

2929 

3013 

3098 

3185 

3274 

3364 

48 

49 

2531 

2608 

2687 

2767 

2848 

2931 

3014 

3100 

3187 

3275 

3365 

49 

50 

2532 

2610 

2088 

2708 

2849 

2932 

3010 

3101 

3188 

3277 

3307 

50  ' 

51 

2533 

2611 

2690 

2770 

2851 

2933 

3017 

3103 

3190 

3278 

3368 

51 

52 

2535 

2612 

2691 

2771 

2852 

2935 

3019 

3104 

3191 

3280 

3370 

52 

53 

2533 

2614 

2692 

2772 

2854 

2936 

3020 

3105 

3192 

3281 

3371 

53 

54 

2537 

2615 

2694 

2774 

2855 

2937 

3021 

3107 

3194 

3283 

3373 

54 

55 

2538 

2616 

2695 

2775 

2856 

2939 

3023 

3108 

3195 

3284 

3374 

55 

56 

2540 

2617 

2696 

2776 

2858 

2940 

3024 

3110 

3197 

3286 

3376 

56 

57 

2541 

2619 

2698 

2778 

2859 

2942 

3026 

3111 

3198 

3287 

3378 

57 

58 

2542 

2620 

2699 

2779 

2860 

2943 

3027 

3113 

3200 

3289 

3379 

58 

59 

2544 

2621 

2700 

2780 

2862 

2944 

3029 

3114 

3201 

3290 

3381 

59 

M. 

38° 

39° 

40° 

41o 

42° 

43° 

44° 

45° 

46° 

470 

48° 

M. 

TABLE  V.                 253 

MERIDIONAL  PARTS. 

M. 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

M. 

0 

3382 

3474  3569 

3665 

3764 

3665 

3968 

4074 

4183 

4294 

4409 

0 

1 

3384 

3476 

3570 

3667 

3765 

3866 

3970 

4076 

4184 

4296 

4411 

1 

2 

3385 

3478 

3572 

3668 

3767 

3868 

3971 

4077 

4186 

4298 

4413 

2 

3 

3387 

3479 

3574 

3670 

3769 

3870 

3973 

4079 

4188 

4300 

4415 

3 

4 

3388 

3481 

3575 

3672 

3770 

3871 

3775 

4081 

4190 

4302 

4417 

4 

5 

3390 

3482 

3577 

3673 

3772 

3873 

3977 

4033 

4192 

4304 

4419 

5 

6 

3391 

3484 

3578 

3675 

3774 

3875 

3978 

4085 

4194 

4306 

4421 

6 

7 

3393 

3485 

3580 

3677 

3775 

3877 

3980 

4086 

4195 

4308 

4423 

7 

8 

3394 

3487 

3582 

3678 

3777 

3878 

3982 

4088 

4197 

4309 

4425 

8 

9 

3396 

3488 

3583 

3680 

3779 

3880 

3984 

4090 

4199 

4311 

4427 

9 

10 

3397 

3490 

3585 

3681 

3780 

3882 

3985 

4092 

4*01 

4313 

4429 

10 

11 

3399 

3492 

3586 

3683 

3782 

3883 

3987 

4094 

4203 

4315 

4431 

11 

12 

3400 

3493 

3588 

3685 

3784 

3885 

3989 

4095 

4205 

4317 

4433 

12 

13 

3402 

3495 

3590 

3686 

3785 

3887 

3991 

4097 

4207 

4319 

4434 

13 

14 

3403 

3496 

3591 

3688 

3787 

3889 

3992 

4099 

4208 

4321 

4436 

14 

15 

3405 

3498 

3593 

3690 

3789 

3890 

3994 

4101 

4210 

4323 

4438 

15 

16 

3407 

3499 

3594 

3691 

3790 

3892 

3996 

4103 

4212 

4325 

4440 

16 

17 

3408 

3501 

3596 

3693 

3792 

3894 

3998 

4104 

4214 

4327 

4442 

17 

18 

3410 

3503 

3598 

3695 

3794 

3895 

3999 

4106 

4216 

4328 

4444 

18 

19 

3411 

3504 

3599 

3696 

379o 

3897 

4001 

4108 

4218 

4330 

4446 

19 

20 

3413 

3506 

3601 

3098 

3797 

3899 

40U3 

4140 

4220 

4332 

4448 

20 

21 

3414 

3507 

3602 

3699 

3799 

3901 

4005 

4112 

4221 

4334 

4450 

21 

22 

3416 

3509 

3604 

3701 

3800 

3902 

4006 

4113 

4223 

4336 

4452 

22 

23 

3417 

3510 

3606 

3703 

3802 

3904 

4008 

4115 

4225 

4338 

4454 

23 

24 

3419 

3512 

3607 

3704 

3804 

3906 

4010 

4117 

4227 

4340 

4456 

21  , 

25 

3420 

3514 

3609 

3706 

3806 

3907 

4012 

4119 

4229 

4342 

4458 

25 

26 

3422 

3515 

3610 

3708 

3807 

3909 

4014 

4121 

4231 

4344 

4460 

26 

27 

3423 

3517 

3612 

3709 

3809 

3910 

4015 

4122 

"4232 

4346 

4462 

27 

28 

3425 

3518 

3614 

3711 

3811 

3913 

4017 

4124 

4234 

4347 

4464 

28 

29 

3427 

3520 

3G15 

3713 

3812 

3914 

4019 

4126 

4236 

4349 

446G 

29 

30 

3428 

3521 

3617 

3714 

3814 

3916 

4021 

4128 

4238 

4354 

44G8 

30 

31 

3430 

3523 

3618 

3716 

3816 

3918 

4022 

4130 

4240 

4353 

4470 

31 

32 

3431 

3525 

3620 

3717 

3817 

3919 

4024 

4132 

4242 

4355 

4472 

32 

33 

3433 

3526 

3622 

3719 

3819 

3921 

4026 

4133 

4244 

4357 

4474 

33 

34 

3434 

3528 

3623 

3721 

3821 

3923 

4028 

4135 

4246 

4359 

4476 

34 

35 

3436 

3529 

3625 

3722 

3822 

3925 

4029 

4137 

4247 

4361 

4478 

35 

36 

3437 

3531 

3626 

3724 

3824 

3926 

4031 

4139 

4249 

4363 

4480 

36 

37 

3139 

3532 

3628 

3726 

3826 

3928 

4033 

4141 

4251 

43(55 

4482 

37 

38 

3440 

3534 

3630 

3727 

3827 

3930 

4035 

4142 

4253 

4367 

4484 

38 

39 

3442 

3536 

3631 

3729 

3829 

3'i32 

4037 

4144 

4255 

4369 

4486 

39 

40 

3443 

3537 

3633 

3731 

383  L 

3933 

4038 

4446 

4257 

4370 

4488 

40 

41 

3445 

3539 

3634 

3732 

3832 

3935 

4040 

4148 

4259 

4372 

4490 

41 

42 

3447 

3540 

3636 

3734 

3834 

3937 

4042 

4150 

4260 

4374 

4492 

42 

43 

3448 

3542 

3638 

3736 

3836 

3938 

4044 

4152 

4262 

4376 

4494 

43 

44 

3450 

3543 

3639 

3737 

3838 

3940 

4045 

4153 

4264 

4378 

4495 

44 

45 

3451 

3545 

3G41 

3739 

3839 

3942 

4047 

4155 

4266 

4380 

4497 

45 

46 

3453 

3547 

3643 

3741 

3841 

3944 

4049 

4157 

4268 

4382 

4499 

46 

47 

3454 

3548 

3644 

3742 

3843 

3945 

4051 

4159 

4270 

4384 

4501 

47 

48 

3456 

3550 

3646 

3744 

3844 

3947 

4052 

4161 

4272 

4386 

4503 

48 

49 

3457 

3551 

3647 

3746 

3846 

3949 

4054 

4162 

4274 

4388 

4505 

49 

50 

3459 

3553 

3649 

3747 

3«48 

3951 

4056 

4164 

4275 

4390 

4507 

50 

51 

3460 

3555 

3651 

3749 

3849 

3952 

4058 

4166 

4277 

4392 

4509 

51 

52 

3462 

3556 

3652 

3750 

3851 

3954 

4060 

4168 

4279 

4394 

4511 

52 

53 

3164 

3558 

3654 

3752 

3853 

3956 

4061 

4170 

4281 

4396 

4513 

53 

54 

3465 

3559 

3655 

3754 

3854 

3958 

4063 

4172 

4283 

4398 

4515 

54 

55 

3467 

3561 

3657 

3755 

3856 

3959 

4065 

4173 

4285 

4399 

4517 

55 

56 

3468 

3562 

3659 

3757 

3858 

3961 

4067 

4175 

4287 

4401 

4519 

56 

57 

3470 

3564 

3660 

3759 

3860 

3963 

4069 

4177 

4289 

4403 

4521 

57 

58 

3471 

3566 

3662 

3760 

3861 

3964 

4070 

4179 

4291 

4405 

4523 

58 

59 

3473 

3567 

3664 

3762 

3863 

3966 

4072 

4181 

4292 

4407 

4525 

59 

M. 

49° 

5(P 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

M. 

254                 TABLE  V. 

MERIDIONAL  PARTS. 

M. 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

70° 

M. 

0 

4527 

4649 

4775 

4905 

5059 

5179 

5324 

5474 

5631 

5795 

59GO 

0 

1 

4529 

4651 

4777 

4907 

5042 

5181 

5326 

5477 

5633 

5797 

59G9 

1 

2 

4531 

4653 

4779 

4909 

5044 

5184 

5328 

5479 

5G36 

5800 

5972 

2 

3 

4533 

4655 

4781 

4912 

5046 

5186 

5331 

5482 

5639 

5803 

5975 

3 

4 

4535 

4657 

4784 

4914 

5049 

5188 

5333 

5484 

5642 

5806 

5978 

4 

5 

4537 

4660 

4786 

4916 

5051 

5191 

5336 

5487 

5644 

5809 

5931 

5 

6 

4539 

4662 

4788 

4918 

5053 

5193 

5338 

5489 

5647 

5811 

5984 

6 

7 

4541 

4664 

4790 

4920 

5055 

5195 

5341 

5492 

5650 

5814 

5986 

7 

8 

4543 

4666 

4792 

4923 

5058 

5198 

5343 

5495 

5652 

5817 

5989 

8 

9 

4545 

4668 

4794 

4925 

5060 

5200 

5346 

5497 

5655 

5820 

5992 

9 

la 

4547 

4070 

4796 

4927 

5062 

5203 

5348 

5500 

5658 

5823 

5995 

10 

11 

4549 

4672 

4798 

4929 

5065 

5205 

5351 

5502 

5660 

5825 

5998 

11 

12 

4551 

4674 

4801 

4931 

5067 

5207 

5353 

5505 

5663 

5828 

6001 

12 

13 

4553 

4676 

4803 

4934 

5069 

5210 

5356 

5507 

5666 

5831 

6004 

13 

14 

4555 

4678 

4805 

4936 

5071 

5212 

5358 

5510 

5668 

5834 

6007 

14 

15 

4557 

4680 

4807 

4938 

5074 

5214 

5361 

5513 

5671 

5837 

6010 

15 

1C 

4559 

4682 

4809 

4940 

5076 

5217 

5363 

5515 

5674 

5839 

6013 

16 

17 

4562 

4684 

4811 

4943 

5078 

5219 

5368 

5518 

567G 

5842 

6016 

17 

18 

4564 

4687 

4814 

4945 

5081 

5222 

5368 

5520 

5679 

5845 

6019 

18 

19 

45GG 

4689 

4816 

4947 

5083 

5224 

5371 

5523 

5682 

5848 

6022 

19 

20 

4568 

4691 

4818 

4949 

5085 

5226 

5373 

5526 

5685 

5851 

6025 

20 

21 

4570 

4693 

4820 

4951 

5088 

5229 

5376 

5528 

5687 

5854 

6028 

21 

22 

4572 

4695 

4822 

4954 

5090 

5231 

5378 

5531 

5690 

5856 

6031 

22 

23 

4574 

4697 

4324 

4956 

5092 

5234 

5380 

5533 

5693 

5859 

6034 

23 

24 

4576 

4699 

4826 

4958 

5095 

5236 

5383 

5536 

5695 

5862 

6037 

24 

25 

4578 

4701 

4829 

4960 

5097 

5238 

5385 

5539 

5C98 

5865 

6040 

25 

26 

4580 

4703 

4831 

4963 

5099 

5241 

5388 

5541 

5701 

5868 

6043 

26 

27 

4582 

4705 

4833 

4985 

5102 

5243 

5390 

5544 

5704 

5871 

6016 

27 

28 

4584 

4707 

4835 

4967 

5104 

5246 

5393 

5546 

5706 

5874 

6049 

28 

29 

4586 

4710 

4837 

49G9 

5106 

5248 

5395 

5549 

5709 

5876 

6052 

29 

30 

4588 

4712 

48^9 

4972 

51U8 

5250 

5398 

5552 

5712 

5879 

6055 

30 

31 

4590 

4714 

4812 

4974 

5111 

5253 

5401 

5554 

5715 

5882 

6058 

31 

32 

4592 

4716 

4844 

4976 

5113 

5255 

5403 

5557 

5717 

5885 

6061 

32 

33 

4594 

4718 

4846 

4978 

5115 

5258 

5406 

5559 

5720 

5888 

6064 

33 

34 

4596 

4720 

4848 

4981 

5118 

5260 

5408 

5562 

5723 

5891 

60G7 

34 

35 

4598 

4722 

4850 

4983 

5120 

5263 

5411 

5565 

5725 

5894 

6070 

35 

36 

4600 

4724 

4352 

4985 

5122 

5265 

5413 

5567 

5728 

5896 

6073 

36 

37 

4602 

4726 

4855 

4987 

5125 

5267 

5116 

5570 

5731 

5899 

6076 

37 

38 

4604 

4728 

4857 

4990 

5127 

5270 

5418 

5573 

5734 

5902 

6079 

38 

39 

4606 

4731 

4859 

4992 

5129 

5272 

f421 

5575 

5736 

5905 

6082 

39 

40 

4608 

4733 

4301 

4994 

5132 

5275 

5423 

5578 

5739 

5908 

6085 

40 

41 

4610 

4735 

4863 

4996 

5134 

5277 

5426 

5580 

5742 

5911 

6088 

41 

42 

4612 

4737 

4865 

4999 

5136 

5280 

5428 

5583 

5745 

5914 

6091 

42 

43 

4614 

4739 

4868 

5001 

5139 

5282 

5431 

5586 

5747 

5917 

6094 

43 

44 

4616 

4741 

4870 

5003 

5141 

5284 

5433 

5588 

5750 

5919 

6097 

44 

45 

4618 

4743 

4872 

5005 

5143 

5287 

5436 

5591 

5753 

5922 

6100 

45 

46 

4620 

4745 

4874 

5008 

5146 

5289 

5438 

5594 

5756 

5925 

6103 

46 

47 

4623 

4747 

4876 

5010 

5148 

5292 

5441 

5596 

5758 

5928 

6106 

47 

48 

4625 

4750 

4879 

5012 

5151 

5294 

5443 

5599 

5761 

5931 

6109 

48 

49 

4627 

4752 

4881 

5014 

5153 

5297 

5446 

5602 

5764 

5934 

6112 

49 

50 

4629 

4754 

4883 

5017 

5155 

5299 

5448 

5604 

5767 

5937 

6115 

~50~ 

51 

4631 

4756 

4885 

5019 

5158 

5301 

5451 

5607 

5770 

5940 

6118 

51 

52 

4633 

4758 

4887 

5021 

5160 

5304 

5454 

5610 

5772 

5943 

6121 

52 

53 

4635 

4760 

4890 

5023 

5162 

5306 

5456 

5612 

5775 

5946 

6124 

53 

54 

4637 

4762 

4892 

5026 

5165 

5309 

5459 

5615 

5778 

5948 

6147 

54 

55 

4639 

4764 

48tf4 

5028 

5167 

5311 

5461 

5617 

5781 

5951 

6130 

55 

56 

4641 

4766 

4896 

5030 

5169 

5314 

5464 

5620 

5783 

5954 

6133 

56 

57 

4643 

4769 

4898 

5033 

5172 

5316 

5466 

5623 

5786 

5957 

6136 

57 

58 

4645 

4771 

4901 

5035 

5174 

5319 

5469 

5625 

5789 

59GO 

6140 

58 

59 

4647 

4773 

4903 

5037 

5176 

5321 

5471 

5628 

5792 

5963 

6143 

59 

If. 

60° 

61^ 

62^ 

03° 

64° 

G5° 

66° 

67° 

68° 

09° 

70° 

H. 

TABLE  V.                 235 

MERIDIONAL  PARTS. 

1C. 

71° 

72° 

73° 

74° 

75°  |  76° 

77° 

78° 

79° 

80° 

81°  |  M. 

0 

6146 

0335 

0534 

0746 

0970 

7210 

Uo7 

7745 

6046 

8375 

8739 

0 

1 

6149 

6338 

6538 

6749 

6974 

7214 

7472 

7749 

8051 

8381 

8745 

1 

2 

6152 

6341 

6541 

6753 

6978 

7218 

7476 

7754 

8056 

8387 

8752 

2 

3 

6155 

6345 

6545 

6757 

6982 

7222 

7481 

7759 

8061 

8393 

8758 

3 

4 

6158 

6348 

6548 

6760 

6986 

7227 

7485 

7764 

8067 

8398 

8r*ft  — 
/Go 

4 

5 

6161 

6351 

6552 

6764 

6990 

7231 

7490 

7769 

8072 

8404 

8771 

5 

6 

6164 

6354 

6555 

6768 

6994 

7235 

7494 

7774 

8077 

8410 

8778 

6 

7 

6167 

6358 

6558 

6771 

6997 

7239 

7498 

7778 

8083 

8416 

8784 

7 

8 

6170 

6361 

6562 

6775 

7001 

7243 

7503 

7783 

8088 

8422 

8791 

8 

9 

G173 

6364 

6565 

6779 

7005 

7247 

7507 

7788 

8093 

8427 

8797 

9 

10 

6177 

630/ 

0509 

0/62 

7009 

7252 

7512 

7793 

8099 

8433 

8801 

JO 

11 

6180 

6371 

6572 

6786 

7013 

7256 

7516 

7798 

8104 

8439 

8810 

11 

12 

6183 

6374 

6576 

6790 

7017 

7260 

7521 

7803 

8109 

8445 

8817 

12 

13 

6186 

6377 

6579 

6793 

7021 

7264 

7525 

7808 

8115 

8451 

8823 

13 

14 

•6189 

6380 

6583 

6797 

7025 

7268 

7530 

7813 

8120 

8457 

8830 

14 

15 

6192 

6384 

6586 

6801 

7029 

7273 

7535 

7817 

8125 

8463 

8836 

15 

16 

61915 

6387 

6590 

6804 

7033 

7277 

7539 

7822 

8131 

8469 

8843 

16 

17 

6198 

6390 

6593 

6808 

7037 

7281 

7544 

7827 

8136 

8474 

8849 

17 

18 

6201 

6394 

6597 

6812 

7041 

7285 

7548 

7832 

8141 

8480 

8856 

18 

19 

6205 

6397 

6600 

6815 

7045 

7-289 

7553 

7837 

8147 

8486 

8863 

19 

20 

6208 

0400 

6G03 

0819 

70i8 

7zy4 

7ooV 

7842 

8152 

8492 

8869 

20 

21 

6211 

6403 

6607 

6823 

7052 

7298 

7562 

7847 

8158 

8498 

8876 

21 

22 

6214 

6407 

6610 

6826 

7056 

7302 

7566 

7852 

8163 

8504 

8883 

22 

23 

6217 

6410 

6614 

6830 

7060 

7306 

7571 

7857 

8168 

8510 

8889 

23 

24 

6220 

6413 

6617 

6834 

7064 

7311 

7576 

7862 

8174 

8516 

8896 

24 

25 

6223 

6417 

6621 

6838 

7GG8 

7315 

7580 

7867 

8179 

8522 

8903 

25 

2G 

6226 

6420 

6624 

6841 

7072 

7319 

7585 

7872 

8185 

8528 

8909 

26 

27 

6230 

6423 

6628 

6845 

7076 

7323 

7589 

7877 

8190 

9534 

8916 

27 

28 

6233 

6427 

6631 

6849 

7080 

7328 

7594 

7882 

8196 

8540 

8923 

28 

29 

6236 

6430 

6635 

6853 

7084 

7332 

7599 

7887 

8201 

8546 

8930 

29 

30 

G:i39 

0433 

OGo9 

0850 

70S8 

'<3o6 

7603 

V892 

8207 

8552 

8936 

30 

31 

6242 

6437 

6642 

6860 

7092 

7341 

7608 

7897 

8212 

8558 

8943 

31 

32 

6245 

6140 

6646 

6864 

7096 

7345 

7612 

7902 

8218 

8565 

8950 

32 

33 

6249 

6443 

6649 

6868 

7100 

7319 

7617 

7907 

8223 

8571 

8957 

33 

34 

6252 

6447 

6653 

6871 

7104 

7353 

7622 

7912 

8229 

8577 

8963 

34 

35 

6255 

6450 

6656 

6875 

7108 

7358 

7626 

7917 

8234 

8583 

8970 

35 

36 

6258 

6453 

C660 

6879 

7112 

7362 

7631 

7922 

8240 

8589 

8977 

36 

37 

6261 

6457 

6663 

6883 

7116 

7366 

7636 

7927 

8245 

8595 

8984 

37 

38 

6264 

6460 

6667 

6886 

7120 

7371 

7640 

7932 

8251 

8601 

8991 

38 

39 

6268 

6463 

6670 

6890 

7124 

7375 

7645 

7937 

8256 

8607 

8998 

39 

40 

0271 

046  / 

6074 

0894 

7128 

73'<9 

7050 

7942 

8202 

8014 

9005 

40 

41 

6274 

6470 

6677 

6898 

7132 

7384 

7654 

7948 

8267 

8620 

9012 

41 

42 

6277 

6473 

6681 

6901 

7136 

7388 

7659 

7953 

8273 

8626 

9018 

42 

43 

6280 

6477 

6685 

6905 

7140 

7392 

7664 

7938 

8279 

8632 

9025 

43 

44 

6283 

6480 

6688 

6909 

7145 

7397 

7668 

7963 

8284 

8638 

9032 

44 

45 

6287 

6483 

6692 

6913 

7149 

7401 

7673 

7968 

8290 

8644 

9039 

45 

46 

6290 

6187 

6695 

6917 

7153 

7406 

7678 

7973 

8295 

8651 

9046 

46 

47 

6293 

6490 

6699 

6920 

7157 

7410 

7683 

7978 

8301 

8657 

9053 

47 

48 

6296 

6494 

0702 

6924 

7161 

7414 

7687 

7983 

8307 

8663 

9060 

48 

49 

6>99 

6497 

6706 

6928 

7165 

7419 

7692 

7989 

8312 

8669 

9067 

49 

50 

6303 

6500 

6710 

6U32 

7169 

7423 

7097 

7994 

8318 

8070 

9074 

50 

51 

6306 

6504 

6713 

6936 

7173 

7427 

7702 

7999 

8324 

8682 

9081 

51 

52 

6309 

6507 

6717 

6940 

7177 

74-32 

7706 

8004 

8329 

8688 

908S 

52 

53 

6312 

6511 

6720 

6943 

7181 

7436 

7711 

8009 

8335 

8695 

9096 

53 

54 

6315 

6514 

6724 

6947 

7185 

7441 

7716 

8014 

8341 

8701 

9103 

54 

55 

6319 

6517 

6728 

6951 

7189 

7445 

7721 

8020 

8347 

8707 

9110 

55 

56 

6322 

6521 

6731 

6955 

7194 

7449 

7725 

8025 

8352 

8714 

9117 

56 

57 

6325 

6524 

6735 

6959 

7198 

7454 

7730 

8030 

8358 

8720 

9124 

57 

58 

6328 

6528 

6738 

69G3 

7202 

7458 

7735 

8035 

8364 

8726 

9131 

58 

59 

6332 

6531 

6742 

6966 

7206 

7463 

7740 

8040 

8309 

8733 

9138 

59 

M. 

71o 

72° 

73° 

74° 

75° 

76° 

770 

78J 

79° 

80° 

81° 

M. 

256                 TABLE  V. 

MERIDIONAL  PARTS. 

M. 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

1C. 

0 

91-15 

9006 

1U137 

1U765 

11533 

12522 

13916 

16300 

0 

1 

9153 

9614 

10147 

10776 

11547 

12541 

13945 

16357 

1 

2 

91CO 

9622 

10156 

10788 

11561 

12561 

13974 

16416 

2 

3 

9167 

9631 

10166 

10799 

11576 

12580 

14004 

16476 

3 

4 

9174 

9639 

10175 

10811 

11590 

12599 

14033 

16537 

4 

5 

9182 

9647 

10185 

10823 

11605 

12G19 

14063 

D6599 

5 

6 

9189 

9655 

10195 

10834 

11620 

12639 

14093 

16662 

6 

7 

9196 

9664 

10205 

10846 

11634 

12659 

14123 

16726 

7 

8 

9203 

9672 

10214 

10858 

11649 

12679 

14154 

16792 

8 

9 

9211 

9G80 

10224 

10870 

11664 

12699 

14185 

16858 

9 

ID 

9218 

9689 

10^34 

10881 

11679 

T/719 

14216 

169.6 

10 

11 

9225 

9G97 

10244 

10893 

11694 

12739 

14247 

16996 

11 

12 

9233 

9706 

10254 

10905 

11709 

12759 

14279 

17067 

12 

13 

9240 

9714 

10264 

10917 

11724 

12780 

14311 

17139 

13 

14 

9248 

9723 

10274 

10929 

11739 

12801 

14343 

17213 

14 

15 

9255 

9731 

10284 

10941 

11755 

12821 

14376 

17289 

15 

16 

9262 

9740 

10294 

10953 

11770 

12842 

14409 

17366 

16 

17 

9270 

9748 

10304 

10965 

11785 

12863 

14442 

17445 

17 

18 

9277 

9757 

10314 

10978 

11801 

12885 

14475 

17526 

18 

19 

9285 

9765 

10324 

10990 

11816 

12906 

14509 

17609 

19 

20 

9292 

97/4 

10334 

11002 

11832 

12927 

14543 

17G94 

20 

21 

9300 

9783 

10344 

11014 

11848 

12949 

14578 

17781 

21 

22 

9307 

9791 

10354 

11027 

11863 

12970 

14G13 

17870 

22 

23 

9315 

9800 

10364 

11039 

11879 

12992 

14648 

17962 

23 

24 

9322 

9809 

10374 

11052 

11895 

13014 

14684 

18056 

24 

25 

9330 

9817 

10385 

11064 

11911 

13036 

14720 

18153 

25 

26 

9337 

9826 

10395 

11077 

11927 

13059 

14756 

18252 

26 

27 

9345 

9835 

10405 

11089 

11943 

13081 

14793 

18355 

27 

28 

9353 

9344 

10416 

11102 

11959 

13104 

14830 

18461 

28 

29 

9360 

9852 

10426 

11115 

11976 

13126 

14868 

18570 

29 

oO 

9368 

9861 

10437 

11127 

11992 

13149 

14906 

18683 

30 

31 

9376 

9870 

10447 

11140 

12008 

13172 

14944 

18799 

31 

32 

9383 

9879 

10457 

11153 

12025 

13195 

14983 

18920 

32 

33 

9391 

9888 

10468 

11166 

12041 

13219 

15022 

19045 

33 

34 

9399 

9897 

10478 

11179 

12058 

13242 

15062 

19174 

34 

35 

9407 

9903 

10489 

11192 

12075 

13266 

15102 

19309 

35 

36 

9415 

9915 

10500 

11205 

12092 

13290 

15143 

19450 

36 

37 

9422 

9924 

10510 

11218 

12109 

13314 

15184 

19596 

37 

38 

9430 

9933 

10521 

11231 

12126 

13338 

15226 

19749 

38 

39 

9437 

9942 

10532 

11244 

12143 

13362 

15268 

19909 

39 

40 

9445 

9951 

1U542 

11257 

12160 

13366 

15311 

20076 

40 

41 

9453 

99GO 

10553 

11270 

12177 

13411 

15354 

20253 

41 

42 

9461 

9969 

10564 

11284 

12194 

13436 

15398 

20439 

42 

43 

94G9 

9978 

10575 

11297 

12212 

13461 

15442 

20635 

43 

44 

9477 

9987 

10586 

11310 

12229 

13486 

15487 

20844 

44 

45 

9485 

9996 

10597 

11324 

12247 

13511 

15532 

21065 

45 

4G 

9493 

10005 

10608 

11338 

12265 

13537 

15579 

21303 

46 

47 

9501 

10015 

10619 

11351 

12282 

13563 

15625 

21557 

47 

48 

9509 

10024 

10630 

11365 

12300 

13589 

15673 

21833 

48 

49 

9517 

10033 

10641 

11378 

12318 

13615 

15721 

22132 

49  , 

50 

9525 

10U43 

10652 

11392 

12336 

13G41 

15770 

22459 

50 

51 

9533 

10052 

10663 

11406 

12354 

136G8 

15819 

22822 

51 

52 

9541 

10061 

10674 

11420 

12373 

13695 

15869 

23226 

52 

53 

9549 

10071 

10u85 

11434 

12391 

13722 

15920 

23685 

53 

54 

9557 

10080 

10696 

11448 

12409 

13749 

15972 

24215 

54 

55 

9565 

10089 

10708 

11462 

12428 

13776 

16024 

24842 

55 

56 

9573 

10099 

10719 

11476 

12440 

13804 

16078 

25609 

56 

57 

9581 

10108 

10730 

11490 

12465 

13832 

16132 

26598 

57 

58 

9589 

10118 

10742 

11504 

12484 

13860 

16187 

27992 

58 

59 

9598 

10127 

10753 

11518 

12503 

13888 

16243 

30375 

59 

M. 

82° 

83° 

84° 

85° 

86J 

87° 

88° 

89° 

M. 

TABLE  VI. 

MEAN  REFRACTION. 

257 
TABLE  VII. 

DIP  OF  THE  HORIZON. 

4PP 
Alt. 

Rcfr. 

4PP 
Alt. 

Ref. 

App. 
Alt. 

Ref. 

App. 
Alt, 

Ref. 

App. 
Alt. 

Ref. 

Height. 

Dip. 

O   / 

0  0 
0  5 
0  10 
0  15 
0  20 
0  25 
0  30 
0  35 
0  40 
0  45 

33  0 
32  10 
31  22 
30  35 
29  50 
29  6 
28  23 
27  41 
27  0 
26  20 

o  / 
5  0 
5  5 
5  10 
5  15 
|5  20 
5  25 
5  30 
5  35 
j5  49 
5  45 

9  54 
9  46 
9  33 
9  30 
9  23 
9  15 
9  8 
9  1 
8  54 
8  47 

o  / 
10  0 
10  10 
10  20 
10  30 
10  40 
10  50 
11  0 
11  10 
11  20 
11  30 

5'  15 
5  10 
5  5 
5  0 
4  56 
4  51 
4  47 
4  43 
4  39 
4  34 

o  / 
20  0 
20  10 
20  20 
20  30 
20  40 
20  50 
21  0 
21  10 
21  20 
21  30 

2'  35 
2  34 
2  32 
2  31 
2  29 
2  28 
2  27 
2  26 
2  25 
2  24 

o  / 
34  0 
34  30 
35  0 
35  30 
3(5  0 
36  30 
37  0 
37  30 
38  0 
38  30 

1  24 
1  23 
1  21 
1  20 
1  18 
1  17 
1  16 
1  14 
1  13 
1  11 

1  10 
1  9 
1  8 
1  5 
1  3 
1  1 
0  59 
0  57 
0  55 
0  53 

Feet. 

, 

1 
2 
3 

4 
5 
6 

7 
8 
9 
10 

0  58 
1  21 
1  40 
1  56 
2  9 
2  21 
2  33 
2  44 
2  53 
3  2 

0  50 
0  55 
1  0 
1  5 
1  10 
1  15 
1  20 
1  25 
1  30 
1  3" 

25  42 
25  5 
24  29 
23  54 
23  20 
22  47 
22  15 
21  41 
21  15 
20  46 

5  50 
5  55 
,6  0 
,6  5 
6  10 
6  15 
6  20 
6  25 
6  30 
6  35 

8  41 
8  34 
8  28 
8  21 
8  15 
8  9 
8  3 
7  57 
7  51 
7  45 

11  40 
11  50 
12  0 
12  10 
12  20 
12  30 
12  40 
12  50 
13  0 
13  10 

4  31 
4  27 
4  23 
4  20 
4  16 
4  13 
4  9 
4  6 
4  3 
4  0 

21  40 
21  50 
22  0 
22  10 
22  20 
22  30 
22  40 
22  50 
23  0 
23  Id 

2  23 
2  21 
2  20 
2  19 
2  18 
1  17 
2  16 
1  15 
2  14 
1  13 

,59  0 
39  30 
40  0 
41  0 
42  0 
43  0 
44  0 
45  0 
46  0 
47  0 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

3  10 
3  19 
3  27 
3  36 
3  42 
3  50 
3  57 
4  4 
4  11 
4  17 

1  4U 
1  45 
1  50 
1  55 
2  0 
2  5 
2  10 
2  15 
2  20 
2  25 

20  18 
19  51 
19  25 
19  0 
18  35 
18  11 
17  48 
17  26 
17  4 
]6  44 

6  40 
6  45 
!6  50 

:c  55 

7  0 
7  5 
7  10 
7  15 

7  20 
,7  25 

7~30 
7  35 
7  40 
7  45 
7  50 
7  55 
8  0 
8  5 
8  10 
;8  15 

7  40 
7  35 
7  30 
7  25 
7  20 
7  15 
7  11 
7  6 
7  2 
6  57 

13  20 
13  30 
13  40 
13  50 
14  0 
14  10 
14  20 
14  30 
14  40 
14  50 

3  57 
3  54 
3  51 
3  48 
3  45 
3  43 
3  40 
3  38 
3  35 
3  33 

23  20 
23  30 
23  40 
23  50 
24  0 
24  10 
24  20 
24  30 
24  40 
24  50 

•I  12 
1  11 
2  10 
2  9 
2  8 
2  7 
2  6 
2  5 
2  4 
2  3 

48  0 
49  0 
50  0 
51  0 
52  0 
53  0 
54  0 
55  0 
56  0 
57  0 

0  51 
0  49 
0  48 
0  46 
0  44 
0  43 
0  41 
0  40 
0  38 
0  35 

21 
22 
23 
24 
26 
28 
30 
35 
40 
45 

4  23 
4  30 
4  36 
4  42 
4  52 
5  5 
5  15 
5  39 
6  4 
6  27 

2  30 
2  35 
2  40 
2  45 
2  50 
2  55 
3  0 
3  5 
3  10 
3  15 

16  24 
16  4 
15  45 
15  27 
15  9 
14  52 
14  36 
14  20 
14  4 
13  49 

6  53 
6  49 
6  45 
6  41 
6  37 
6  33 
6  29 
6  25 
6  22 
6  18 

15  0 
15  10 
15  20 
15  30 
15  40 
15  50 
16  0 
16  10 
16  20 
16  30 

3  30 
3  28 
3  26 
3  24 
3  21 
3  19 
3  17 
3  15 
3  12 
3  10 

25  0 
25  10 
25  20 
25  30 
25  40 
25  50 
26  0 
26  10 
26  20 
26  30 

2  2 
2  1 
2  0 
1  59 
1  58 
1  57 
1  56 
1  55 
1  55 
1  54 

58  0 
59  0 
60  0 
61  0 
62  C 
63  0 
64  0 
65  0 
66  0 
67  0 

0  35 
0  34 
0  33 
0  32 
0  30 
0  29 
0  28 
0  26 
0  25 
0  24 

50 
60 
70 
80 
90 
100 

6  46 
7  25 
8  1 
8  34 
9  6 
9  35 

TABLE  VIII. 

SUN'S  PARALLAX  IN 
ALTITUDE. 

3  20 
3  25 
3  30 
3  35 
3  40 
3  45 
3  50 
3  55 
4  0 
4  5 

13  34 
13  20 
13  6 
12  53 
12  40 
12  27 
12  15 
12  3 
11  51 
11  40 

8  20 
8  25 
8  30 
8  35 
8  40 
8  45 
8  50 
8  55 
9  0 
9  5 

6  15 
6  11 
6  8 
6  5 
6  1 
5  58 
5  55 
5  52 
5  48 
5  45 

16  40 
16  50 
17  0 
17  10 
17  20 
17  30 
17  40 
17  50 
18  0 
18  10 

3  8 
3  6 
3  4 
3  3 
3  1 
2  59 
2  57 
2  55 
2  54 
2  52 

26  40 
26  50 
27  0 
27  15 
27  30 
27  45 
28  0 
28  15 
28  30 
28  45 

1  53 
1  52 
1  51 
1  50 
1  49 
1  48 
I  47 
1  46 
1  45 
1  44 

08  0 
69  0 
70  0 
71  0 
72  0 
73  0 
74  0 
75  0 
76  0 
77  0 

0  23 
0  22 
0  21 
0  19 
0  18 
0  17 
0  16 
0  15 
0  14 
0  13 

Altitude. 

Parallax. 

0 

„ 

0 
10 

20 
30 
40 
50 
55 

9 
9 

8 
8 
7 
6 
5 

4  JO 
4  15 
4  20 
4  25 
4  30 
4  35 
4  40 
4  45 
4  50 
4  55 

11  29 
11  18 
11  8 
10  58 
10  48 
10  39 
10  29 
10  20 
10  11 
10  2 

9  10 
9  15 

9  20 
9  25 
9  30 
9  35 
9  40 
9  45 
9  50 
9  55 

5  42 
5  39 
5  36 
5  34 
5  31 
5  28 
5  25 
5  23 
5  20 
5  18 

18  20 
18  30 
18  40 
18  50 
19  0 
19  10 
19  20 
19  30 
19  40 
19  50 

2  51 
2-49 
2  47 
2  46 
2  44 
2  43 
2  41 
2  40 
2  38 
2  37 

29  0 
29  30 
30  0 
30  30 
31  0 
31  30 
32  0 
32  30 
33  0 
33  30 

1  42 
1  40 
1  38 
1  37 
1  35 
1  33 
1  31 
1  30 
1  28 
1  26 

78  0 
79  0 
80  0 
81  0 
82  0 
83  0 
84  0 
86  0 
88  0 
90  0 

0  12 
0  11 
0  10 
0  9 
0  8 
0  7 
0  6 
0  4 
0  2 
0  0 

00 
65 
70 
75 
80 
85 
'JO 

4 

4 
3 

2 
2 

1 
0 

258                                         TABLE  IX. 

TO  REDUCE    THE    EQUATION  OF    TIME  TO  ANY  TIME   UNDER  THE    MERIDIAN 
OF    GREENWICH. 

Green 
Time. 

DAILY  VARIATION. 

Is. 

2s. 

4s. 

6s. 

8s. 

10s. 

12s. 

14s. 

16s. 

18s. 

20s. 

22s 

24s. 

26s. 

28s. 

30s. 

h.  m. 
0  30 
1     0 
1  30 
2    0 
2  30 
3    0 
3  30 
4    0 

s. 
0  0 

8. 

0  0 

s. 
0  1 

s. 
0  1 

s. 
0  9 

s. 
0  9 

s. 
0  3 

s. 
0  3 

s. 
0  3 

s. 
0  4 

8. 
0  4 

8. 

0  R 

8. 

0  R 

s. 
0  5 

s. 
0  fi 

s. 
0  6 

0  0 

0  1 

0  9 

0  9 

0  3 

0  4 

0  R 

0  fi 

0  7 

0  8 

0  8 

0  9 

1  0 

1   1 

1    9 

1  2 

01 
0.1 
0  1 

0.1 
0.2 
0  9 

0.2 
0.3 
0  4 

0.4 
0.5 

o  r, 

0.5 
0  7 
0  8 

0.6 

0  8 

0.8 
1  0 

0  9 
1  9 

1.0 
1   3 

1.1 
1  R 

1.3 

1  7 

1.4 
1   8 

1  5 

9  0 

1.6 

9  9 

1.7 

9  3 

1.8 
2.5 

1   0 

1   3 

1  R 

1  7 

1  9 

9  1 

9  3 

9  R 

9  7 

9  9 

3  1 

0  1 

0  3 

0  R 

0  7 

1   0 

1   9 

1  R 

1  8 

9  0 

9  9 

9  R 

9  7 

3  0 

3  9 

3  R 

3  7 

0.1 

0.2 

0.3 
0  3 

0.6 

0  7 

0.9 
1  0 

1.2 
1   3 

1.5 

1  7 

1.8 
2  0 

2.0 

9  3 

2.3 

9  fi 

2  6 
3  0 

2.9 
3  3 

3.  '2 
3  7 

3.5 

4  0 

3.7 
4  3 

4.1 

4  7 

4.4 

5.0 

4  30 
5    0 
5  30 
6    0 
6  30 
7    0 
7  30 
8    0 

0.2 
0.2 
02 

0  9 

0.4 
0.4 
0.5 
0  5 

0.7 
0.8 
0.9 
1  0 

1.1 
1.2 
1  4 

1  5 
1.7 
1  8 

1.9 
2.1 
2  3 

2.3 

2.5 

9  8 

2.6 
2  9 
3  2 

3.0 
3.3 

3  7 

3.4 
3.8 
4  1 

3.7 
4.2 
4  fi 

4.1 
4.6 
R  0 

4  5 
5.0 

R  R 

4.9 
5  4 
R  9 

5.2 
5.8 
fi  4 

5.6 
6.2 
6.8 

1  R 

9  0 

9  R 

3  0 

3  R 

4  0 

4  R 

R  0 

R  R 

fi  0 

fi  R 

7  0 

7.5 

0  3 

0  5 

1   1 

i  r. 

9  9 

9  7 

3  3 

3  8 

4  3 

4  9 

R  4 

5  9 

fi  R 

7  0 

7  fi 

8  1 

0.3 
0.3 
0  3 

0.6 
0.6 
0.7 

"OV7 

0  7 

1.2 
1.2 
1  3 

1  7 
1  9 

9  0 

9  3 

9  9 

3  5 

4  1 

4  7 

5  9 

R  8 

6  4 

7  0 

7  R 

8  1 

8.7 

2.5 

9  7 

3.1 
3  3 

3.8 
4  0 

4.4 

4  7 

5.0 

R  3 

5  6 
fi  0 

6.3 

6  7 

6.9 

7  3 

7.5 
8  0 

8.1 

8  fi 

8.7 
9  3 

9.4 

10.0 

8  30 
9    0 
9  30 
10    0 
10  30 
11     0 
11  30 
12    0 

0.4 

0  4 

1.4 
1  5 

2.1 

9  9 

2.8 
3  0 

3  5 

3  7 

4.3 
4  R 

5.0 

R  9 

5.7 
6  0 

6.4 
fi  8 

7.1 

7  R 

7.8 
8  9 

8.5 
9  0 

9.2 
9  7 

9.9 
10  4 

10.6 
11.2 

0.4 
0.4 
0  4 

0.8 
0.8 
0  9 

1.6 
1.7 
1  7 

2.4 

9  R 

3.2 
3  3 

4.0 

4  9 

4.8 
5  0 

5  5 

5  8 

6.3 

6  7 

7.1 

7  R 

7.9 
8  3 

8.7 
9  9 

9.5 
10  0 

10.2 
10  8 

11.0 
11  fi 

11.8 
12  5 

9  fi 

3  R 

4  4 

R  3 

6  1 

7  0 

7  9 

8  7 

9  fi 

10  5 
11  0 

11.4 

11  9 

12.2 
19  8 

13.1 
13.7 

0.5 
0  ft 

09 
1  0 

1   8 

9  7 

3  7 

4  fi 

R  5 

6  4 

7  3 

8  9 

9  9 

10  0 

1   9 

9  9 

3  8 

4  8 

R  8 

fi  7 

7  7 

8  fi 

9  fi 

10  R 

11  R 

19  4 

13  4 

14.4 

0  R 

1  0 

9  0 

3  0 

4  0 

R  0 

fi  0 

7  0 

8  0 

9  0 

10  0 

11  0 

19  0 

13  0 

14  0 

15.0 

TABLE  X. 

TO  OBTAIN  THE  PROPORTIONAL   PART    OF   THE    RATE    OF   A  CHRONOMETER, 
FROM  NOON,  TO  ANY  GIVEN   HOUR  AT  GREENWICH. 

Green 
Time. 

DAILY  RATE  OF  CHRONOMETER. 

Is. 

2s. 

4s. 

6s. 

8s. 

10s. 

12s. 

14s. 

16s. 

18s. 

20s. 

22s. 

24s. 

26s. 

28s. 

30s. 

h.  m. 
0  30 
1    0 
1  30 
2    0 
2  30 
3    0 
3  30 
4    0 

a. 

0  0 

s. 
0  0 

s. 
0  1 

s. 
0  1 

s. 
0  9 

s. 
0  9 

s. 
0  3 

s. 
0  3 

s. 
0  3 

8. 

0  4 

s. 
0  4 

8. 

0  5 

s. 
0  R 

s. 
0  R 

s. 
0  fi 

s. 
0  6 

0  0 

0  1 

0  9 

0  9 

0  3 

0  4 

0  R 

0  6 

0  7 

0  8 

0  8 

0  9 

1  0 

1  1 

1  9 

1  2 

0  1 

0  1 

0  9 

0  4 

0  R 

0  6 

0  8 

0  9 

1  0 

1   1 

1   3 

1  4 

1  5 

1  fi 

1  7 

1  8 

0  1 

0  9 

0  3 

0  R 

0  7 

0  8 

1   0 

1  9 

1   3 

1  5 

1  7 

1  8 

9  0 

9  9 

9  3 

2  5 

0.1 
0  1 

0.2 
0  3 

0.4 
0  R 

0.6 
0  7 

0.8 
1  0 

1.0 
1  9 

1.3 
1  5 

1.5 

1  8 

1.7 

9  0 

1.9 

9  9 

2.1 

9  R 

2.3 

9  7 

2.5 
3  0 

2.7 
3  9 

2.9 
3  R 

3.1 
3  7 

0.1 

0.2 

0.3 
0.3 

0.6 
0.7 

0.9 
1.0 

1.2 
1.3 

1.5 
1.7 

1.8 
2.0 

2.0 
2  3 

2.3 

2.6 

2.6 
3.0 

2.9 
3.3 

3.2 
3.7 

3.5 
4.0 

3.7 
4.3 

4.1 
4.7 

4.4 
5.0 

4  30 
5    0 
5  30 
6    0 
6  30 
7    0 
7  30 
8    0 

0.2 
0  9 

0  4 
0  4 

(1  7 

1   1 

1  R 

1  9 

9  :i 

9  fi 

3  0 

3  4 

S  7 

4  1 

4  R 

4  9 

R  9 

5  6 

0  8 

1  9 

1  7 

9  1 

9  R 

9  9 

3  3 

3  8 

4  9 

4  fi 

R  0 

R  4 

R  8 

6.2 
6.8 
7  5 

02 
0  9 

0.5 
0  R 

0.9 
1  0 

1.4 
1  R 

1.8 

9  0 

2.3 

9  R 

2.8 
3  0 

3.2 
3  R 

3.7 
4  0 

4.1 
4  5 

4.6 
R  0 

5.0 
5  R 

5.5 
fi  0 

5.9 
fi  R 

6.4 
70 

o  3 

0  R 

1   1 

1  P 

29 

9  7 

3  3 

3  8 

4  3 

4  9 

R  4 

R  9 

fi  R 

7  0 

7  fi 

8  1 

0.3 
0  3 

o  a 

0.6 
0  6 

1.2 
1  9 

1.7 
1  9 

2.3 

9  5 

2  9 
3  1 

3.5 

3  8 

4.1 
4  4 

4.7 

R  0 

5.2 
5  fi 

5.8 
fi  3 

6.4 
fi-9 

7.0 
7  R 

7.5 
8  1 

8.1 
8  7 

8.7 
9  4 

0  7 

1   3 

9  0 

9  7 

3  3 

4.0 

4  7 

5  3 

fi  0 

fi  7 

7  3 

8  0 

8  fi 

9  3 

10.0 

8  30 
9    0 
9  30 
10    0 
10  30 
11     0 
.11  30 
12    0 

0.4 
0.4 
0  4 

0.7 
0.7 

0  fl 

1.4 
1.5 
1  fi 

2.1 
2.2 
9  4 

2.H 
3.C 
3  9 

3.5 
3.7 

4  0 

4.3    5.0 
4.5   5.2 
4.8   5.5 

5.7 
6.0 
fi  3 

6.4 
6.8 
7  1 

7.1 
7.5 
7  9 

7.8 
8.2 
8  7 

8.5 
9.0 
9  R 

9.2 
9.7 
10  9 

9.9 
10.4 
11  0 

10.  G 
11.2 
11  8 

0.4 
0.4 

0  F 

0.8 
0.9 

0  <1 

1.7 

1.7 

1  fi 

2.5 
2.C 
9  7 

3.3 

3.5 
3  7 

4.2 
4.4 

4  6 

5.0   5.8 
53   6.1 
5  5   fi  4 

6.7 

7.0 
7  3 

7.5 
7.9 
8  9 

8.3 
8.7 

9   9 

9.2 
9.6 
10  0 
10.5 
11  f 

10.0 
10.5 
11.0 
11.5 
19  0 

10.8 
11.4 
11.9 
12.4 
13  ( 

11.6 
12.2 
12.8 
13  4 
14  0 

12.5 
13.1 
13.7 
14.4 
15  0 

0.5 

o  r 

1.0 

1  (I 

1.9 
9  f 

2.8 
3  ( 

3.8 
4  ( 

4.8 

r>  c 

5.8 
6  0 

6.7 

7  n 

7  7 
8  f 

8.6 
9  ( 

9.6 
10  0 

TABLE  XI.                                           259 

TO    TURN   DEGREES   INTO    TIME,    OR   TIME   INTO   DEGREES. 

Degrees. 

Time. 

Degrees. 

Time. 

Degrees. 

Time. 

Minutes 
of  Deg. 

Time. 

Seconds 
of  Deg. 

Time. 

H.   M. 

H.  M. 

H.  M. 

M.  8. 

B.  T. 

1 
2 
3 
4 
5 

0.    4 
0.    8 
0.12 
0.16 
0  20 

61 
62 
63 
64 
65 

4.  4 
4.  8 
4.12 
4.16 

4.20 

121 
122 
123 
124 
125 

8.  4 
8.  8 
8.12 
8.16 
8.20 

1 

2 
3 
4 
5 

0.  4 
0.  8 
0.12 
0.16 
0.20 

1 

2 
3 
4 
5 

0.   4 
0.   8 
0.12 
0.16 
0.20 

6 

7 
8 
9 
10 

0.24 
0.28 
0.32 
0.36 
0.40 

66 
67 
68 
69 
70 

4.24 
4.28 
4.32 
4.36 
4.40 

126 
127 
128 
129 
130 

b.24 
8.28 
8.32 
8.36 
8.40 

6 
7 
8 
9 
10 

0.24 
0  28 
0.32 
0.36 
0.40 

6 
7 
8 
9 
10 

0.24 
0.28 
0.32 
0.36 
0  40 

11 

12 
13 
14 
15 

0.44 
0.48 
0.52 
0.56 
1.  0 

71 
72 
73 

74 
75 

4.44 
4.48 
4  52 
4.56 
5    0 

131 
132 
133 
134 
135 

8.44 
8.48 
8  52 
8.56 
9.  0 

11 
12 
13 
14 
15 

0.44 
0.48 
0.52 
0.56 
1.  0 

11 
12 
13 
14 
15 

0.44 
0.48 
0.52 
0.56 
1.  0 

16 
17 
18 
19 
20 

1.  4 

1.  8 
1.12 
1.16 
1.20 

76 
77 
78 
79 
80 

5.  4 
5.  8 
5.12 
5.16 
5.20 

136 
137 
138 
139 
140 

y.  4 

9.  8 
9  12 
9.16 
9.20 

16 
17 
18 
19 
20 

1.  4 
1.  8 
1.12 
1.16 
1.20 

16 
17 
18 
19 
20 

1.  4 
1.  8 
1.12 
1  16 
1.20 

21 
22 
23 
24 
25 

1.24 
1.28 
1.32 
1.36 

1.40 

81 
82 
83 

,-    84 
85 

5.24 
5.28 
5.32 
5.36 
5  40 

141 
142 
143 
144 
145 

9.24 
9.28 
9.32 
9.36 
9.40 

21 
22 
23 
24 
25 

1.24 
1.28 
1.32 
1.36 
1.40 

21 
22 
23 
24 
25 

1.24 
1.28 
1.32 
1.36 
1.40 

'26 
27 
28 
29 
30 

1.44 
1.48 
1.52 
1.56 
2.  0 

86 
87 
88 
89 
90 

5.44 
5.48 
5.52 
5.56 
6.  0 

146 
147 
148 
149 

150 

y.44 
9.48 
9.52 
9.56 
10.  0 

26 
27 
28 
29 
30 

1.44 
1.48 
1.52 
1  56 
2.  0 

26 
27 
28 
29 
30 

1.44 
1.48 
1.52 
1.56 
2.  0 

31 
32 
33 
34 
35 

2.  4 
2,  8 
2.12 
2.16 

2.20 

91 
92 
93 
94 
95 

6.  4 
6.  8 
6.12 
6.16 
6.20 

151 
152 
153 
154 
155 

10.  4 
10.  8 
10.12 
10.16 
10.20 

31 
32 
33 
34 
35 

2.  4 
2.  8 
2.12 
2.16 
2.20 

31 
32 
33 
34 
35 

2.  4 
2.  8 
2.12 

2.16 
2.20 

36 
37 
38 
39 
40 

2.24 
2.28 
2.32 
2.36 
2.40 

96 
97 
98 
99 
100 

6.24 
6  28 
6.32 
6.36 
6.40 

156 
157 
158 
159 

1GO 

10.24 
10.28 
10.32 
10.36 
10.40 

36 
37 
38 
39 

40 

2.24 
2.28 
2.32 
2.36 
2.40 

/36 
37 
38 
39 
40 

2.24 
2.28 
2.32 
2.36 
2.40 

41 
42 
43 

44 

45 

2.44 
2.48 
2.52 
2.56 
3.  0 

101 
102 
103 
104 
105 

6.44 
6.48 
6.52 
6.56 
7.  0 

161 
162 
163 
164 
165 

10.44 
10.48 
10.52 
10.56 
11.  0 

41 
42 
43 
44 
45 

2.44 
2.48 
2.52 
2.56 
3    0 

41 
42 
43 
44 
45 

2.44 
2.48 
2.52 
2.56 
3.  0 

46 
47 
48 
49 
50 

3.  4 
3.  8 
3.12 
3.16 

3.20 

106 
107 
108 
109 
110 

7.  4 
7.  8 
7.12 
7.16 
7.20 

16»i 
167 
168 
169 
170 

11.  4 
11.  8 
11.12 
11.16 
11.20 

46 
47 
48 
49 

50 

3.  4 
3.  8 
3.12 
3.16 
3.20 

46 
47 
48 
49 
50 

3.  4 
3.  8 
3.12 
3.16 
3.20 

51 
52 
53 
54 
55 

3.24 
3.28 
3  32 
3.36 
3.40 

111 
112 
113 
ll4 
115 

7.24 
7.28 
7.32 
7.36 
7.40 

171 
172 
173 
174 
175 

11.24 
11.28 
11.32 
11.36 
11.40 

51 
52 
53 
54 
55 

3.24 
3.28 
3.32 
3.36 
3.40 

51 
52 
53 
54 
55 

3.24 
3.28 
3.32 
3.36 
3.40 

56 
57 
58 
59 
CO 

3.44 
3.48 
3.52 
3.56 
4.  0 

116 
117 
118 
119 

120 

7.44 

7.48 
7.52 
7.56 
8.  0 

176 
177 
178 
179 
180 

11.44 

11  48 
11.52 
11.56 

12     0 

56 
57 
58 
59 
60 

3.44 
3.48 
3.52 
3.56 
4.  0 

56 
57 
58 
59 
60 

3.44 
3.48 
3.52 
3.56 
4.  0 

2GO                TABLE  XII. 

FOB  REDUCING  THE  SUX's  DECLINATION  TO  NOON  AT  ANY  GIVEN  MERIDIAN, 

AND  TO  ANY  TIME  AT  THE  MERIDIAN  OF  GREENWICH. 

When  Sun's  dec.  (  add  in  W.  Ion.  )   Add  tor   1  1  When  Sun's  dec. 

sub.  in  W.  Ion.  )   Sub.  for 

is  increasing,  (sub.  in  E.  lou.  )  Green,  time.  |[   is  decreasing. 

add  in  E.  Ion.)  Green,  time. 

SUN'S  DECLINATION. 

Time 

Long. 

from 

0° 

2° 

4° 

6° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

Noon  . 

0° 

O'O" 

O'O" 

O'O" 

O'O" 

O'O" 

O'O" 

0'  0" 

O'O" 

O'O" 

O'O" 

O'O" 

O'O" 

O'O" 

Oh  Om 

3 

0  12 

0  12 

0  12 

0  11 

0  11 

0  11 

0  11 

0  11 

0  10 

0  10 

0  9 

0  9 

0  9 

0  12 

6 

0  24 

0  24 

0  24 

0  23 

0  23 

0  22 

0  22 

0  21 

0  20 

0  20 

0  18 

0  18 

0  18 

0  24 

9 

0  35 

0  35 

0  35 

0  34 

0  34 

0  33 

0  32 

0  32 

0  31 

0  30 

0  28 

0  27 

0  27 

0  36 

12 

0  47 

0  47 

0  47 

0  46 

0  45 

0  44 

0  43 

0  42 

0  41 

0  40 

0  38 

0  37 

0  36 

0  48 

15 

0  59 

0  59 

0  58 

0  57 

0  56 

0  55 

0  54 

0  53 

0  51 

0  50 

0  48 

0  46 

0  44 

1  0 

18 

1  11 

1  10 

1  10 

1  9 

1  7 

1  6 

1  5 

1  3 

1  1 

1  0 

0  58 

0  55 

0  53 

1  12 

21 

1  22 

1  22 

1  22 

1  21 

1  18 

1  17 

1  16 

1  14 

1  12 

1  9 

1  7 

1  5 

1  2 

1  24 

u 

1  34 

1  34 

1  33 

1  32 

1  29 

1  28 

1  27 

1  24 

1  22 

1  19 

1  17 

1  14 

1  11 

1  36 

27 

1  46 

1  45 

1  44 

1  43 

1  41 

1  39 

1  38 

1  35 

1  32 

1  29 

1  27 

1  23 

1  20 

1  48 

30 

1  58 

1  57 

1  56 

1  54 

1  51 

1  49 

1  48 

1  45 

.1  43 

1  39 

1  36 

1  32 

1  28 

2  0 

33 

2  10 

2  10 

2  8 

2  6 

2  3 

2  1 

1  59 

1  55 

1  53 

1  49 

1  46 

1  42 

1  37 

2  12 

36 

2  22 

2  21 

2  19 

2  17 

2  14 

2  12 

2  Id 

2  6 

2  3 

1  59 

1  56 

1  51 

I  46 

2  24 

39 

2  33 

2  32 

2  31 

2  29 

2  25 

2  23 

2  20 

2  16 

2  14 

2  9 

2  5 

2  1 

1  55 

2  36 

42 

2  45 

2  44 

2  43 

2  40 

2  36 

2  34 

2  31 

2  27 

2  24 

2  19 

2  15 

2  10 

2  4 

2  48 

45 

2  57 

2,56 

2  54 

2  51 

2  47 

2  44 

2  41 

2  38 

2  34 

2  29 

2  24 

2  19 

2  12 

3  0 

48 

3  9 

3  -8 

3  6 

3  3 

2  59 

2  55 

2  52 

2  49 

2  44 

2  39 

2  34 

2  28 

2  21 

3  12 

51 

3  20 

3  19 

3  18 

3  15 

3  10 

3  6 

3  3 

3  0 

2  55 

2  49 

2  44 

2  38 

2  30 

3  24 

54 

3  32 

3  31 

3  30 

3  26 

3  21 

3  17 

3  14 

3  10 

3  5 

2  59 

2  53 

2  47 

2  39 

3  36 

57 

3  43 

3  42 

3  41 

3  37 

3  32 

3  28 

3  25 

3  21 

3  15 

3  9 

3  3 

2  56 

2  48 

3  48 

GO 

3  55 

3  54 

3  52 

3  48 

3  43 

3  39 

3  35 

3  31 

3  25 

3  19 

3  13 

3  5 

2  56 

4  0 

03 

4  7 

4  G 

4  4 

4  it 

3  54 

3  50 

3  46 

3  42 

3  35 

J  29 

3  22 

3  14 

3  5 

4  12 

G6 

4  19 

4  18 

4  16 

4  12 

4  5 

4  1 

3  57 

3  52 

3  46 

3  39 

3  32 

3  23 

3  14 

4  24 

G9 

4  31 

4  30 

4  27 

4  23 

4  16 

4  12 

4  8 

4  3 

3  56 

3  49 

3  4i 

3  32 

3  23 

4  36 

72 

4  43 

4  42 

4  39 

4  34 

4  27 

4  23 

4  19 

4  13 

4  G 

3  59 

3  51 

3  41 

3  32 

4  48 

75 

4  54 

4  53 

4  50 

4  45 

4  38 

4  34 

4  29 

4  23 

4  16 

1  9 

4  1 

3  51 

3  40 

5  0 

78 

5  6 

5  5 

5  2 

4  57 

4  50 

4  45 

4  40 

4  34 

4  27 

4  19 

4  11 

4  0 

3  49 

5  12 

81 

5  18 

5  17 

5  14 

5  9 

5  1 

4  56 

4  51 

4  44 

4  37 

4  29 

4  20 

4  9 

3  58 

5  2t 

84 

5  30 

5  28 

5  26 

5  20 

5  12 

5  7 

5  2 

4  55 

4  47 

t  39 

1  30 

4  18 

4  7 

5  36 

87 

5  41 

5  40 

5  37 

5  31 

5  23 

5  18 

5  13 

5  5 

4  58 

t  49 

4  40 

4  27 

4  16 

5  48 

90 

5  53 

5  52 

5  48 

5  42 

5  34 

5  29 

5  23 

5  16 

5  8 

4  59 

4  49 

4  37 

4  25 

6  0 

'J3 

G  5 

G  4 

6  0 

5  54 

5  40 

5  41 

5  34 

5  27 

5  18 

9 

4  59 

4  4U 

4  34 

G  12 

93 

6  17 

6  15 

6  12 

6  6 

5  57 

5  52 

5  45 

5  37 

5  28 

19 

5  9 

4  55 

4  43 

G  24 

99 

G  28 

6  27 

6  23 

6  17 

6  8 

G  3 

5  56 

5  48 

5  39 

29 

5  18 

5  5 

4  52 

G  36 

102 

6  40 

6  39 

6  35 

6  28 

6  19 

G  14 

6  7 

5  58 

5  49 

39 

5  28 

5  14 

5  0 

G  48 

105 

6  52 

6  51 

G  46 

6  39 

G  30 

G  24 

6  17 

6  9 

5  59 

49 

5  37 

5  23 

5  8 

7  0 

108 

7  4 

7  2 

6  58 

G  51 

6  41 

6  35 

6  28 

6  19 

6  9 

59 

5  47 

5  32 

5  17 

7  12 

111 

7  15 

7  14 

7  10 

7  3 

G  52 

G  46 

G  39 

6  30 

6  20 

9 

5  50 

5  42 

5  26 

7  24 

114 

7  27 

7  26 

7  22 

7  15 

7  3 

6  57 

6  50 

6  40 

G  30 

19 

6  G 

5  51 

5  35 

7  3G 

117 

7  39 

7  37 

7  33 

7  26 

7  14 

7  8 

7  1 

6  51 

6  40 

29 

6  15 

6  1 

5  44 

7  48 

120 

7  51 

7  49 

7  44 

7  37 

7  25 

7  18 

7  11 

7  1 

6  51 

39 

6  25 

6  10 

5  53 

8  0 

12.J 

8  3 

8  1 

7  56 

7  49 

7  37 

7  29 

7  22 

7  12 

7  1 

6  49 

G  35 

6  19 

6  2 

8  J2 

126 

8  11 

8  13 

8  8 

8  0 

7  48 

7  40 

7  33 

7  22 

7  11 

6  59 

G  44 

6  28 

6  11 

8  24 

129 

8  26 

8  21 

8  20 

8  11 

7  59 

7  51 

7  43 

7  33 

7  22 

7  9 

6  54 

G  37 

6  19 

8  36 

132 

8  38 

8  36 

8  31 

8  22 

8  10 

8  2 

7  54 

7  43 

7  32 

7  18 

7  4 

3  46 

6  28 

8  48 

135 

8  50 

8  48 

8  42 

8  33 

8  21 

8  13 

8  4 

7  54 

7  42 

7  28 

7  13 

G  56 

6  33 

9  0 

138 

9  1 

8  59 

8  54 

8  45 

8  33 

8  24 

8  15 

8  5 

7  52 

7  38 

7  23 

7  5 

6  45 

9  12 

141 

9  13 

9  11 

9  6 

8  57 

8  44 

8  35 

8  26 

8  15 

8  3 

7  48 

7  33 

7  14 

6  54 

9  24 

144 

9  25 

9  23 

9  18 

9  8 

8  55 

8  46 

8  37 

8  26 

8  13 

7  58 

7  42 

7  23 

7  3 

9  36 

117 

9  37 

9  35 

9  29 

9  19 

9  6 

8  57 

8  48 

8  3G 

8  23 

8  8 

7  52 

7  32 

7  12 

9  48 

550 

9  48 

9  45 

9  40 

9  30 

9  17 

9  8 

8  58 

8  47 

8  33 

8  18 

8  2 

7  42 

7  21 

10  0 

153 

10  0 

9  57 

U  52' 

9  42 

9  28 

9  19 

9  9 

8  57 

8  43 

8  28 

8  12 

7  51 

7  30 

10  12 

156 

10  12 

10  9 

10  4 

9  54 

9  39 

9  30 

9  20 

9  8 

8  54 

8  38 

8  21 

8  0 

7  39 

10  24 

159 

10  24 

10  21 

10  16 

10  5 

9  50 

9  41 

9  31 

9  18 

9  4 

8  48 

8  31 

8  10 

7  48 

10  36 

162 

10  36 

10  33 

10  27 

10  16 

10  1 

9  52 

9  42 

9  29 

9  14 

8  58 

8  41 

8  19 

7  57 

10  48 

165 

10  47 

10  44 

10  38 

10  27 

10  12 

10  3 

9  52 

9  39 

9  24 

9  8 

8  50 

8  28 

8  5 

11  0 

168 

10  59 

10  56 

10  50 

10  39 

10  24 

10  14 

10  3 

9  50 

9  35 

9  18 

9  0 

8  38 

8  14 

H  12 

171 

11  11 

11  8 

11  2 

10  51  10  35 

10  25 

10  14 

10  0 

9  45 

9  28 

9  10 

8  47 

8  23 

U  24 

171 

11  23 

11  2011  14 

11  310  46 

10  36 

10  25 

10  11 

9  55 

'.)  38 

0   J.  J 

8  57 

3  32 

U  33 

177 

11  34 

11  31  1  1  25 

11  14 

10  57  10  47 

10  36 

10  21 

10  G 

9  48 

9  29 

9  6 

8  41 

11  48 

180 

11  4G 

11  43 

11  37 

11  25 

11  8 

10  58 

10  46 

10  32 

10  16 

J  58 

9  389  15 

S  49 

12  0 

TABLE  XII.                261 

FOB  REDUCING  THE  SUN*S  DECLINATION  TO  NOON  AT  ANY  GIVEN  MERIDIAN, 

AND  TO  ANY  TIME  AT  THE  MERIDIAN  OF  GREENWICH. 

When  Sun's  dec.  i  add  in  W.  Ion.  1   Add  for 

When  Snn's  dec.  j  sub.  in  W.  Ion.  )   sub.  for 

is  increasing,  (sub  in  E.  Ion.  J  Green,  time. 

is  decreasing,  (add  in  E.  Ion.  J  Green,  time. 

SUN'S  DECLINATION. 

Time 

Lon 

from 

17- 

18° 

19° 

19°  30 

20° 

20°  30 

21° 

21°  30 

22° 

22°  30 

'23' 

23°  15 

23°  28' 

Noon. 

o- 

0'0"0'0"0'0" 

0'  0" 

O'O' 

0'  0' 

O'O' 

0'  0"0'0" 

0'  0"0'0' 

0'  0' 

O'O" 

OhOm 

3 

0  80  80  7 

0  7 

o  e 

0  6 

0  £ 

0  5 

0  4 

0  3 

0  2 

0  2 

0  0 

0  12 

6 

0  160  160  14 

0  13 

0  12 

0  11 

0  1C 

0  9 

0  8 

0  6 

0  4 

0  4 

0  0 

0  24 

9 

0  240  240  21 

0  20 

0  18 

0  17 

0  15 

0  14 

0  12 

0  10 

0  n 

0  5 

0  0 

0  36 

12 

0  35 

0  31!0  28 

0  27 

0  25 

0  23 

0  21 

0  19 

0  16 

0  14 

0  9 

0  7 

0  0 

0  48 

15 

0  41 

0  490  35 

0  34 

0  32 

0  29 

0  27 

0  24 

0  21 

0  18 

0  12 

0  9 

0  0 

0  0 

18 

0  4£ 

0  460  42 

0  40 

0  38 

0  35 

0  32 

0  29 

0  25 

0  21 

0  14 

0  10 

0  0 

1  12 

'21 

0  57 

0  540  4S 

0  47 

0  44 

0  41 

0  38 

0  34 

0  29 

0  24 

0  17 

0  12 

0  0 

1  24 

24 

1  £ 

1  '2 

0  5G 

0  54 

0  50 

0  47 

0  44 

0  39 

0  34 

0  28 

0  19 

0  14 

0  0 

1  36 

27 

I  14 

I  1C 

1  j 

1  1 

0  57 

0  53 

0  50 

0  44 

0  39 

0  32 

0  22 

0  15 

0  0 

1  48 

30 

1  23 

1  18 

1  11 

1  8 

1  4 

0  59 

0  55 

0  49 

0  43 

0  36 

0  25 

0  17 

0  0 

2  0 

33 

1  31 

1  25 

1  Ib 

1  14 

1  10 

1  4 

1  .(J 

0  53 

0  4" 

0  39 

0  27 

0  19 

0  0 

2  12 

3u 

1  39 

I  33 

1  25 

1  21 

L  16 

1  10 

1  5 

0  58 

0  5 

0  42 

0  30 

0  20 

0  0 

2  24 

39 

1  47 

I  41 

1  32 

1  28 

1  2'2 

1  16 

1  10 

1  3 

0  5o 

0  46 

0  32 

0  22 

0  0 

2  36 

42 

1  5G 

1  49 

I  39 

1  35 

1  29 

1  22 

1  16 

1  8 

0  59 

0  50 

0  34 

0  24 

0  0 

2  48 

45 

2  5 

1  57 

1  46 

1  42 

1  36 

1  28 

1  22 

1  13 

1  4 

0  54 

0  36 

0  25 

0  0 

3  0 

48 

2  13 

2  4 

1  53 

1  48 

I  42 

1  33 

1  27 

1  18 

1  8 

0  57 

0  39 

0  27 

0  0 

3  12 

51 

2  21 

2  12 

2  0 

1  55 

1  48 

1  39 

1  32 

1  23 

1  12 

1  0 

0  42 

0  29 

0  0 

3  24 

54 

2  29 

2  20 

2  7 

2  2 

1  54 

1  45 

1  38 

1  28 

1  16 

1  3 

0  44 

0  30 

0  0 

3  36 

57 

•2  38 

2  28 

2  15 

2  9 

2  1 

1  52 

1  44 

1  33 

1  21 

1  7 

0  47 

0  32 

0  0 

3  48 

CO 

2  47 

2  36 

2  23 

2  16 

2  8 

1  59 

1  49 

1  39 

1  26 

1  11 

0  49 

0  34 

0  0 

4  0 

03 

•2  55 

2  43 

2  29 

2  '22 

2  14 

2  4 

1  54 

1  4J 

1  30 

1  14 

0  51 

0  3-5 

0  0 

4  12 

CG 

3  3 

2  51 

2  36 

2  29 

2  20 

2  10 

1  59 

1  48 

1  34 

1  17 

0  54 

0  37 

0  0 

4  24 

69 

3  11 

2  59 

2  43 

2  36 

2  26 

2  16 

2  4 

1  53 

1  38 

1  21 

0  56 

0  39 

0  0 

4  36 

72 

3  19 

3  7 

2  5U 

2  43 

2  33 

2  21 

2  10 

1  58 

1  4'^ 

1  25 

0  59 

0  40 

0  0 

4  48 

75 

3  28 

3  15 

2  58 

2  50 

2  40 

2  27 

2  16 

2  3 

1  47 

1  29 

1  1 

0  42 

0  0 

5  0 

78 

3  36 

3  2. 

3  5 

2  56 

2  46 

2  33 

2  21 

2  8 

1  51 

1  32 

1  4 

0  44 

0  0 

5  12 

81 

3  44 

3  30 

3  12 

3  3 

2  52 

2  39 

2  26 

2  13 

1  55 

1  35 

1  6 

0  45 

0  0 

5  21 

84 

3  52 

J  3.->3  19 

3  10 

2  58 

2  45 

2  32 

2  18 

1  59 

1  39 

1  9 

0  47 

0  0 

5  36 

87 

4  1 

3  463  20 

3  17 

3  5 

2  52 

2  38 

2  23 

2  4 

1  43 

1  11 

0  49 

0  0 

5  48 

90 

4  10 

3  51 

3  34 

3  24 

3  12 

2  59 

2  41 

2  28 

2  1 

1  47 

1  14 

0  50 

0  0 

6  0 

93 

4  181  13  41 

3  30 

3  18 

3  4 

^  49 

•2  32 

2  13 

1  50 

1  16 

0  52 

0  0 

6  J2 

96 

4  264  93  48 

3  37 

3  24 

3  9 

2  54 

2  37 

2  17 

1  53 

1  19 

0  54 

0  0 

6  24 

90 

4  344  17 

3  55 

3  44 

3  30 

3  15 

2  59 

2  42 

2  21 

1  57 

1  21 

0  55 

0  0 

6  36 

102 

4  43  1  25 

4  2 

3  51 

3  37 

3  21 

3  5 

2  47 

2  25 

2  1 

1  24 

0  57 

0  0 

6  48 

105 

4  524  33 

4  9 

3  58 

3  44 

3  27 

3  11 

2  52 

2  30 

2  5 

1  26 

0  59 

0  0 

7  0 

108 

5  04  404  16 

4  4 

3  50 

3  33 

3  16 

2  57 

2  34 

2  9 

1  29 

1  0 

0  0 

7  12 

111 

5  84  484  23 

4  11 

3  56 

3  39 

3  21 

3  2 

2  38 

2  12 

1  31 

1  2 

0  0 

7  24 

114 

16 

4  56  4  30 

4  18 

4  2 

3  46 

3  27 

3  7 

2  43 

2  16 

1  34 

1  4 

0  0 

7  36 

117 

25 

5  44  38 

4  25 

4  9 

3  52 

3  33 

3  12 

2  48 

2  20 

1  37 

1  5 

0  0 

7  48 

120 

31 

.5  12 

4  46 

4  32 

4  16 

3  59  3  39 

3  17 

2  53 

2  23 

1  39 

1  7 

0  0 

8  0 

123 

42 

5  19 

4  53 

4  38 

i  22 

4  4 

3  41 

3  22 

2  57 

2  20 

1  41 

1  9 

0  0 

8  12 

12G 

50 

5  27 

5  0 

4  45 

4  28 

4  10 

3  49 

3  27 

3  1 

2  29 

1  44 

1  10 

0  0 

8  24 

129 

58 

5  30 

5  7 

4  52 

1  34 

4  16 

3  54 

3  32 

3  5 

2  33 

1  4G 

1  12 

0  0 

8  36 

132 

6 

5  43 

5  14 

4  59 

1  41 

4  22 

3  59 

3  37 

3  9 

2  36 

1  49 

1  14 

0  0 

8  48 

185 

15 

5  51 

5  21 

5  6 

1  48 

4  28 

4  5 

3  42 

13 

2  40 

1  51 

1  15 

0  0 

9  0 

138 

23 

3  58 

5  2b 

5  12 

4  54 

4  34 

4  10 

3  47 

17 

2  43 

1  54 

1  17 

0  0 

9  12 

141 

31 

6  6 

5  3? 

5  19 

5  0 

4  40 

4.  15 

3  52 

21 

2  46 

1  56 

1  19 

0  0 

9  24 

lit 

39 

a  14 

5  42 

5  2G 

3  0 

4  46 

4  21 

3  57 

26 

2  50 

1  59 

1  20 

0  0 

9  36 

147 

0  48 

6  22 

5  49 

5  33 

5  13 

4  52 

4  27 

4  2 

30 

2  54 

2  1 

1  22 

0  0 

9  48 

150 

G  57 

6  30 

5  57 

5  40 

5  20 

4  58 

4  33 

4  7 

35 

2  58 

2  4 

1  24 

0  0 

10  0 

153 

7  5 

G  37 

G  4 

5  4G 

3  '26 

5  3 

i  38 

4  11 

39 

3  1 

I  6 

1  25 

0  0 

10  12 

156 

7  13 

6  45 

G  11 

5  53 

3  32 

5  9 

t  43 

4  16 

43 

3  4 

2  9 

1  27 

0  0 

10  24 

159 

7  21 

6  53 

G  18 

6  0 

3  38 

5  15 

4  48 

4  21 

47 

3  8 

2  11 

1  29 

0  0 

10  36 

162 

7  29 

7  1 

G  25 

6  7 

3  45 

5  21 

4  54 

4  26 

51 

3  12 

2  13 

1  30 

0  0 

10  48 

1G5 

7  38 

7  9 

6  32 

G  14 

5  52 

5  26 

3  0 

4  31 

56 

3  16 

2  15 

1  32 

0  0 

LI  0 

168 

7  4G 

7  1C 

G  39 

6  20 

3  58 

5  32 

5  6 

4  36 

t  0 

3  19 

2  17 

1  34 

0  0 

11  12 

171 

7  54 

7  24 

G  40 

G  27 

>  4. 

5  38 

3  11 

4  41 

1  4 

3  22 

2  20 

1  35 

0  0 

11  24 

174 

8  3 

7  3± 

G  53 

G  34 

j  10 

5  4t 

3  17 

4  46 

I  9 

3  26 

2  22 

1  37 

0  0 

11  36 

177 

s  i-j 

1  4d 

7  1 

6  41 

j  17 

:,  .M 

5  23 

4  51 

I  14 

3  30 

2  25 

1  39 

0  0 

11  48 

180 

8  21 

7  48 

7  9 

6  48 

3  24 

5  58 

5  29 

4  56 

t  19 

3  34 

2  28 

1  40 

0  0 

12  0 

262                TABLE  XIII. 

CORRECTIONS  OF  THE  APPARENT  ALTITUDES  OF  THE  SUN  AND  STARS. 

App, 
Alt. 

Sun's 
Corr. 

Star's 
Corr. 

Diff. 
to  1' 

App. 
Alt. 

Sun's 
Corr. 

Star's 
Corr. 

App. 
AH. 

Sun's 
Corr. 

Star's 
Corr. 

App. 
Alt. 

Sun's 
Corr. 

Star's 
Corr. 

o   / 

0  0 
5 
10 
15 
20 
25 

32  51 
32  1 
31  13 
30  26 
29  41 
28  56 

33  0 
32  10 
31  22 
30  35 
29  49 
29  5 

10.0 
9.6 
9.4 
9.1 
8.9 
8.6 

5  0 
1 
2 
3 
4 
5 

9  44 
9  42 
9  41 
9  39 
9  37 
9  36 

9  52 
9  51 
9  49 
9  48 
9  46 
9  44 

6  0 
1 
2 
3 
4 
5 

8  18 
8  17 
8  15 
8  14 
8  13 
8  12 

8  26 
8  25 
8  24 
8  23 
8  22 
8  20 

7  0 
1 
2 
3 

4 
5 

7  12 

7  11 
7  10 

7  9 
7  8 
7  7 

7  21 
7  20 
7  19 
7  18 
7  17 
7  16 

0  30 
35 
40 
45 
50 
55 

28  13 
27  31 
26  51 
26  11 
25  33 
24  55 

28  22 
27  40 
26  59 
26  20 
25  41 
25  4 

8  4 
8.1 

7.9 

7.7 
7.4 
7.2 

5  6 
7 
8 
9 
10 
11 

9  34 
9  32 
9  31 
9  29 

9  28 
9  26 

9  43 
9  41 
9  40 
9  38 
9  36 
9  35 

6  6 
7 
8 
9 
10 
11 

8  10 
8  9 
8  8 
8  7 
8  6 
8  4 

8  19 
8  18 
8  17 
8  15 
8  14 
8  13 

7  6 
7 
8 
9 
10 
11 

7  6 
7  6 
7  5 
7  4 
7  3 
7  2 

7  15 
7  14 
7  13 
7  12 
7  11 
7  10 

1  0 
5 
10 
15 

20 
25 

24  19 
23  44 
23  10 
22  38 
22  6 
21  35 

24  28 
23  53 
23  19 
22  46 
22  15 
21  44 

7.0 
6.7 
6.5 
6.4 
6.2 
6.1 

5  12 
13 
14 
15 
16 
17 

9  25 
9  23 
9  21 
9  20 
9  18 
9  17 

9  33 
9  32 
9  30 
9  29 
9  27 
9  25 

6  12 
13 
14 
15 
16 
17 

8  3 
8  2 

8  1 
8  0 
7  59 
7  57 

8  12 
8  11 
8  10 
8  8 
8  7 
8  6 

7  12 
13 
14 
15 
16 
17 

7  1 
7  0 
6  59 
6  58 
6  57 
6  56 

7  10 
7  9 
7  8 
7  7 
7  6 
7  5 

1  30 
35 
40 
45 

50 
55 

21  5 
20  36 
20  8 
19  41 
19  15 
18  50 

21  14 
20  45 
20  17 
19  50 
19  24 
18  59 

5.7 
5.6 
5.3 
5.2 
5.0 
.4.9 

5  18 
19 
20 
21 
22 
23 

9  15 
9  14 
9  12 
9  11 
9  9 
9  8 

9  24 
9  22 
9  21 
9  19 
9  18 
9  16 

6  18 
19 
20 
•21 
22 
23 

7  56 
7  55 
7  54 
7  53 
7  52 
7  50 

8  5 
8  4 
8  3 
8  1 
8  0 
7  59 

7  18 
19 
20 
21 
22 
23 

6  55 
6  55 
6  54 
6  53 
6  52 
6  51 

7  4 
7  3 
7  2 
7  1 
7  1 
7  0 

2  0 
5 
10 
15 
20 
25 

18  25 
18  2 
17  39 
17  17 
16  55 
16  34 

18  34 
18  10 
17  48 
17  25 
17  4 
16  43 

4.7 
4.5 
4.5 
4.3 
42 
4.0 

5  24 
25 
26 
27 
28 
29 

9  6 
9  5 
9  3 
9  2 
9  0 
8  59 

9  15 
9  13 
9  12 
9  11 
9  9 
9  8 

6  24 
25 
26 
27 
28 
29 

7  49 
7  48 
7  47 
7  46 
7  45 
7  44 

7  58 
7  57 
7  56 
7  55 
7  54 
7  53 

7  24 
25 
26 
27 

28 
29 

6  50 
6  49 
6  48 
6  48 
6  47 
6  46 

6  59 
6  58 
6  57 
6  56 
6  55 
6  54 

2  30 
35 
40 
45 
50 
55 

16  14 
15  55 
15  36 
15  17 
15  0 
14  43 

16  23 
16  3 
15  44 
15  26 
15  8 
14  51 

3.9 
3.8 
3.6 
3.5 
3.4 
3  4 

5  30 
31 
32 
33 
34 
35 

8  58 
8  56 
8  55 
8  53 
8  52 
8  51 

9  6 
9  5 
8  3 
9  2 
9  1 
8  59 

6  30 
31 
32 
33 
34 
35 

7  43 
7  42 
7  41 
7  40 
7  38 
7  37 

7  51 

7  50 
7  49 
7  48 
7  47 
7  46 

7  30 
31 
32 
33 
34 
35 

6  45 
6  44 
6  43 
6  42 
6  42 
6  41 

6  54 
6  53 
6  52 
6  51 

6  50 
6  49 

3  0 
5 
10 
15 
20 
25 

14  26 
14  10 
13  54 
13  39 
13  24 
13  10 

14  35 
14  19 
14  3 
13  48 
13  33 
13  19 

3.3 
3.2 
3.1 
3.0 

2.8 
2.8 

5  36 
37 
38 
39 
40 
41 

8  49 
8  48 
8  46 
8  45 
8  44 
8  42 

8  58 
8  56 
8  55 
8  54 
8  52 
8  51 

6  36 
37 
38 
39 
40 
41 

7  36 
7  35 
7  34 
7  33 
7  32 
7  31 

7  45 
7  44 
7  43 
7  42 
7  41 
7  40 

7  36 
37 
38 
39 
40 
41 

6  40 
6  39 
6  38 
6  37 
6  37 
6  36 

6  49 
6  48 
6  47 
6  46 
6  45 
6  44 

3  30 
35 
40 
45 
50 
55 

12  56 
12  43 
12  30 
12  17 
12  5 
11  53 

13  5 
12  51 
12  38 
12  26 
12  13 
12  1 

2.7 
2.6 
2.6 
2.5 
2.4 
2.3 

5  42 
43 
44 
45 
46 
47 

8  41 
8  40 
8  38 
8  37 
8  36 
8  34 

8  50 
8  48 
8  47 
8  46 
8  44 
8  43 

6  42 
43 
44 
45 
46 
47 

7  30 
7  29 
7  28 
7  27 
7  26 
7  25 

7  39 
7  38 
7  37 
7  36 
7  35 
7  34 

7  42 
43 
44 
45 
46 
47 

6  35 
6  34 
6  33 
6  33 
6  32 
6  31 

6  44 
6  43 
6  42 
6  41 
6  40 
6  40 

4  0 
5 
10 
15 
20 
25 

11  41 
11  30 
11  19 
11  8 

10  58 
10  48 

11  50 
11  38 
11  27 
11  17 
11  6 
10  56 

2.3 
2.2 
2.1 
2.1 
2.0 
2.0 

5  48 
49 
50 
51 
52 
53 

8  33 
8  32 
8  30 
8  29 
8  28 
8  27 

8  42 
8  40 
8  39 
8  38 
8  36 
8  35 

6  48 
49 
50 
51 
52 
53 

7  24 
7  23 
7  22 
7  21 
7  20 
7  19 

7  33 
7  32 
7  31 
7  30 

7  29 
7  28 

7  48 
49 
50 
51 
52 
53 

6  30 
6  29 
6  29 
6  28 
6  27 
6  26 

6  39 
6  38 
6  37 
6  36 
6  36 
6  35 

4  30 
35 
40 
45 
50 
55 

10  38 
10  28 
10  19 
10  10 
10  1 
9  52 

10  46 
10  37 
10  28 
10  18 
10  10 
10  1 

1.9 
1.9 
1.8 
1.8 
1.7 
1.7 

5  54 
55 
56 

57 
58 
59 

8  25 
8  24 
8  23 
8  21 
8  20 
8  19 

8  34 
8  33 
8  31 
8  30 
8  29 
8  28 

6  54 
55 
56 
57 

58 
59 

7  18 
7  17 
7  16 
7  15 
7  14 
7  13 

7  27 
7  26 
7  25 
7  24 
7  23 
7  22 

7  54 
55 
56 
57 

58 
59 

6  25 
6  25 
6  24 
6  23 
6  22 
6  22 

6  34 
6  33 
6  33 
6  32 
6  31 
6  30 

TABLE  XIII.                263 

CORKECTIONS  OF  THE  APPAEENT  ALTITUDES  OF  THE  SUN  AND  STARS. 

App. 
Alt. 

Sun's 
Corr. 

Star's 
Corr. 

App. 

Alt. 

Sun's 
Corr. 

Star's 
Corr. 

App. 

Alt. 

Sun's 
Corr. 

Star's 
Corr. 

App. 
Alt. 

Sun's 
Corr. 

Star's 
Corr. 

O     ' 

8  0 
1 
2 
3 
4 
5 

6  21 

6  20 
6  19 
6  19 
6  18 
G  17 

6  30 
6  29 
6  28 
6  27 
6  27 
6  26 

9  0 
2 
4 
6 
8 
10 

5  40 
5  39 
5  37 
5  35 
5  34 
5  34 

5  48 
5  47 
5  46 
5  45 
5  44 
5  42 

11  0 
2 
4 
6 
8 
10 

4  38 
4  37 
4  37 
4  36 
4  35 
4  34 

4  47 
4  46 
4  45 
4  44 
4  43 
4  43 

o   / 

13  0 

2 
4 
6 
8 
10 

3  54 
3  54 
3  53 
3  53 
3  52 
3  51 

4  3 
4  2 
4  2 
4  1 
4  1 
4  0 

8  G 
7 
8 
9 
10 
11 

6  1G 
6  16 
6  15 
6  14 
6  13 
6  13 

G  25 
6  24 
6  24 
6  23 
6  22 
6  21 

9  12 
14 
16 
18 
20 
22 

5  33 
5  31 
5  30 
5  29 

5  28 
5  27 

5  41 
5  40 
5  39 
5  38 
5  36 
5  35 

11  12 
14 
16 

18 
20 

22 

4  33 
4  32 
4  32 
4  31 

4  30 
4  29 

4  42 
4  41 
4  40 
4  89 
4  39 
4  38 

13  12 
14 
16 
18 
20 
22 

3  51 
3  50 
3  50 
3  49 
3  48 
3  48 

3  59 
3  59 
3  58 
3  57 
3  57 
3  56 

8  12 
13 
14 
15 
16 
17 

G  12 
6  11 
6  10 
6  10 
6  9 
6  8 

6  21 
6  20 
6  19 
6  18 
6  18 
6  17 

9  24 
26 
28 
30 
32 
34 

5  iiG 
5  24 
5  23 
5  22 
5  21 
5  20 

5  34 
5  33 
5  32 
5  31 
5  30 
5  29 

11  24 
26 
28 
30 
32 
34 

4  28 
4  28 
4  27 
4  26 
4  25 
4  24 

4  37 
4  36 
4  35 
4  35 
4  34 
4  33 

13  24 
26 
28 
30 
32 
34 

3  47 
3  47 
3  46 
3  45 
3  45 
3  44 

3  5G 
3  55 
3  54 
3  54 
3  53 
3  53 

8  18 
19 
20 
21 
22 
23 

6  8 
6  7 
6  6 
6  5 
6  5 
6  4 

6  JG 
6  16 
6  15 
6  14 
6  13 
6  13 

9  3G 
38 
40 
42 
44 
46 

5  1U 
5  18 
5  17 
5  16 
5  15 
5  13 

5  'z7 
5  26 
5  25 
5  24 
5  23 
5  22 

11  36 
38 
40 
42 
44 
46 

4  24 
4  23 
4  22 
4  21 
4  21 
4  20 

4  32 
4  31 
4  31 
4  30 
4  29 
4  28 

13  3G 
38 
40 
42 
44 
46 

3  44 
3  43 
3  43 
3  42 
3  41 
3  41 

3  52 
3  52 
3  51 
3  51 
3  50 
3  49 

8  24 
25 
26 

27 
28 
29 

G  3 
6  3 
6  2 
6  1 
6  1 
6  0 

6  la 
6  11 
6  11 
6  10 
6  9 
G  9 

9  48 
60 
52 
54 
56 
58 

5  12 
5  11 
5  10 
5  9 
5  8 
5  7 

5  21 
5  20 
5  19 
5  18 
5  17 
5  16 

11  48 
50 
52 
54 

56 

58 

4  19 
4  18 
4  18 
4  17 
4  16 
4  15 

4  28 
4  27 
4  26 
4  25 
4  25 
4  24 

13  48 
50 
52 
54 
56 
58 

3  40 
3  40 
3  39 
3  39 
3  38 
3  38 

3  49 
3  48 
3  48 
3  47 
3  47 
3  46 

8  u() 
31 
32 
33 
34 
35 

5  59 
5  59 
5  58 
5  57 
5  57 
5  56 

6  8 
6  7 
6  7 
6  6 
6  5 
6  5 

10  0 
2 
4 
6 
8 
10 

5  6 
5  5 
5  4 
5  3 
5  2 
5  1 

5  15 
5  14 
5  13 
5  12 
5  11 
5  10 

12  0 
2 
4 
6 
8 
10 

4  15 
4  14 
4  13 
4  12 
4  12 
4  11 

4  23 

4  22 
4  22 
4  21 
4  20 
4  20 

14  0 
2 
4 
6 
8 
10 

3  37 
3  36 
3  36 
3  35 
3  35 
3  34 

3  45 
3  45 
3  44 
3  44 
3  43 
3  43 

8  30 
37 
38 
39 
40 
41 

5  55 
5  55 
5  54 
5  53 
5  53 
5  52 

o  4 
6  3 
6  3 
6  2 
6  1 
6  1 

10  12 
14 
16 

18 
20 
22 

5  0 
4  59 
4  58 
4  57 
4  56 
4  55 

5  9 
5  8 
5  7 
5  6 
5  5 
5  4 

12  12 
14 
16 

18 
20 
22 

4  1U 
4  10 
4  9 
4  8 
4  8 
4  7 

4  19 
4  18 
4  17 
4  17 
4  16 
4  15 

14  12 
14 
16 
18 
20 
22 

3  34 
3  33 
3  33 
3  32 
3  32 
3  31 

3  42 
3  42 
3  41 
3  41 
3  40 
3  40 

8  42 
43 
44 
45 
46 
47 

5  51 
5  51 
5  50 
5  49 
5  49 
5  48 

G  0 
5  59 
5  59 
5  58 
5  57 
5  57 

10  24 
26 
28 
30 
32 
34 

4  54 
4  53 
4  53 
4  52 
4  51 
4  50 

5  3 

5  2 
5  1 
5  0 
4  59 
4  58 

12  24 
26 
28 
30 
32 
34 

4  6 
4  6 
4  5 
4  4 
4  3 
4  3 

4  15 
4  14 
4  13 
4  13 
4  12 
4  11 

14  24 
26 
28 
30 
32 
34 

3  31 
3  30 
3  30 
3  29 
3  29 
3  28 

3  39 
3  39 
3  38 
3  38 
3  37 
3  37 

8  48 
49 
50 
51 
52 
53 

5  47 
5  47 
5  46 
5  45 
5  45 
5  44 

5  56 
5  55 
5  55 
5  54 
5  53 
5  53 

10  36 
38 
40 
42 
44 
46 

4  49 
4  48 
4  47 
4  46 
4  45 
4  44 

4  57 
4  57 
4  56 
4  55 
4  54 
4  53 

12  3G 
38 
40 
42 
44 
46 

4  2 
4  2 
4  1 
4  0 
4  0 
3  59 

4  n 

4  10 
4  9 
4  9 
4  8 
4  7 

14  3G 
38 
40 
42 
44 
46 

3  28 
3  27 
3  27 
3  26 
3  26 
3  25 

3  36 
3  36 
3  35 
3  35 
3  34 
3  34 

8  54 
55 
56 
57 
58 
59 

5  44 
5  43 
5  42 
5  42 
5  41 
5  40 

5  52 
5  52 
5  51 
5  50 
5  50 
5  49 

10  48 
50 
52 
54 
56 
58 

4  43 
4  43 
4  42 
4-41 
4  40 
4  39 

4  52 
4  51 
4  50 
4  49 
4  49 
4  48 

12  48 
50 
52 
54 
56 
58 

3  58 
3  58 
3  57 
3  56 
3  56 
3  55 

4  7 
4  6 
4  5 
4  5 
4  4 
4  4 

14  48 
50 
52 
54 
66 
68 

3  25 
3  24 
3  24 
3  23 
3  23 
3  22 

3  33 
3  33 
3  32 
3  32 
3  31 
3  31 

264                TABLE  XIII. 

CORRECTIONS  OF  THE  APPARENT  ALTITUDES  OF  THE  SUN  AND  STARS. 

App. 
Alt. 

Sun's 
Corr. 

Star's 
Corr. 

App.   Sun's 
Alt.   Corr. 

Star's 
Corr. 

App. 
Alt. 

Sun's 
Corr. 

Star's 
Corr. 

App. 
Alt. 

Sun's 
Corr. 

Star's 

Corr. 

O      / 

15  0 
5 
10 
15 
20 
25 

3  22 
3  21 
3  19 
3  18 
3  17 
3  16 

3  30 

3  29 
3  28 
3  27 
3  26 
3  24 

20  0 
10 
20 
30 
40 
50 

2  27 
2  26 
2  25 
2  23 
2  22 
2  21 

2  35 
2  34 
2  33 
2  31 

2  30 

2  29 

30  0 
20 
40 
31  0 
20 
40 

1  31 
1  30 

1  28 
1  27 
1  26 
1  25 

1  38 
1  37 
1  36 
1  35 
1  33 
1  32 

50  0 
30 
51  0 
30 
52  0 
30 

0  42 
0  41 
0  41 
0  40 
0  39 
0  38 

0  48 
0  47 
0  46 
0  45 
0  44 
0  44 

15  30 
35 
40 
45 
50 
55 

3  15 
3  14 
3  13 
3  11 
3  10 
3  9 

3  23 
3  22 
3  21 
3  20 
3  19 
3  18 

21  0 
10 
20 
30 

40 
50 

•2  TJ 
2  18 
2  17 
2  16 
2  14 
2  13 

'2  'z7 
2  26 
2  25 
2  24 
2  23 
2  21 

32  0 
20 
40 
33  0 
20 
40 

1  '24 
1  22 
1  21 
1  20 
1  19 
1  18 

1  31 
1  30 
1  29 
1  27 
1  26 
1  25 

53  0 
30 
54  0 
30 
55  0 
30 

0  38 
0  37 
0  36 
0  36 
0  35 
0  34 

0  43 
0  42 
0  41 
0  41 
0  40 
0  39 

16  0 
5 
10 
15 
20 
25 

3  8 
3  7 
3  6 
3  5 
3  4 
3  3 

3  17 
3  16 
3  15 
3  14 
3  13 
3  12 

22  0 
10 
20 
30 
40 
50 

2  12 
2  11 
2  10 
2  9 
2  8 
2  7 

•2  20 
2  19 
2  18 
2  17 
2  16 
2  15 

34  0 
20 
40 
35  0 
20 
40 

1  17 
1  16 
1  15 
1  14 
1  13 
1  12 

1  24 
1  23 
1  22 
1  21 
1  20 
1  19 

56  0 
30 
57  0 
30 
58  0 
30 

0  34 
0  33 
0  32 
0  32 
0  31 
0  30 

0  38 
0  38 
0  37 
0  36 
0  36 
0  35 

16  30 
35 
40 
45 
50 
55 

3  2 
3  1 
3  0 

2  59 
2  58 
2  57 

3  11 
3  10 
3  9 
3  8 
3  7 
3  6 

23  0 
10 
20 
30 
40 
50 

2  6 
2  4 
2  3 
2  2 
2  1 
2  0 

2  14 
2  13 
2  11 

2  10 
2  9 

2  8 

36  0 
20 
40 
37  0 
20 
40 

1  11 
1  10 
1  9 
1  9 

1  8 
1  7 

1  18 
1  17 
1  16 
1  15 
1  15 
1  14 

59  0 
30 
60  0 
30 
61  0 
30 

0  30 
0  29 
0  29 
0  5-8 
0  27 
0  '27 

0  34 
0  34 
0  33 
0  32 
0  32 
0  31 

17  0 
5 
10 
15 
20 
25 

2  56 
2  55 
2  54 
2  54 
2  53 
2  52 

3  5 
3  4 
3  3 
3  2 
3  1 
3  0 

24  0 
10 
20 
30 

40 
50 

1  59 
1  58 
1  57 
1  57 
1  56 
1  55 

2  7 
2  6 
2  5 
2  4 
2  4 
2  3 

38  0 
20 
40 
39  0 
20 
40 

1  6 
1  5 
1  4 
1  3 
1  3 
1  2 

1  13 
1  12 
1  11 
1  10 
1  9 
1  9 

62  0 
30 
63  0 
30 
64  0 
30 

U  26 
0  26 
0  25 
0  24 
0  24 
0  23 

0  30 
0  30 
0  29 
0  28 
0  28 
0  27 

17  30 
35 
40 
45 
50 
55 

2  51 
2  50 
2  49 
2  48 
2  47 
2  46 

2  59 
2  58 
2  57 
2  56 
2  56 
2  55 

25  0 
10- 
20 
30 
40 
50 

1  54 
1  53 
1  52 
1  51 
1  50 
1  49 

2  2 
2  1 
2  0 
1  59 
1  58 
1  57 

40  0 
20 
40 
41  0 
20 
40 

1  1 

1  0 
0  59 
0  59 
0  58 
0  57 

I  8 
1  7 
1  6 
1  5 
1  5 
1  4 

65  0 
30 

66  0 
30 
67  0 
30 

0  '23 
0  22 
0  22 
0  21 
0  21 
0  20 

0  '27 
0  26 
0  25 
0  25 
0  24 
0  24 

1«  0 
5 
10 
15 
20 
25 

2  46 
2  45 
2  44 
2  43 
2  42 
2  41 

2  54 
2  53 
2  52 
2  51 
2  51 
2  50 

26  0 
10 
20 
30 
40 
50 

1  49 
1  48 
1  47 
1  46 
1  45 
1  44 

1  56 
1  56 
1  55 
1  54 
1  53 
1  52 

4'2  U 
20 
40 
43  0 

20 
40 

0  57 
0  56 
0  55 
0  55 
0  54 
0  53 

1  3 
1  2 
1  2 
1  1 
1  0 
1  0 

68  0 
69  0 
70  0 
71  0 
72  0 
73  0 

0  20 
0  19 
0  18 
0  17 
0  16 
0  15 

0  23 
0  22 
0  21 
0  20 
0  18 
0  17 

18  30 
35 
40 
45 
50 
55 

2  41 
2  40 
2  39 
2  38 
2  38 
2  37 

2  49 
2  48 
2  47 
2  47 
2  46 
2  45 

27  0 
10 
20 
30 
40 
50 

1  44 
1  43 
1  42 
1  41 
1  41 
1  40 

1  51 
1  51 
1  50 
1  49 
1  48 
1  48 

44  0 
20 
40 
45  0 

20 
40 

0  53 
0  52 
0  51 
0  51 
0  50 
0  49 

0  59 
0  58 
0  58 
0  57 
0  56 
0  56 

74  0 
75  0 
76  0 

77  0 
78  0 
79  0 

0  14 
0  13 
0  12 
0  11 
0  10 
0  9 

0  16 
0  15 
0  14 
0  13 
0  12 
0  11 

19  0 
5 
10 
15 
20 
25 

2  36 
2  35 
2  35 
2  34 
2  33 
2  32 

2  44 
2  44 
2  43 
2  42 
2  41 
2  41 

28  0 
10 
20 
30 

40 
50 

1  39 
1  38 
1  38 
1  37 
1  36 
1  35 

1  47 
1  46 
1  45 
1  45 
]  44 
1  43 

46  0 
20 
40 
47  0 
20 
40 

o  49 
0  48 
0  48 
0  47 
0  47 
0  46 

0  55 
0  54 
0  54 
0  53 
0  52 
0  52 

bO  0 
81  0 
82  0 
83  0 
84  0 
85  0 

0  8 
0  8 
0  7 
0  6 
0  5 
0  4 

0  10 
0  9 
0  8 
0  7 
0  6 
0  5 

19  30 
35 
40 
45 
50 
55 

2  32 
2  31 
2  30 
2  29 
2  29 
2  28 

2  40 
2  39 
2  38 
2  38 
2  37 
2  36 

29  0 
10 
20 
30 
40 
50 

1  35 
1  34 
1  33 
1  33 
1  32 
1  31 

1  42 
1  42 
1  41 
1  40 
1  40 
1  39 

48  0 
20 
40 
49  0 
20 
40 

0  45 
0  45 
0  44 
0  44 
0  43 
0  43 

0  51 
0  51 
0  50 
0  49 
0  49 
0  48 

86  0 
87  0 
88  0 
89  0 
90  0 

0  3 
0  3 
0  2 
0  1 
0  0 

0  4 
0  3 
0  2 
0  1 
0  0 

TABLE  XIV.                265 

TO  FIND  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

Natural  Sines. 

M. 

0° 

1° 

2° 

3° 

40 

5° 

6° 

7° 

8° 

9° 

M. 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

UOOOOO 
000291 
000582 
000873 
001164 
001454 
001745 
002036 
002327 
002618 
002909 

017452 
017743 

oisoai 

018325 
018616 
018907 
019197 
019488 
019779 
020070 
020361 

034899 
035190 
035481 
035772 
036062 
036353 
036644 
036934 
037225 
037516 
037806 

052336 
052626 
052917 
053207 
053498 
053788 
054079 
054369 
05466(i 
054950 
055241 

069756 
070047 
070337 
070627 
070917 
071207 
071497 
071788 
072078 
072368 
072G58 

087156 
087446 
087735 
088025 
088315 
088605 
088894 
089184 
089474 
089763 
090053 

104528 
104818 
105107 
105396 
105686 
105975 
106264 
106553 
106843 
107132 
107421 

121809 
122158 
122447 
122735 
123024 
123313 
123601 
123890 
124179 
124467 
124756 

139173 
139461 
139749 
140037 
140325 
140613 
140901 
141189 
141477 
141765 
142053 

156434 
156722 
157009 
157296 
157584 
157871 
158158 
158445 
158732 
159020 
159307 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

U03200 
003491 
003782 
004072 
004363 
004G54 
004945 
005236 
005527 
005818 

02065i: 
020942 
021233 
021524 
021815 
022106 
022397 
022687 
022978 
023269 

03b097 
038388 
038678 
038969 
039260 
039550 
039841 
040132 
040422 
040713 

055531 
055822 
056112 
056402 
056693 
056983 
057274 
057564 
C57854 
058145 

072948 
073238 
073528 
073818 
074108 
074399 
074689 
074979 
075269 
075559 

OU0343 
090633 
090922 
091212 
091502 
091791 
092081 
092371 
092660 
092950 

107710 
107999 
108289 
108578 
108867 
109  156 
109445 
109734 
110023 
110313 

125045 
125333 
125622 
125910 
126199 
126488 
126776 
127065 
127353 
127G42 

142341 
142629 
142917 
143205 
143493 
143780 
144068 
144356 
144644 
144932 

159594 
159881 
160168 
160455 
160743 
161030 
161317 
161604 
161891 
162178 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

006109 
006399 
006690 
006981 
007272 
007563 
007854 
008145 
008436 
008727 

023560 
023851 
024141 
024432 
024723 
025014 
025305 
025595 
025886 
026177 

041004 
041294 
041585 
041876 
042166 
042457 
042748 
043038 
043329 
043619 

058435 
058726 
059016 
059306 
059597 
059887 
060177 
060468 
060758 
061049 

075849 
076139 
076429 
076719 
077009 
077299 
077589 
077879 
078169 
078459 

093-39 
093529 
093819 
094108 
094398 
094687 
094977 
095267 
095556 
095846 

110602 
110891 
111180 
111469 
111758 
112047 
112336 
112625 
112914 
113203 

127930 
128219 
128507 
128796 
129084 
129373 
129661 
129949 
130238 
130526 

145220 
145507 
145795 
146083 
146371 
146659 
146946 
147234 
147522 
147809 

162465 
162752 
163039 
163326 
163613 
163900 
164187 
164474 
164761 
165048 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

009017 
009308 
009599 
009890 
010181 
01047-2 
010763 
011054 
011344 
011635 

026468 
026759 
027049 
027340 
027631 
027922 
028212 
028503 
028794 
029085 

043910 
014201 
044491 
044782 
045072 
0453G3 
045654 
045944 
046235 
046525 

061339 
061629 
061920 
062210 
062500 
062791 
063081 
063371 
063661 
063952 

078749 
079039 
079329 
079619 
079909 
080199 
080489 
080779 
081069 
081359 

090135 
096425 
096714 
097004 
097293 
097583 
097872 
098162 
098451 
098741 

113492 
113781 
114070 
114359 
114648 
114937 
115226 
115515 
115804 
116093 

130815 
131103 
131391 
131680 
131968 
132256 
132545 
132833 
133121 
133410 

148097 
148385 
148672 
148960 
149248 
149535 
149823 
150111 
150398 
150686 

165334 
165621 
165908 
166195 
166482 
166769 
167056 
167342 
167629 
167916 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

011926 
012217 
012508 
012799 
013090 
013380 
013671 
013962 
014253 
014541 

029375 
029666 
029957 
030248 
030539 
030829 
031120 
031411 
031702 
031992 

046816 
047106 
047397 
047688 
047978 
048269 
048559 
048850 
049140 
049431 

064242 
064532 
064S23 
065113 
065403 
065693 
065984 
066274 
066564 
066854 

081649 
081939 
082228 
082518 
082808 
083098 
083388 
083678 
083968 
084258 

(199030 
099320 
099609 
099899 
100188 
100477 
100767 
101056 
101346 
101635 

116382 
116671 
116960 
117249 
117537 
117826 
118115 
118404 
118693 
118982 

133698 
133986 
134274 
134563 
134851 
135139 
135427 
135716 
136004 
136292 

150973 
151261 
151548 
151836 
152123 
152411 
152698 
152986 
153273 
153561 

168203 
168489 
168776 
169063 
169350 
16963G 
169923 
170209 
170496 
170783 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
GO 

014835 
015126 
015416 
015707 
015998 
016289 
016580 
016871 
017162 
017452 

03-2283 
032574 
032864 
033155 
033446 
033737 
034027 
034318 
034609 
034899 

049721 
050012 
050302 
050593 
050883 
051174 
051464 
051755 
052045 
052336 

067145 
067435 
067725 
068015 
068306 
068596 
068886 
069170 
069466 
069750 

084547 
084837 
085127 
085417 
085707 
085997 
086286 
086576 
086866 
087156 

101924 
102214 
102503 
102793 
103082 
103371 
103661 
103950 
104239 
104528 

119270 
119559 
119848 
120137 
120426 
120714 
121003 
121292 
121581 
121869 

136580 
136868 
137156 
137445 
137733 
138021 
138309 
138597 
138885 
139173 

153848 
154136 
154423 
154710 
154998 
155285 
155572 
155860 
156147 
156434 

171069 
171356 
171643 
171929 
172216 
172502 
172789 
173075 
173362 
173648 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

BE. 

89°  1  88° 

87° 

86° 

85°  I  84°  83°  |  82°  1  81°  |  80° 

1C. 

Natural  Co-sines. 

266                TABLE  XIV. 

TO  FIND  LATITUDE  BY  SEDUCTION  TO  THE  MERIDIAN. 

Natural  Sines. 

M. 

10° 

11° 

12°  13° 

14° 

15° 

16° 

17° 

18° 

19°   M. 

0 

1 

2 
3 

4 
5 
6 

7 
8 
9 
10 

73(548 
73935 
74221 
74508 
74794 
75080 
75367 
75653 
75939 
76226 
76512 

L90609 
191095 
L91380 
191666 
L91951 
L92237 
192522 
192807 
193093 
193378 
193664 

07912224951 
08196,225234 
08481225518 
08765  225801 
09050226085 
09334226368 
09619226651 
09903226935 
10187227218 
10472227501 
10756227784 

24192-2 
242204 
242486 
242769 
243051 
243333 
243615 
243897 
244179 
244461 
244743 

^58819 
259100 
259381 
259662 
259943 
260224 
260505 
260785 
261066 
261347 
261628 

275637 
275917 
276197 
276476 
276756 
277035 
277315 
277594 
277874 
278153 
278432 

2923721 
292650 
292928 
293206 
293484 
293762 
294040 
294318 
294596 
294874 
295152 

3U9017  3-255681 
3092941325843 
309570326118 
309847326393 
310123226668 
310400326943 
310676327218 
310953327493 
311229327768 
311506328042 
311782328317 

00 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

76798 
77085 
77371 
77657 
77944 
78230 
78516 
78802 
179088 
179375 

193949 
194234 
194520 
194805 
195090 
195376 
195661 
195946 
196231 
196517 

11040228068 
11325228351 
11609  228634 
11893228917 
212178229200 
212462  229484 
-12746229767 
213030230050 
213315230333 
213599230616 

245025 
245307 
245589 
245871 
246153 
246435 
246717 
246999 
247281 
247563 

261908 
262189 
262470 
262751 
263031 
263312 
263592 
263873 
264154 
264434 

278712 
278991 
279270 
279550 
279829 
280108 
280388 
280667 
280946 
281225 

295430 
295708 
295986 
296264 
296542 
296819 
297097 
•297375 
297653 
297930 

311059328592 
312335i328867 
312611)829141 

312888,329416 
313164329691 
313440329965 
313716330240 
313992330514 
314269:330789 
314545,331063 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

179061 
179947 
180233 
180519 
180805 
181091 
181377 
181663 
181950 
182236 

196802 
197087 
197372 
197657 
197942 
198228 
198513 
198798 
199083 
199368 

213883230899 
214167231182 
214451231465 
214735231748 
215019232031 
215303232314 
215588232597 
215872-232880 
216156233163 
216440233445 

247845 
248126 
248408 
248690 
248972 
249253 
249535 
249817 
250098 
250380 

264715 
264'J95 
265276 
265556 
265837 
266117 
266397 
266678 
266958 
267238 

281504 
281783 
282062 
282341 
282620 
282900 
283179 
283457 
283736 
284015 

298208 
298486 
298763 
299041 
299318 
299596 
299873 
300151 
300428 
300706 

314821331338 
316097331612 

315373331887 
315649|332161 
316928332435 

3162011332710 
316477|332984 
316753333258 
317029,333533 
317305,333807 

49 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

18252-2 
182808 
183094 
183379 
183665 
183951 
184237 
184523 
184809 
185095 

199053 
199938 
200223 
200508 
200793 
201078 
201363 
201648 
201933 
202218 

21(5724233728 
217008234011 
217292234294 
217575234577 
217859234859 
218143235142 
218427235425 
218711235708 
218995235990 
219279236273 

250662 
250943 
251225 
2515Gb 
251788 
252069 
252351 
252632 
252914 
253195 

207519 
267799 
268079 
268359 
268640 
268920 
269200 
269480 
269760 
27004G 

284294 
284573 
284852 
285131 
285410 
285688 
285967 
286246 
286525 
j-286803 

300983 
301261 
301538 
301815 
302093 
302370 
302647 
302924 
303202 
303479 

317580|334081 
317856,334355 
318132334629 
318408334903 
318684335178 
318959335452 
319235335726 
319511336000 
319786336274 
320062;336547 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

185381 
185667 
185952 
186238 
186524 
18681C 
187096 
187381 
187667 
187953 

202502 
20278" 
203072 
203357 
203642 
20392" 
20421 
•204496 
20478 
20506 

2195U2  236556 
219846236838 
220130237121 
220414237403 
220697  237686 
220981237968 
221265238251 
221548  238533 
221832238816 
222116239096 

253477 
253758 
254039 
254321 
254602 
25488? 
255165 
255446 
255727 
256008 

27032U 
27060C 
27088C 
27116C 
27144C 
27172C 
27200C 
27228C 
27256C 
272841 

287082 
287361 
287639 
•287918 
28819G 
288475 
288753 
289032 
28931C 
28958S 

303750 
304033 
304310 
304587 
304864 
305141 
305418 
305695 
305972 
300249 

320337i336821 
320613:337095 
320889337369 
321164:337643 
321439337917 
3217151338190 
321990338464 
322266338738 
322541339012 
322816339285 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

188238 
188524 
18881C 
18909S 
189381 
189667 
189952 
190238 
190522 
19080S 

20535 
20563 
20592 
20620 
20648 
20677 
20705 
20734 
20762 
20791 

222399  2393U1 
222683239665 

222967  23994C 
223250240228 
223534  24051C 
223817  24079; 
224101  24107E 
•22438424135'J 
224668  24164C 
224951  24192: 

•256*89 
256571 
256852 
25713S 
257414 
25769c 
25797C 
258257 
258538 
25881£ 

•27312C 
27340C 
27367i 
27395£ 
274231 
27451J 
274798 
275078 
27535* 
27563r 

289867 
29014E 
290424 
290705 
290981 
29125C 
!'29153'J 
J29181£ 
(  292094 
292375 

30052d 
306803 
30708(1 
307357 
307633 
3079K 
308187 
308464 
30874C 
309017 

323092  33955S3 
323367  339832 
323642340106 
32391734038C 
324193340653 
324468340927 
324743  34120C 
325018341472 
325293341747 
325568  34202C 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

M.  |  79° 

78° 

77°  76° 

75° 

74° 

73° 

72°  !  71° 

70° 

M. 

Natural  Co-sines. 

TABLE  XIV.                267 

TO  FIND  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

Natural  JSincs. 

M.   20° 

210 

22°' 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

M. 

0 

2 
3 
4 
5 
6 
7 
8 
9 
10 

342020 
342293 
342567 
342840 
343113 
343387 
343660 
343933 
344206 
344479 
344752 

358368 
358640 
358911 
359183 
359454 
359725 
359997 
360268 
360540 
360811 
361082 

374607 
374876 
375146 
375416 
375685 
375955 
376224 
376494 
376763 
377033 
377302 

390731  406737 
390999407002 
391267  407268 
391534407534 
391802407799 
392070408065 
392337408330 
392605408596 
392872  408861 
393140409127 
393407  409392 

4226181438371 
4228821438633 

423145438894 
423409  439155 
423673439417 
423936:439678 
424199  439939 
424463440200 
424726  440462 
424990440723 
425253440984 

453990 
454250 
454509 
454768 
455027 
45528G 
155545 
455804 
456063 
456322 
456580 

46947v 
469728 
469985 
470242 
470499 
470755 
471012 
471268 
471525 
471782 
472038 

484810 
485064 
485318 
485573 
485827 
486081 
486335 
486590 
486844 
487098 
487352 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

345025 
345298 
345571 
345844 
346117 
346390 
346G63 
346936 
347208 
347481 

301353 
361625 
361896 
362167 
362438 
3G2709 
362980 
363251 
363522 
363793 

377571 
377841 
37H110 
378379 
378649 
378918 
379187 
379456 
379725 
379994 

393675 
393942 
394209 
394477 
394744 
395011 
395278 
395546 
395813 
396080 

409G58 
409923 
410188 
410454 
410719 
410984 
411249 
411514 
411779 
412045 

425516441245 
425779  441506 
426042|441767 
426306,442028 
426569  442289 
426832  442550 
427095442810 
427358443071 
427621  443332 
427884443593 

456839 
457098 
457357 
457615 
457874 
458133 
458391 
458650 
458908 
459166 

472294 
472551 
472807 
473063 
473320 
473576 
473832 
474088 
474344 
474GOO 

487606 
487860 
488114 
488367 
488621 
488875 
489129 
489382 
489636 
489890 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

347754 
348027 
348299 
348572 
348845 
349117 
349390 
349662 
349935 
350207 

364U64 
364335 
364606 
3C4S77 
365148 
365418 
365689 
365960 
366231 
366501 

380263 
380532 
380801 
381070 
381339 
381608 
381877 
382146 
382415 
382683 

396347 
396614 
396881 
397148 
397415 
397682 
397949 
398215 
398482 
398749 

412310 
412575 
412840 
413104 
413369 
413634 
413899 
414164 
414429 
414693 

428147  443853 
428410444114 
428672444375 
428935444635 
429198444896 
429461  445156 
429723445417 
429986445677 
430249  445937 
430511  446198 

459425 
459683 
459942 
460200 
460458 
460716 
460974 
461232 
461491 
461749 

474856 
475112 
475368 
475624 
475880 
476136 
476392 
476647 
476903 
477159 

490143 
490397 
490650 
490904 
491157 
491411 
491664 
491917 
492170 
492424 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

350480 
350752 
351025 
351297 
351569 
351842 
352114 
35238G 
352658 
352931 

366772 
367042 
367313 
367584 
367854 
368125 
368395 
368665 
368936 
369206 

382952 
383221 
383490 
383758 
384027 
384i95 
384564 
384832 
385101 
385369 

399016 
399283 
399549 
399816 
400082 
400349 
400616 
400882 
401149 
401415 

414958 
415223 
415487 
415752 
416016 
416281 
416545 
416810 
417074 
417338 

430774  446458 
431036  146718 
431299446979 
431561  447239 
431823  447499 
432086447759 
432348  448019 
432610  448279 
432873  448539 
433135448799 

462007 
462265 
462523 
462780 
463038 
463296 
463554 
463812 
464069 
464327 

477414 
477670 
477925 
478181 
478436 
478692 
478947 
479203 
479458 
479713 

492677 
492930 
493183 
493436 
493689 
493942 
494195 
494448 
494700 
494953 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

353203 
353475 
353747 
354019 
354291 
3545G3 
354835 
355107 
355379 
355651 

cft'.947G 
369747 
370017 
370287 
370557 
370828 
371098 
371368 
371G38 
371908 

385638 
385906 
386174 
386443 
386711 
386979 
387247 
387516 
387784 
388052 

401681  417603 
401948417867 
102214418131 
402480  418396 
402747  4186GO 
403013418924 
403279419188 
403545  419452 
403811419716 
404078419980 

433397,449059 
433659  449319 
433921  449579 
434183449839 
434445  450098 
434707  450358 
434969450618 
435231  450878 
435493451137 
435755451397 

464584 
464842 
465100 
465357 
4G5615 
465872 
466129 
466387 
466644 
466901 

479968 
480223 
480479 
480734 
480989 
481244 
481499 
481754 
482009 
482263 

495206 
495459 
495711 
495964 
496217 
49G469 
496722 
496974 
497226 
497479 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
GO 

355923 
356194 
3564GG 
356738 
357010 
357281 
357553 
357825 
35809G 
3583R8 

37217S 
372448 
372718 
372988 
373258 
373528 
373797 
374067 
374337 
374607 

388320 
388588 
388856 
389124 
389392 
389660 
389928 
390196 
390463 
390731 

4043444-20244 
404610420508 
404876'420772 
405142421036 
405408421300 
405G73  421563 
405939421827 
406205  422091 
406471  422355 
406737  422618 

436017  451656 
436278451916 
436540452175 
436802452435 
437063  452694 
437325452953 
437587453213 
437848453472 
438110453731 
438371  453990 

467158 
467416 
467673 
467930 
468187 
468441 
468701 
468958 
469215 
469472 

482518 
482773 
483028 
483282 
483537 
483792 
484046 
484301 
484555 
484810 

497731 
497983 
498236 
498488 
498740 
498992 
499244 
499496 
499748 
500000 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

M.  |  69C 

68° 

67° 

66°  65° 

64° 

63>J 

62° 

Gl° 

60° 

M. 

Natural  Co-sines. 

268                TABLE  XIV. 

TO  FIND  LATITUDE  BY  KEDUCTION  TO  THE  MERIDIAN. 

Natural  Sines. 

M. 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

M. 

0 
1 

2 
3 

4 
5 
6 
7 
8 
9 
10 

50000U 
500252 
.300504 
500756 
501007 
501259 
501511 
501762 
502014 
502268 
502517 

515038 
515287 
515537 
515786 
516035 
516284 
516533 
516782 
517031 
517280 
•517529 

5-^9919 
530166 
530413 
530659 
530906 
531152 
531399 
531645 
531891 
532138 
532384 

544639 
544883 
545127 
545371 
545615 
545858 
546102 
546346 
546589 
546833 
547076 

559193  573576 
559434  573815 
559675  574053 
559916  574291 
560157  574529 
560398574767 
560639  575005 
560880575243 
561121  575481 
561361  575719 
561602  575957 

587785 
588021 
588256 
588491 
588726 
588961 
589196 
589431 
589666 
589901 
590136 

601815 
602047 
602280 
602512 
602744 
60297G 
60320b 
603440 
603672 
603904 
604136 

615661 
615891 
616120 
616349 
616578 
616807 
617036 
617265 
617494 
617722 
617951 

629320 
629546 
629772 
629998 
630224 
630450 
630676 
630902 
631127 
631353 
631578 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

502769 
503020 
503271 
503523 
503774 
504025 
504276 
504528 
504779 
505030 

517778 
518027 
518276 
518525 
518773 
519022 
519271 
519519 
519768 
520016 

532630 
532876 
533122 
533368 
533615 
533861 
534106 
534352 
534598 
534844 

547320 
547563 
547807 
548050 
548293 
548536 
548780 
549023 
549266 
549509 

561843 
562083 
562324 
562564 
562805 
563045 
563286 
563526 
563766 
564007 

576195 
576432 
576670 
576908 
577145 
577383 
577620 
577858 
578095 
578332 

59037  1 
590606 
590840 
591075 
591310 
591544 
591779 
592013 
592248 
592482 

604367 
604599 
60483! 
605062 
605294 
605526 
6G5757 
605988 
606220 
606451 

018180 
618408 
618637 
618865 
619094 
619322 
619551 
619779 
620007 
620235 

631804 
632029 
632255 
632480 
632705 
632931 
633  15c 
633381 
633606 
633831 

49 
48 
47 
46  ' 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

505281 
505532 
505783 
506034 
506285 
506535 
506786 
507037 
507288 
507538 

520265 
520513 
520761 
52101G 
521258 
521506 
521754 
522002 
522251 
522499 

53509U 
535335 
535581 
535827 
536072 
536318 
536563 
5J6809 
537054 
537300 

549752 
549993 
550238 
550481 
550724 
550966 
551209 
551452 
551694 
551937 

564247 
564487 
564727 
564967 
565207 
565447 
565687 
565927 
566166 
566406 

578570 
578807 
579044 
579281 
579518 
579755 
579992 
580229 
580466 
580703 

592716 
592951 
593185 
593419 
593653 
593887 
594121 
594355 
594589 
594823 

60668^ 
606914 
607145 
607376 
607607 
607838 
608069 
608300 
608531 
608761 

620464 
620692 
620920 
621148 
621376 
621604 
621831 
622059 
622287 
622515 

634056 
634281 
634506 
634731 
634955 
635180 
635405 
635629 
635854 
636078 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

507789 
508040 
508290 
508541 
508791 
509041 
509292 
50954-2 
509792 
510043 

522747  537545 
522995  537790 
523242538035 
523490538281 
523738  538526 
523986538771 
524234  539016 
524481539261 
524729;539506 
524977  539751 

55218U 
552422 
552664 
552907 
553149 
553392 
553634 
553876 
554118 
554360 

566646 
566886 
567125 
567365 
567604 
567844 
568083 
568323 
568562 
568801 

580940 
581176 
581413 
581650 
581886 
582123 
582359 
582596 
582832 
583069 

595057 
595290 
595524 
595758 
595991 
596225 
596458 
596692 
596925 
597159 

608992 
609223 
609454 
609684 
609915 
610145 
610376 
610606 
610836 
611067 

62274* 
622970 
623197 
623425 
623652 
623880 
624107 
624334 
624561 
624789 

636303 
636527 
636751 
636976 
637200 
637424 
637648 
637872 
638096 
638320 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

510293 
510543 
510793 
511043 
511293 
511543 
511793 
512043 
512293 
512543 

525224539996 
525472  540240 
525719  540485 
525967  540730 
526214540974 
526461  541219 
526709  541464 
526956541708 
527203  541953 
527450542197 

554602 
554844 
555086 
555328 
555570 
555812 
556054 
556296 
556537 
556779 

56904U 
569280 
569519 
569758 
569997 
570236 
570475 
570714 
570952 
571191 

583305 
583541 
583777 
584014 
584250 
584486 
584722 
584958 
585194 
585429 

597392 
597625 
597858 
598092 
598325 
598558 
598791 
599024 
599256 
599489 

611297 
611527 
611757 
611987 
612217 
612447 
612677 
612907 
613137 
613367 

625016 
625243 
625470 
625697 
525923 
626150 
626377 
626604 
626830 
627057 

638544 
638768 
638992 
639215 
639439 
639663 
639886 
640110 
640333 
640557 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
fiO 

512792 
513042 
513292 
513541 
513791 
514040 
514290 
514539 
514789 
515038 

527697 
527944 
528191 
528438 
528685 
528932 
529179 
529426 
529673 
529919 

542242 
542886 
542930 
543174 
543419 
543663 
543907 
544151 
544395 
544639 

557021 
557262 
557504 
557745 
557987 
558228 
558469 
558710 
558952 
559193 

571430 
571669 
571907 
572146 
572384 
572623 
572861 
573100 
573338 
573576 

585665599722 
585901  599955 
586137600188 
586372  600420 
586608  600653 
586844600885 
587079601118 
587314601350 
587550601583 
587785601815 

613596 
613826 
614056 
614285 
614515 
614744 
614974 
615203 
615432 
615G61 

627284 
627510 
627737 
627963 
628189 
628416 
628642 
628868 
629094 
629320 

640780 
G41003 
641226 
641450 
641673 
641896 
642119 
642342 
642565 
642788 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

M. 

59°  58°  57°  |  56°  |  55° 

54°  |  53° 

52° 

51° 

50° 

M. 

Natural  Co-sines. 

TABLE  XIV.                269 

TO  FIND  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

Natural  Sines. 

M. 

40°  41° 

42° 

43° 

44° 

45° 

46° 

47° 

48°  49° 

M. 

0 
1 

2 
3 
4 
5 
6 
7 
8 
9 
10 

4-2788  650059 
43010  656279 
43233656498 
43456656717 
43679  65G937 
43901  657156 
44124657375 
44346657594 
44569657814 
44791  658033 
45013,658252 

669131 
669347 
669563 
669779 
669995 
670211 
670427 
670642 
670858 
671074 
671289 

081998 
682211 
682424 
682636 
682849 
683061 
683274 
683486 
683698 
G83911 
684123 

594658 
694868 
695077 
69528G 
695495 
695704 
695913 
696122 
696330 
696539 
69G748 

707107 
707312 
707518 
707723 
707929 
708134 
708340 
708545 
708750 
708956 
709161 

719340 
719542 
'19744 
"19946 
720148 
720349 
720551 
720753 
720954 
721156 
721357 

731354 
731552 
731750 
731949 
732147 
732345 
732543 
732741 
732939 
733137 
733334 

743145J754710 
743339,754900 
743534755091 
743728755282 
743923755472 
744117755663 
744312  755853 
744506  756044 
744700  756234 
744894756425 
745088j756615 

00 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 

M 

15 

16 
17 

18 
19 
20 

045^36658471 
645458658689 
45680  658908 
645902  659127 
46124,659346 
>46346  659565 
646568659783 
646790660002 
647012  660220 
647233  G60439 

671505 
671721 
671936 
672151 
672367 
672582 
672797 
673013 
673228 
673443 

684335 
684547 
684759 
684971 
685183 
685395 
685607 
685818 
686030 
686242 

696957 
697165 
697374 
697582 
G97790 
687999 
698207 
698415 
698623 
698832 

7U9366 
709571 
709776 
709981 
710185 
710390 
710595 
710799 
711004 
711209 

721559 
721760 
721962 
722163 
722364 
722565 
722766 
722967 
723168 
723369 

733532 
733730 
733927 
734125 
734323 
734520 
734717 
734915 
735112 
735309 

745282  756805 
745476756995 
745670757185 
745864  757375 
746057757565 
746251  757755 
7464451757945 
7466381758134 
746832(758324 
747025:758514 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

647455  G6U657 
647677  660875 
647898  661094 
648120661312 
648341  661530 
648563661748 
648784661966 
649006662184 
649227  662402 
649448662620 

673658 
673873 
674088 
674302 
674517 
674732 
674947 
675161 
675376 
675590 

686453 
686665 
686876 
687088 
687299 
687510 
687721 
687932 
688144 
688355 

699J40 
699248 
699455 
699663 
699871 
700079 
700287 
700494 
700702 
700909 

711413 
711617 
711822 
712026 
712230 
712434 
712639 
712843 
713047 
713250 

723570 
723771 
723971 
724172 
724372 
724573 
724773 
724974 
725174 
725374 

7^5506 
735703 
735900 
736097 
736294 
736491 
736687 
736884 
737081 
737£77 

747218  758703 
747412  758893 
747605759082 
747798759271 
747991  759461 
748184759650 
748377  1759839 
748570J760028 
748763760217 
748956,760106 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

64%6'J  662838 
649890663056 
650111663273 
650332  663491 
650553  663709 
650774663926 
650995664144 
651216664361 
651437664579 
651657|66479G 

675805 
G76019 
G7G233 
676448 
676662 
676876 
677090 
677304 
677518 
677732 

G88566 
688776 
688987 
689198 
689409 
689620 
689830 
690041 
690251 
690462 

701117 
701324 
701531 
701739 
701946 
702153 
702360 
702567 
702774 
702981 

713454 
713658 
7138G2 
714066 
714269 
714473 
714676 
714880 
715083 
715286 

725575 
725775 
725975 
726175 
726375 
726575 
72G775 
726974 
727174 
727374 

737474 
737670 
7378G7 
738063 
738259 
738455 
738651 
738848 
739043 
739239 

749148760595 
749341  '760784 
749534,760972 
749726761161 
749919761350 
750111761538 
750303761727 
750496761915 
750688762104 
750880,762292 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 

41 
42 
43 
44 
45 
46 
47 
48 
49 
60 

651878  6651)13)677940 
652098665230678160 
652319  665448  678373 
652539665665678587 
652760665882678801 
652980666099679014 
653200  666316  G79228 
653421666532679441 
653641  666749  67965E 
653861666966679868 

690672 
690882 
G91093 
691303 
691513 
691723 
691933 
692143 
692353 
69256! 

703188 
703395 
703601 
703808 
704015 
704221 
704428 
704634 
704841 
705047 

715490 
715693 
715896 
716099 
71630-2 
716505 
716708 
716911 
717113 
717316 

727573 
727773 
727972 
728172 
728371 
728570 
728769 
728969 
729168 
729367 

739435 
739631 
739827 
740023 
740218 
740414 
740609 
740805 
74100U 
741195 

751072762480 
7512641762668 
751456762850 
7516481763044 
751840763232 
752032,763420 
752223)763608 
752415,763796 
752606763984 
752798764171 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

654081667183680081 
654301  667399  68029i 
654521  667616  68050i 
654741  667833  68072] 
654961668049680934 
655180  668265  G8114r 
655400  668482  68136( 
655620668698081571 
655839  668914  68178( 
656059  669131  68199! 

692771 
69298c 
693192 
69340-2 
1693611 
69382] 
)69403( 
!694*24C 
5  694441 
J  69465* 

705253 
705453 
705665 
705872 
706078 
706284 
70648S 
70669L 
1  706901 
(707107 

717519 
717721 
717924 
718126 
718328 
718531 
71873S 
71893C 
719136 
71934C 

729560 
729763 
729963 
730162 
730361 
73056C 
730756 
730957 
73115C 
731354 

741391 
74158G 
741781 
741976 
742171 
742361 
742561 
74275E 
74295C 
74314E 

752989764359 
753181764547 
753372764734 
753563,764921 
753755765109 
753946,765290 
754137,765483 
754328,765670 
754519765857 
754710|766044 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

M.   49°  1  48°  47°  46°  I  45°  1  44°  1  43°  1  42°  1  41^  1  40° 

M. 

Natural  Co-sines. 

270                TABLE  XIV. 

TO  FIND  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

Natural  Sines. 

M. 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58°   59° 

M. 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

760044 
766231 
766418 
766605 
76G792 
766979 
767165 
767352 
767538 
767725 
767911 

777146,7b8011 
777329788190 
777512788369 
777695788548 
777878788727 
778060788905 
778243789084 
778426789263 
778608789441 
778791789620 
778973789798 

798636 
798811 
798985 
7991CO 
799335 
799510 
799685 
799859 
800034 
800208 
800383 

809017 
809188 
809359 
8C9530 
809700 
809881 
810042 
810212 
810383 
810553 
810723 

819152 
819319 
819486 
819652 
819819 
8199S5 
820152 
820318 
820485 
820651 
820817 

8-^9038 
829200 
829363 
829525 
829688 
829850 
830012 
830174 
830337 
830499 
830661 

838671 
838829 
838987 
839146 
839304 
839462 
839620 
839778 
839936 
840094 
840251 

848048J857167 
848202  857317 
848356  857467 
848510857616 
848664  857766 
848818857915 
848972  858065 
849125858214 
849279858364 
849433858513 
849586  858662 

GO 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

7G8097 
768284 
768170 
768656 
768842 
769028 
769214 
769400 
769585 
769771 

779156789977 
779338790155 
779520790333 
779702790511 
779884790690 
780067  790868 
780249  791046 
780430791224 
780612791401 
780794791579 

801)557 
800731 
800906 
801080 
801254 
801428 
801602 
801776 
801949 
802123 

810894 
811064 
811234 
811404 
811574 
811744 
811914 
812084 
812253 
812423 

820983 
821149 
821315 
821481 
821647 
821813 
821978 
822144 
822310 
822475 

830823 
830984 
831146 
831308 
831470 
831631 
831793 
831954 
832115 
832277 

840409 
840567 
840724 
840882 
841039 
841196 
841354 
841511 
841668 
841825 

849739858811 
849893  858960 
85004C  859109 
850199859258 
850352859406 
850505  859555 
850658859704 
850811  859852 
850964  860001 
851117  8G0149 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

769957 
770142 
770328 
770513 
770699 
770884 
771069 
771254 
771440 
771625 

780976791757 
781157791935 
781339792112 
781520792290 
781702792467 
781883792644 
782065792822 
782246792999 
782427793176 
782608793353 

802297 
802470 
802644 
802817 
802991 
803164 
803337 
803511 
803684 
803857 

812592 
812762 
812931 
813101 
813270 
813439 
813608 
813778 
813947 
814116 

822641 
822806 
822971 
823136 
823302 
823467 
823632 
823797 
823961 
824126 

832438 
832599 
832760 
832921 
833082 
833243 
833404 
833565 
833725 
833886 

841982 
84-2139 
842296 
842452 
842609 
842766 
842922 
843079 
843235 
843391 

851269860297 
851422860446 
851575860594 
851727  860742 
851879860890 
852032,861038 
852184861186 
852336861334 
852488861481 
852640861629 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

771810 
771995 
772179 
772364 
772549 
772734 
772918 
773103 
773287 
773-472 

782789793530 
782970793707 
783151793881 
78333279106] 
783513  79423S 
783693794415 
783874794591 
784055794768 
784235794944 
784416795121 

80403U 
804203 
804376 
804548 
804721 
804894 
805066 
805239 
805411 
805584 

814^84 
814453 
814622 
814791 
314959 
815128 
S1529G 
815465 
815633 
815801 

824291 
824456 
824620 
824785 
824949 
825113 
825278 
825442 
825606 
825770 

834046 
834207 
8343G7 
834527 
834688 
834848 
835008 
835168 
835328 
835488 

843548 
843704 
843860 
844016 
844172 
844328 
844484 
844640 
844795 
844951 

852792:861777 
852944  861924 
853096862072 
853248862219 
853399862366 
853551  862514 
853702862661 
853854  862808 
854005,862955 
854156863102 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

773656 
773840 
774024 
774209 
774393 
774577 
774761 
774944 
775128 
775312 

784596  795297 
784776795473 
784957  795650 
785137795826 
785317796002 
785497796178 
785677796354 
785857796530 
786037  796706 
786217796882 

805756 
805928 
806100 
806273 
806445 
806617 
806788 
806960 
807132 
807304 

615969 
816138 
816306 
816474 
816642 
816809 
816977 
817145 
817313 
817480 

825934 
826098 
826262 
826426 
826590 
826753 
826917 
827081 
827244 
827407 

835648 
835807 
835967 
836127 
836286 
836446 
836605 
836764 
836924 
837083 

845106 
845262 
845417 
845573 
845728 
845883 
846038 
846193 
846348 
846503 

854308863249 
854459863396 
854610863542 
854761  863689 
854912863836 
855063863982 
855214:864128 
855364;864275 
855515:864421 
855665J864567 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

775496 
775679 
775863 
776046 
776230 
776113 
776596 
776780 
77G963 
777146 

786396 
786576 
786756 
786935 
787114 
787294 
787473 
787652 
787832 
788011 

797057 
797233 
797408 
797584 
797759 
797935 
798110 
798285 
798460 
798636 

807475 
807647 
807818 
807990 
808161 
808333 
808504 
808675 
808846 
809017 

817648 
817815 
817982 
818150 
818317 
818484 
818651 
818818 
818985 
819152 

827571 
827734 
827897 
828060 
828223 
828386 
828549 
828712 
828875 
829038 

837242 
837401 
837560 
837719 
837878 
838036 
838195 
838354 
838512 
838671 

846658 
846813 
846967 
847122 
847277 
847431 
847585 
847740 
847894 
848048 

855816864713 
855966864860 
856117865006 
856267865151 
856417  865297 
856567865443 
856718865589 
856868;805734 
857017865880 
857167866025 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

M. 

39° 

38° 

37° 

36° 

35° 

34° 

33°  1  32° 

31°  30° 

M. 

Natural  Co-sines. 

TABLE  XIV.  271 

TO   FIND    LATITUDE   BY    REDUCTION   TO   THE   MERIDIAN. 
Natural  Sines. 


M.   60°  61°  62°  63°  64°  65°  66°  67°  -68°  69°  M. 


866025  874620,882948  891007!898794|9063U8i913545|(J2U5u5  927184:933580 
866171874761  883084  891139  898922  906431 913664  920618  92729J  933685 
866316,874902:883221891270899049906554913782920732927402933789 
866461875042883357891402,899176906676,913900920846,927510933893 


8GGG07  875183  883492 


891534|899304|906799!914018l920959te27619!033997 

i70Q077 


866752W5324  883629  8916668994311906922,914136  921072  927728  934101 
869897,875465883766891798,899558:9070449142549211859278361934204 
867042J875605|883902  891929,8996851907166  914372  921299,927945  934308 
867187,375746  884038  892061 893812  907289914490  921412  928053  934412 
867331,875886  884174  892192j899939j907411 914607  921525  928161 934515 
367476  876026  884309  892323!900065  907533  914725  921638  928270  934619 


60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 


11 
12 
13 
14 
15 
IG 
17 
18 
19 
20 


867621  8701GY  884445  892455jlKJ0192j(J07u55,914842  921750  928378:934722 
867765^876307  884581 892586,900319  907777,914960  921863  928486  934826 
867910,876447  884717  892717,900445,907899  915077  921976  9285941934929 
808054  876587  384852  892848,900572  908021,915194,922088  928702935032 
868199^876727  884988  892979,900698  908143,915311192220119288101935135 

868487J87700G  88525: 

868632.877146  885394  8933711901077  9085081915663  922588I929133J936444 

868776877286  885529  893502,901203  908630  915779  922650  929240  935547 
8G8920  877425!885664  893633  901329  90875l'915896  922762!929348!935650 


49 
48 
47 
46 
45 
44 
43 
42 
41 
40 


21 
22 
23 
24 
25 
26 
27 
28 
29 
30 


8G9064  877565  88579U  893763  901455  90887 
869207!377704!S85934  893894  901581 


2^16013922874;929455935752 
908994  ;916130  922986  929562'935855 


3693511877844  886069  894024:901707  909115  916246  923098  929669,935957 
869495;877983!886204  894154J901833  909236  9163G3  923210  929776:936060 
869639,878122  886338  894284'901958  909357  916479  923322  9298841936162 
869782  878261 886473  894415,902084  909478,916595  923434  929990*936264 


809926  8784001886608  894545,902209  909599  916712  923545 


742  894675  902335  909720  916826  923G57  930204  936468 
878678  886876  894805  902460  909841916944  923768  930311 936570 

917060  923880  930418  936672 


8700G9  878539  88 

87021 

870356  878817  887011  834934'902585  909961 


930097  9363G6 


39 
38 
37 
36 
35 
34 
33 
32 
31 
30 


31 
32 
33 
34 
35 
36 
37 
38 
39 
40 


870199  87  8956  387145  89d004;yU27iU940U82s91717Gl923991  930524  936774 
870642  879095  887279  895194  902836  910202  917292  924102  930631  936876 
870785879233887413895323,902961910323917408924213930737936977 
870928  879372  887548  395453  903086  910443,917523  924324  930843  937079 
871071  879510  887681  8955S2  903210  910563,917639  924435  930950  937181 
8712141879649  887815  895712  903335  910684  917755  924546  931056  937282 


8713578797871887949895841903460910804917870924657 


871499879925 


871642  881)063  888217 


888083  895970,903585 


89C099,90370'J  911044  918101  924878  931374  937586 


8717841880201 888350  896229903834  911164  318216924989  931480:937687 


910924 


931162937383 


917986  924768  931268,937485 


29 
28 
27 
26 
25 
24 
23 
22 
21 
20 


41 
42 
43 
44 
45 
46 
47 
48 
49 
50 


871lJ27j88033(J;868484  896358  903958J911284918331I92509JJ931586  937788 
872069  880477  888617  896486,904083  911403  918446  925210  93169l'937889 


87221 2  880615  888751  896615,904207 


872354  S80753  888834 
87249G  880891  889017 


396744  904331 


911528Bl8561 925320  931797  937990 

911643918676925430931902938091 
896873904455911762918791  925541  932008,938191 


872638  881028  889150  897001 904579  911881018906  925651 982118938292 
872780881166889283  897130,904703  912001 919021  925761  932219938393 
8729221881303  88941618972581904827  912120  919135  925871  932324  938493 

912239B19260  925980  932429  938593 

912358  919364  926090  932534  938694 


389.349897387:904951 
873206:881578  889632  897515,905075 


19 
18 
17 
16 
15 
14 
13 
12 
11 
10 


51 
52 
53 
54 
55 
56 
57 
58 
59 
60 


873347  881716  889815 


«9  i'G43  903198,912477  919479  92621HH932639  938794 


373489881853889948397771905322912596,919593926310932744938894 
873631 881990j890030  397900  905445  912715  91 9707.926419  9328491938994 
873772  882127,89021 3  898028'905569  9 12834'91982 1926529  932954  939094 
873914J882264  890345  898156:905692  912953  919936'926638  933058  939194 
874055;882401  390478  898283  905815  913072  920050  920747  933*63  939294 
874196:882038|890610  898411  905939  913190'920164  926857  933267'939394 
874338  882674  890742  898539  906062  913309'920277,926966  933372  939493 
874479,882811  890874  898666906185  913427,920391  927075  933476  939593 
874620^882948  891007  898794!90G308  913545920505  927184  933580939693 


M.   29°  I  28°  1  27°  I  26°  25^  24°  I  23°  22°  21°  I  20°  I  M. 


Natural  Co-sines. 


272 

TO  FIND 

TABLE  XIV. 

LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN'. 

Natural  Sines. 

St. 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

M. 

0 

1 

2 
3 
4 
5 
6 
7 
8 
9 
10 

939693 
339792 
339891 
939991 
910090 
t)40189 
940288 
3403S7 
940186 
340585 
J40684 

945519 
945613 
945708 
345802 
945897 
945991 
946085 
346180 
946274 
946388 
94646-2 

951057 
951146 
951236 
951326 
951415 
351505 
951594 
951684 
951773 
951862 
951951 

956305 
956390 
956175 
356560 
956614 
956729 
956814 
956898 
956983 
957067 
957151 

961262 
961342 
961422 
961502 
961582 
961662 
981741 
961821 
961901 
961980 
962059 

965926 
9C6001 
966076 
966151 
966226 
966301 
966376 
966451 
966526 
966600 
966675 

970290 
970366 
97043G 
970506 
970577 
970647 
970711 
97078G 
970856 
970920 
970995 

974370 
974435 
974501 
974566 
974631 
974696 
974761 
37182C 
974891 
97495. 
975020 

9781489*1027 
378208  981683 
378268981738 
978329  981793 
978389981849 
978449981904 
978509  981959 
3785G9  982014 
978629982069 
978689  982123 
978748982178 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

940782 

940881 
340979 
J41078 
341176 
941274 
941372 
941471 
9415G9 
941666 

94(3655 
946649 
916743 
946837 
946930 
947024 
947117 
947210 
947301 
947397 

352040 
952129 
952218 
952307 
952396 
952484 
35257,3 
952661 
952750 
952838 

957235 
957319 
957404 
357487 
957571 
957655 
957739 
957822 
957906 
957990 

962139 
9G2218 
962297 
962376 
962455 
962534 
962613 
962692 
962770 
962819 

J66719 
966823 
966898 
366972 
967046 
967120 
967194 
967268 
967342 
967415 

971065 
971134 
971204 
971273 
971312 
971111 
971480 
971519 
971618 
971687 

375085 
975119 
375214 
975278 
975312 
975106 
975171 
975535 
975598 
375662 

978608 
378867 
978927 
978980 
979045 
979105 
979164 
979223 
979282 
970341 

982233 
982287 
982342 
98239G 
982450 
982505 
982559 
982613 
982667 
982721 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

941764 
341862 
941960 
942057 
942155 
942252 
942350 
942447 
942544 
942641 

947490  95-920 
947583  953015 
94767C  953103 
947768953191 
947861953279 
947954953366 
918016  953454 
918139953512 
918231  953629 
918321  953717 

9580/3 
958156 
958239 
958323 
958406 
958489 
958572 
958651 
958737 
958820 

962928 
96300G 
963084 
963163 
963241 
963319 
963397 
963475 
963553 
9G3630 

967489 
967562 
987636 
967709 
967782 
957856 
967929 
968002 
968075 
968148 

971755 
971824 
971893 
971961 
972030 
972098 
972166 
972234 
972302 
972370 

975726 
975790 
975853 
975917 
975980 
976014 
976107 
976170 
976233 
97629G 

979399  982774 
979458  982828 
979517  982882 
979575982935 
979634982989 
979692983042 
979750  983096 
979809983149 
9798671983202 
979925983255 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

942739 
942836 
942932 
943029 
943126 
943223 
943319 
943416 
943512 
943609 

918416  9538U1 
918508  953892 
918600  953979 
948692951066 
948784954153 
948876  944240 
,918968951327 
919059951411 
949151  954501 
949243954588 

958902 
958985 
959067 
959150 
959232 
959314 
959396 
959478 
959560 
959842 

963708 
963786 
963863 
963941 
964018 
961095 
961173 
964250 
964327 
964404 

968220 
968293 
968366 
968438 
968511 
968583 
968656 
968728 
968800 
968872 

972438 
972500 
972573 
972641 
972708 
972776 
972843 
972911 
972978 
973015 

976359 
976422 
976485 
976547 
976610 
976672 
976735 
976797 
976859 
976921 

979983 
980041 
980098 
980156 
980214 
980271 
980329 
980386 
980443 
980500 

983308 
983361 
983414 
983466 
983519 
983571 
983624 
983670 
983729 
983781 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 

41 
42 
.  43 
44 
45 
46 
47 
48 
49 
50 

943705919331951674 
943801  949425  9547G1 
943897  949517  954847 
943993949608954934 
944089949699955020 
944185  949790  955103 
944281  949881  955192 
944376949972955278 
944472  950063'955364 
944568950154955450 

959724 
959805 
959887 
959968 
960050 
960131 
980212 
960294 
960375 
960456 

964181 
964557 
964G34 
9G4711 
964787 
964864 
964940 
935016 
9G5093 
9G5169 

968944 
969016 
969088 
969159 
969231 
989302 
969374 
969445 
969517 
9G95S8 

97311k 
973179 
973210 
973313 
973379 
97311G 
973512 
973579 
973345 
973712 

976984 
977046 
977108 
977169 
977231 
977293 
977351 
977416 
977177 
977539 

980558 
980615 
980672 
980728 
980785 
380842 
980899 
980955 
981012 
981088 

983833 
983885 
983937 
983989 
984041 
984092 
984144 
9S4196 
984247 
984298 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 

53 
54 
55 

56 
57 
58 
59 
60 

944663  950244  955530 
944758950335955622 
944854950425955707 
944949  950516  955793 
945044  950606'955879 
945139,950696  955964 
945234950786956049 
945329'950877  956134 
945424950967956220 
945519951057956305 

960537 
960618 
9G0898 
960779 
960860 
960940 
961021 
961101 
961181 
961262 

965245 
965321 
965397 
965473 
965548 
965624 
965700 
965775 
935850 
965926 

9o9659:97377b 
969730973844 
969801973910 
969872  973970 
969943  974042 
970014  974108 
970084974173 
970155974239 
970225974305 
970296  97437C 

9  <  7600 
977661 
977722 
977783 
977844 
977905 
977936 
978026 
978087 
978148 

981124984350 
981181  981401 
981237984452 
981293984503 
981349'984554 
981405984605 
981460984656 
981516984707 
981572984757 
981027)984808 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

M.  1  19° 

18° 

17° 

10°  |  15°  I  14°  1  13° 

12° 

11° 

10° 

M. 

Natural  Co-sines. 

TABLE  XIV.                273 

TO  FIND  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

Natural  (Sines. 

M. 

80° 

81° 

82°  |  83° 

84°  85°  86° 

87° 

88° 

89° 

M. 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

3tf4SO« 
384858 
384909 
384959 
383009 
385059 
385109 
J85159 
1385209 
985259 
9S5309 

9»7G8b  'J9U268 
987734990309 
987779990349 
987824  990389 
987870990429 
987915990469 
987930  990509 
98S005  990549 
988050990589 
988094  990629 
988139  990G69 

392540 
392582 
992617 

992652 
992687 

992722 
992757 
992792 
992827 
992862 
992890 

994522  99G  1  95  997564 
994552996220997584 
994583  396245  997004 
994613996270997625 
994643996295997645 
994673  996320  997664 
994703996345997684 
994733996370997704 
994762996395997724 
99479-2  99G419  397743 
994822996444997763 

998030 
998045 
398660 
998675 
998690 
998705 
998719 
998734 
998749 
998763 
998778 

999391 
999401 
999411 
999421 
999431 
999441 
999450 
9994GO 
9994G9 
999479 
999488 

999848 
999853 
999858 
999803 
999867 
999872 
999877 
999881 
999386 
999890 
999894 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

J85358 
93540S 
985457 
985507 

no""-  r*/» 
'OOOUO 

985G05 
985G54 
9S5703 
985752 
985801 

988184 
988226 
988273 
988317 
988362 
968400 
988450 
988494 
988538 
988582 

990708 
990746 
990787 
990827 
990866 
990905 
990944 
990983 
991022 
991061 

99*931 
9929G6 
993000 
993034 
993086 
993103 
993137 
993171 
993205 
993238 

994851990408997782 
994881  99G493  997801 
994910996517997821 
984939996541997841 
994969  996565  997859 
994998  996589  997878 
9950279966  14  997897 
99505G  993637  997910 
995084996661997934 
995113993685997953 

996792 
998806 
998820 
998834 
998818 
99S862 
998870 
998890 
998904 
998917 

999497 
999507 
999516 
999525 
999534 
999542 
999551 
999560 
999568 
999577 

i>99t>98 
999903 
999907 
999910 
999914 
999918 
999922 
999925 
999929 
999932 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

985850 
985899 
985947 
985996 
936045 
986093 
986141 
986189 
986238 
986280 

988620 
988669 
988713 
98875C 
988800 
988843 
98888G 
98893C 
988973 
98901G 

991  10U 
991138 
991177 
991216 
991254 
991292 
991331 
991369 
991407 
991445 

993272 
993300 
993339 
993373 
993406 
993439 
993473 
99350G 
993539 
993572 

995142  9907o9  997972  998931 
995170  996732  997990  998944 
995199  996756  998008  998957 
995227  996779  998027  998971 
995256  996802  998045  998984 
993284  996825  998063  998997 
995312  99G848  998081  999010 
995340  996872  998099  999023 
995368  996894  993117  999035 
99539G  990917  998135  999048 

999585 
999594 
999602 
999610 
999618 
899620 
999634 
99964'2 
999650 
999657 

9999oG 
999939 
999942 
999915 
999948 
999951 
999954 
999957 
999959 
999962 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

980334  989059 
986381  989102 
986429989145 
986477  989187 
986525989230 
986572989272 
986620989315 
986667989357 
986714989399 
98G762  98944-2 

991483 
991521 
991558 
991596 
991634 
991671 
991709 
991740 
991783 
991820 

993005 
993638 
993C70 
993703 
993735 
993768 
993800 
993833 
393865 
993897 

995424  990940  998153 
995452996963998170 
995479996985998188 

995507  997008  998205 
995535997030998223 
995562997053998240 
995589997075998257 
995617  997097  998274 
995644997119998291 
995671:997141998308 

999061  999005 
999073999672 
399086  999680 
999098999687 
999111999694 
999123  999701 
999135  999709 
999147:999710 
999  15fJ|999722 
999171;999729 

999904 
999967 
9999G9 
999971 
999974 
999970 
999978 
999980 
999931 
999983 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

966809  989484J991857 
98685G  989526,991894 
986903  989568  991931 
986950989610991968 
98G99G  989651  992005 
987043989693992042 
987090989735.992078 
987136989776992115 
987183,989818992151 
987229,989859  9921  87 

993929 
993961 
993993 
994025 
994050 
994088 
994120 
994151 
994182 
994214 

995098:997163998325 
995725997185998342 
995752997207998259 
99577b  997229  998375 
995805997250998392 
995832  997272  998408 
995858997293998425 
995884*997314  998441 
995911997336998457 
995937997357998173 

999183  999736 
999194999743 
999206999749 
999218  99975G 
999229999762 
999240999768 
999252999775 
999263999781 
999274  999787 
999285999793 

999985 
999986 
999988 
999989 
999990 
999992 
999993 
999994 
999995 
999990 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
CO 

987275,989900992224 
987322,989942  .992200 
987368989983992290 
987414990024:992332 
987460990065992368 
987506990105992404 
98755l'990146  992433 
987597i990187;992475 
987643,990228992511 
937688,990268,992540 

|994245  995903  997378  998489 
99427G  995989  997399  998505 
994307,990015  997420  998521 
994338.9960-11  997441  998537 
994369  99G067  9974G2  998552 
994400  99G093  997482  0985C8 
994430  996118  997503  998583 
994461  996144  997523  998599 
994491  996169  997544  998614 
99452;  99G195  997564  998030 

999296:999799 
999307,999804 
999318999810 
999328999810 
999339999821 
999350999827 
999360999832 
999370  999837 
999381999813 
999391  999846 

999997 
999997 
999998 
999998 
999999 
999999 
1000000 
,1000000 
1000000 
1000000 

9 

8 
7 
6 
5 
4 
3 
2 
1 
0 

X. 

9° 

1  8° 

1  7°  1  G°   5°  1  4°   3° 

2° 

1  1°  1  0°     M. 

Natural  Co-sines. 

274                                        TABLE  XV. 

FOB   FINDING   THE   DISTANCE   OF   TEREESTRIAL    OBJECTS   AT   SEA. 

Height  in 

Distance  in 

Height  in 

Distance  in 

Height  in 

Distance  in 

Feet. 

Miles. 

Feet. 

Miles. 

Feet. 

Miles. 

1 

1.15 

85 

10.6 

660 

29.5 

2 

1.62 

90 

10.9 

680 

30.0 

3 

1.99 

95 

11.2 

700 

30.4 

4 

2.30 

100 

11.5 

720 

30.8 

5 

2.57 

105 

11.8 

740 

31.2 

6 

2.81 

110 

\       12.1 

760 

31.7 

1 

3.04 

115 

12.3 

780 

32.1 

8 

3.25 

120 

12.6 

800 

32.5 

9 

3.45 

125 

12.8 

820 

32.9 

10 

3.63 

130 

13  1 

840 

33.3 

11 

3.81 

135 

13.3 

860 

33.7 

12 

3.98 

140 

13.6 

880 

34.1 

13 

4.14 

145 

13.8 

900 

34.5 

14 

4.30 

150 

14.1 

920 

34.8 

15 

4.45 

160 

14.5 

940 

35.2 

16 

4.60 

170 

15.0 

960 

35.6 

17 

4.73 

180 

15.4 

980 

36.0 

18 

4.87 

190 

15.8 

1000 

36.3 

19 

5.01 

200 

16.2 

1100 

38.1 

20 

5.14 

210 

16.6 

1200 

39.8 

21 

5.26 

220 

17.0 

1300 

41.4 

22 

5.39 

230 

17.4 

1400 

43.0 

23 

5.51 

240 

17.8 

1500 

44.5 

24 

5.62 

250 

18.2 

1600 

46.0 

25 

5.74 

260 

18.5 

1700 

47.3 

26 

5.86 

270 

18.9 

1800 

48.7 

27 

5.97 

280 

19.2 

1900 

50.1 

28 

6.08 

290 

19.6 

2000 

51.4 

29 

6.18 

300 

19.9 

2100 

52.6 

30 

6.30 

310 

20.2 

2200 

53.9 

31 

6.40 

320 

20.6 

2300 

55.1 

32 

6.50 

330 

20.9 

2400 

56.2 

33 

6.60 

340 

21.2 

2500 

57.4 

34 

6.70 

350 

21.5 

2600 

58.6 

35 

6.80 

3GO 

21.8 

2700 

59.7 

36 

6.90 

370 

22.1 

2800 

60.8 

37 

6.99 

380 

22.4 

2900 

61.8 

38 

7.09 

390 

22.7 

3000 

63.0 

39 

7.17 

400 

23.0 

3100 

64.0 

40 

7.27 

410 

23.3 

3200 

65.0 

41 

7.36 

420 

23.5 

3300 

66.0 

42 

7.44 

430 

23.8 

3400 

67.0 

43 

7.54 

440 

24.1 

3500 

.  68.0 

44 

7.62 

450 

24.4 

3600 

69.0 

45 

7.70 

460 

24.6 

3700 

69.9 

46 

7.79 

470 

24.9 

3800 

70.9 

47 

7.88 

480 

25.2 

3900 

71.7 

48 

7.96 

490 

25.4 

4000 

72.7 

49 

8.0 

500 

25.7 

4100 

73.6 

50 

8.1 

520 

26.2 

4200 

74.4 

55 

8.5 

540 

26.7 

4300 

75.4 

60 

8.9 

560 

27.2 

4400 

76.2 

65 

9.3 

580 

27.7 

4500 

77.0 

70 

96 

600 

28.1 

4700 

88.8 

75 

9.0 

620 

28.6 

5000 

81.2 

80 

10.3 

640 

29  1 

1  mile 

83.5    • 

275 

DIP   OF   THE 

HORIZON  AT   DIFFERENT   DISTANCES   FROM   THE   OBSERVER. 

Distance 

£    T          ,1 

HEIGHT  OF  THE  EYE  IN  FEET. 

of  Land, 
in  Miles. 

5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

M". 

o.i 

28 

56 

84 

112 

140 

169 

19'7 

22'5 

252 

28'0 

0.2 

14 

28 

42 

56 

70 

85 

99 

113 

126 

140 

0.3 

9 

19 

28 

3 

7 

47 

56 

65 

75 

84 

93 

0.4 

7 

14 

21 

28 

35 

42 

49 

56 

63 

70 

0.5 

6 

11 

17 

22 

28 

34 

39 

45 

50 

56 

0.6 

5 

9 

14 

19 

23 

28 

33 

37 

42 

47 

0.7 

4 

8 

12 

16 

20 

24 

28 

32 

36 

40 

6  8 

4 

7 

10 

14 

17 

21 

25 

28 

31 

35 

0  9 

3 

6 

9 

12 

15 

19 

22 

25 

28 

31 

1.0 

3 

6 

8 

11 

14 

17 

20 

23 

25 

27 

12 

3 

5 

7 

9 

12 

14 

16 

19 

21 

23 

1.4 

3 

4 

6 

8 

10 

12 

14 

16 

18 

20 

L.6 

3 

4 

5 

7 

9 

11 

13 

14 

16 

18 

1.8 

2 

3 

5 

6 

8 

10 

12 

13 

14 

16 

2.0 

2 

3 

5 

6 

7 

9 

11 

12 

13 

15 

2.2 

2 

3 

5 

6 

7 

8 

10 

11 

12 

14 

2.4 

2 

3 

5 

6 

7 

8 

9 

11 

12 

13 

2.6 

2 

3 

4 

5 

6 

8 

9 

10 

11 

12 

2.8 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

3.0 

2 

3 

4 

5 

6 

7 

8 

8 

9 

10 

3.5 

2 

3 

4 

5 

6 

6 

7 

8 

9 

9 

4.0 

2 

3 

4 

4 

5 

6 

7 

7 

8 

8 

4.5 

2 

3 

4 

4 

5 

5 

6 

6 

7 

8 

5.0 

2 

3 

4 

4 

5 

5 

6 

6 

7 

7 

6.0 

2 

3 

4 

4 

5 

5 

6 

6 

7 

,      7 

7.0 

2 

3 

4 

4 

5 

5 

6 

6 

7 

7 

TABLE,    SHOWING   THE   NUMBER  OF  MINUTES  AND   SECONDS   CONTAINED  IN 

EACH 

DEGREE  OR    60  MILES  OF   LONGITUDE  FOR   EVERY  DEGREE   OF 

LATITUDE. 

LAT. 

MIN.  SEC. 

LAT.    MIN.  SEC. 

LAT. 

MIN.  SEC. 

LAT. 

MIN.  SEC. 

LAT. 

MIN.  SEC. 

O 

,     // 

O               '     " 

O 

,    „ 

O 

/    // 

O 

,     // 

1 

59.59 

19         56.44 

37 

47.55 

55 

34.25 

73 

17.33 

2 

59.58 

20         56.23 

38 

47.15 

56 

33.30 

74 

16.33 

3 

59.55 

21         56.00 

39 

46.38 

57 

32.41 

75 

15.31 

4 

59.51 

22         55.38 

40 

45.58 

58 

31.48 

76 

14.31 

5 

59.46 

23         55  14 

41 

45.17 

59 

30.54 

77 

13.30 

6 

59  40 

24         54.49 

42 

44.35 

60 

30.00 

78 

12.28 

7 

59.33 

25         54.23 

43 

43.53 

61 

29.06 

79 

11.27 

8 

59.25 

26         53.56 

44 

43.10 

62 

28.10 

80 

10.25 

9 

59.16 

27         53.28 

45 

42.26 

63 

27.15 

81 

9.24 

10 

59.06 

28         52.59 

46 

41.41 

64 

26.18 

82 

8.21 

11 

58.54 

29         52.29 

47 

40.55 

65 

25  22 

83 

7.19 

12 

58.41 

30         51.58 

48 

40.09 

66 

24.24 

84 

6.16 

13 

58.28 

31         51.26 

49 

39.22 

67 

23.26 

85 

5.14 

14 

58  14 

32         50.53 

50 

38.44 

68 

22.28 

86 

4.12 

15 

57.58 

33         50.19 

51 

37.46 

69 

21.30 

87 

3.09 

16 

57.41 

34        49.45 

52 

36.57 

70 

20.31 

88 

2.02 

17 

57.23 

35         49.09 

53 

36.07 

71 

19  32 

89 

1.03 

18 

57.04 

36         48.33 

r,i 

35.13 

72 

18.33 

90 

0.00 

276                                         TABLE  XYI. 

LOGARITHMS   FOE   COMPUTING-   THE    EQUATION    OF    EQUAL   ALTITUDES. 

Inter- 
val. 

Log  A 

Log  B 

Inter- 
val. 

Log  A 

Log  B 

Inter- 
val. 

Log  A 

LogB 

Inter- 
val. 

Log  A 

Log  B 

h.  m. 

li.  m. 

la.  m. 

n.  m. 

2      0 

7.7297 

7.7146 

4      0 

7.7447 

7.6823 

6      07.7703 

7.6198 

8      0 

7.8072 

7.5062 

2 

7.7298 

7.7143 

2 

7.7451 

7.6815 

2 

7.7708 

7.6184 

2 

7.8079 

7.503C 

4 

7.7300 

7.7139 

4 

7.7454 

7.6807 

4 

7.7713 

7.6170 

4 

7.8080 

7.5010 

6 

7.7302 

7  7136 

6 

7.7458 

7.6800 

6 

7.7719 

7.6156 

6 

7.8094 

7.4983 

8 

7.7304 

7.7132 

8 

7.7461 

7.6792 

8 

7.7724 

7.6142 

8 

7.8101 

7.4957 

10 

7.73057.7128 

10 

7.7464 

7.6784 

10 

7.7729 

7.6127 

10 

7.81087.4930 

12 

7.73077.7125 

12 

7.7468 

7.6776 

12 

7.7735 

7  6113 

12 

7.81167.4902 

14 

7.7309 

7.7121 

14 

7.7472 

7.6768 

14 

7.7740 

7.6098 

14 

7.8123(7.4874 

16 

7.7311 

7.7117 

167.7475 

7.6759 

16 

7.7745 

7.6083 

16 

7.81307.4846 

18 

7.73137.7113 

18 

7.7479 

7.6751 

18 

7.7751 

7.6068 

18 

7.81387.4818 

2     20 

7.7315 

7.7109 

4    fcO 

7.7482 

7.6743 

6     20 

7.7756 

7  .  6053 

8     2U 

7.8l457.47t9 

22 

7.7317 

7.7105 

22 

7.7486 

7.6734 

22 

7.7762 

7.6038 

22 

7.  8153  7.  4700 

24 

7.7319 

7.7101 

24 

7.7490 

7.6726 

24 

7.7767 

7.6023 

24 

7.81607.4731 

26 

7.7321 

7.7097 

26 

7.7494 

7.6717 

26 

7.7773 

7.6007 

26 

7.81687  4701 

28 

7.7323 

7.7092 

28 

7.7497 

7.6708 

28 

7.7779 

7.5991 

28 

7.8176 

7.4671 

30 

7.7325 

7.7088 

30 

7.7501 

7.6700 

30 

7  7784 

7.5975 

30 

7.8183 

7.  4640 

32 

7.7327 

7.7083 

32 

7.7505 

7.6691 

32 

7.7790 

7.5959 

32 

7.8191 

7.4600 

34 

7.7329 

7.7079 

34 

7.7509 

7.6682 

34 

7.7796 

7.5943 

34 

7.8199 

7.4578 

36 

7.7331 

7.  7075 

36 

7.7513 

7.  6673 

36 

7.7801 

7.5927 

36 

7.8206 

7.4546 

38 

7.7333 

7.7070 

38 

7.7517 

7  6663 

38 

7.7807 

7.5910 

38 

7.8214 

7.4514 

2     40 

7.7330 

7.7065 

4    4U 

7.7521 

7.6654 

6    40 

7.7843 

7.5894 

8    40 

7.8^k. 

V.4482 

42 

7.7338 

7.7061 

42 

7.7525 

7.6645 

42 

7.7819 

7.5877 

42 

7.8230 

7.4449 

44 

7.7340 

7.7056 

44 

7.7529 

7.6635 

44 

7.7825 

7.5860 

44 

7.8238 

7.4415 

46 

7.7342 

7.7051 

46 

7.7533 

7.6626 

46 

7.7831 

7.5843 

46 

7.8246 

7.43811 

48 

7.7345 

7.7046 

48 

7.7537 

7.6616 

48 

7.7836 

7.5825 

48 

7  8254 

7.4347 

50 

7.7347 

7.7041 

50 

7.7541 

7.6606 

50 

7.7812 

7.5808 

50 

7.8262 

7.4312 

52 

7.7349 

7.7036 

52 

7.7545 

7.6597 

52 

7.7848 

7.5790 

52 

7  8270 

7.4277 

54 

7.7352 

7.7031 

54 

7.7549 

7.6587 

54 

7.7854 

7.5772 

54 

7.82787.4241 

56 

7.7354 

7.7026 

56 

7.7553 

7.6577 

56 

7.7860 

7.5754 

56 

7.8286 

7.4205 

58 

7.73577.7021 

58 

7.7557 

7.6567 

58 

7.78G7 

7.5736 

58 

7.8294 

7.4168 

3      0 

7.7359 

7.7015 

5      0 

7.7562 

7.0556 

7      0 

7.7873 

7.5717 

9      0 

7.83027.4131! 

2 

7.7362 

7.7010 

2 

7.7566 

7.6546 

2 

7.7879 

7.5699 

2 

7.8311  7.4093 

4 

7.7364 

7.7005 

4 

7.7570 

7.6536 

4 

7.7885 

7.5680 

4 

7.83197.4055 

6 

7.7367 

7.6999 

6 

7.7575 

7.6525 

6 

7.7891 

7.5661 

6 

7.83.8 

7.4016 

8 

7.7369 

7.6993 

8 

7.7579 

7.6514 

8 

7.7898 

7.5641 

8 

7.8336 

7.3977 

10 

7.7372 

7.6988 

10 

7.7583 

7.6504 

10 

7.7904 

7.5622 

10 

7.8344 

7.3937 

12 

7.7374 

7.6982 

12 

7.7588 

7.6493 

12 

7.7910 

7.5602 

12 

7.8353 

7.3896 

14 

7.7377 

7.6976 

14 

7.7592 

7.6482 

14 

7.7916 

7.5582 

14 

7.8361 

7.3855 

16 

7.7381; 

7.6970 

16 

7.7597 

7.6471 

16 

7.7923 

7.5562 

16 

7.8370 

7.3813 

18 

7.7383 

7  6964 

18 

7.7601 

7.6460 

187.7929 

7  5542 

18 

7  8378 

7  377] 

3    20 

7.7380 

7.0958 

5    2U 

7.7606 

7.6448 

7    20 

7.7930 

7.5522 

9    20 

7.83S7 

7  BV28 

22 

7.7388 

7.6952 

22 

7.7610 

7.6437 

22 

7.7942 

7.5501 

22 

7.8396 

7.3684 

24 

7.7391 

7.6946 

24 

7.7615 

7.6425 

247.7949 

7.5480 

24 

7.8404 

7.36o9 

26 

7.7394 

7.6940 

26 

7.7620 

7.6414 

26 

7.7955 

7.5459 

26 

7.8413 

7.3591 

28 

7.7397 

7.6934 

28 

7.7624 

7.6402 

28 

7.7962 

7.5437 

28 

7.8422 

7.3548 

30 

7.7400 

7.6927 

30 

7.7629 

7.6390 

30 

7.7969 

7.5416 

30 

7.8430 

7.3501 

32 

7.7403 

7  6921 

32 

7.7634 

7.6378 

32 

7.7975 

7.5394 

32 

7.8439 

7.3454 

34 

7.7406 

7.6914 

34 

7.7638 

7.6366 

34 

7.7982 

7.5372 

34 

7.8448 

7  3400 

36 

7.7409 

7.6908 

36 

7.7643 

7.6354 

36 

7.7989 

7.5350 

36 

7.8457J7.3357 

38 

7.7412 

7.6901 

387.7648 

7.6342 

38 

7.7995 

7.5327 

38 

7.84667.3307 

3    4U 

7.7415 

7  .  6894 

5    407.7653 

7.03i:9 

7    40 

7.8002 

7.5304 

9    40 

7.84757.3-^56 

42 

7.7-418 

7.6888 

42'7.7658 

7.6317 

42 

7.8009 

7.5281 

42 

7.848417.3205 

44 

7  7421 

7.6881 

44 

7.7663 

7.6304 

44 

7.8016 

7.  5258 

44 

7.8493j7.3152 

46 

7.7424 

7.6874 

46 

7.7668 

7.6291 

46 

7.8023 

7.5234 

46 

7.8502|7.3099 

48 

7.7428 

7.6867 

48 

7.7673 

7.6278 

487.8030 

7.5211 

48 

7.85117.3045 

50 

7.7431 

7.6859 

.   50 

7.7678 

7.6265 

50 

7.8037 

7.5186 

50 

7.85207.2989 

5-2 

7  7434 

7.6852 

52 

7.7683 

7.6252 

52 

7.8044 

7.5162 

52 

7.85307.2931 

54 

7.7437 

7.6845 

54 

7.7688 

7.6239 

54 

7.8051 

7.5137 

54 

7.85397  2876 

56 

7.7411 

7  6838 

50 

7.7693 

7.6225 

56 

7.8058 

7.5112 

567.85487.2817 

58 

7.7444 

7.6830 

58 

7.7698 

7.621i 

587.80657.5087 

58 

7.8558.7.2758 

4      0 

7.7447 

7.6823 

G      0 

7.7703 

7.  6198 

8      0 

7.8072 

7.5062 

10    0 

7.8567 

7.2697 

TABLE  XVII.                277 

LOG  RISING  —  TO  FIND  THE  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

0  Hour. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.P. 

0 
1 
2 
3 
4 

u. 

J  .97860 
0.5806G 
J.  93284 
1.18271 

04813 
61612 
95664 
20062 

11250 
65019 
97980 
21817 

17242 
68297 
00236 
23537 

02136 
22848 
71455 
J2435 
25224 

2181S 
28114 
74503 
04580 

2G878 

37654 
33079 
77448 
06673 
28502 

51044 
37775 
80296 
08717 
30095 

62642 
4223(J 
83054 
10714 
31660 

72873 
463G8 
85726 
12666 
33198 

82024 
50509 
88319 
14575 
34708 

90303 
54370 
90837 
16443 
36193 

5 

6 

7 
8 
9 

1.37053 
53488 
66877 
78474 
88703 

39088  40501  41*90 
54686  55868  57034 
67905  68920  69924 
79374  -(0265,81147 
89504  90297  j91083 

43256 
58184 
70917 
S2019 
91862 

44G05 
59320 
71898 
32884 
92634 

45931 
60440 
72869 
33739 
93399 

47237 
61547 
73829 
84587 
94157 

48524 
62639 
74778 
8542G 
91909 

19794 

63718 
75717 
86257 
95655 

51041 
64784 
76646 
87080 
9G394 

52273 
65837 
77565 
87896 
97127 

10 
11 
12 
13 
14 

1.97854 
2.06131 
13687 
20638 
27073 

98574 

06786 
14288 
21192 

2758S 

i)9289te999a 

07437  08082 
14885  15477 
21744  22292 
28100(28609 

0070  J 
:  18723 
1606G 
22836 
29116 

0139U 
09359 
16651 
23377 
29619 

02091 
09991 
17232 
23915 
30120 

0^777 
10618 
17809 
24449 
30617 

03456 
11240 
18382 
2498G 
31112 

04134 
11859 
18951 
25508 
31604 

04805 
12472 
19517 
26033 
32093 

05470 
13082 
20079 
26554 
32579 

s 

1 

a 

3 

4 

119 
238 
368 
476 

15 
1G 
17 
18 
19 

2.33063133544 
38G67  39118 
4393044355 
48893  49294 
5338653966 

34023 
39567 
44777 
19693 
54344 

34498 
40013 
45198 
50090 
54721 

34972 
40457 
45616 
5048G 
55096 

35442 
40S99 
46033 
50879 
55469 

35910 
41339 
46447 
51271 
55841 

3637G 
1177C 
46859 
51661 
56211 

36839 
42211 
4727C 
52050 
56580 

37299 
42644 
47678 
52436 
56947 

37756 
43075 
48085 
52821 
57313 

38213 
43504 
48490 
53205 
57676 

s 
1 
2 
3 
1 

84 
168 
252 
336 

20 
21 
22 
23 
24 

2.5803958400 
62274  62618 
6631266640 
70170  70483 
7386374164 

•3875959117 
6296063302 
66967  67292 
7079G  71108 
74464  74762 

59474 
33641 
67617 
71418 
75060 

59829 
G3979 
67940 
71728 
75357 

60182 
64316 
68262 
72036 
75652 

60534 
64652 
G8583 
72343 
75947 

60885 
64987 
68903 
72649 
76241 

61234 
65320 
69221 
72954 
76533 

61582 
65652 
69538 
73258 
76825 

61929 
65982 
69855 
73561 
77116 

s 
1 
2 
3 
4 

65 
130 
195 

260 

25 
26 
27 
28 
29 

2.7740577694 
8080981086 
8408384350 
8723887496 
9028290531 

77982:76269 
8136381639 
84617  84883 
8775388009 
9077991027 

7855578840 
8191482188 
85148,85412 
8826588519 
9127891520 

79124 
82461 
85675 
88773 
91765 

79407 
82734 
85937 
89027 
92010 

79689 
83005 
86199 
89279 
92254 

79970 
83276 
86460 
89531 
92497 

80251 
83546 
8G72G 
89782 
92739 

80530 
83815 
86979 
90032 
92981 

s 
1 
2 
3 
4 

53 
106 
159 
212 

30 
31 
32 
33 
34 

2  .  93223  93463  93703  93942 
96067962999653296763 
g  .  98820  99045  99270  99-195 
3.01488017070192502143 
04077042890450104712 

94161 
96994 
99719 
02360 
04922 

94419 
97224 
99942 
02576 
05133 

94656 
97454 
00164 
02792 
05342 

94893 
97683 
00386 
03008 
05551 

95129 
97912 
00608 
03222 
1)5760 

95364 
98140 
0062.9 
03437 
05968 

95599  95833 
98367  98594 
0104901269 
G3651  03864 
0617606383 

s 

1 

2 
3 
4 

45 
90 
134 
178 

35 
36 
37 
38 
39 

3.06590 
09032 
11406 
13718 
15969 

0679(3 
09232 
11601 
13908 
16154 

0700107207 
0943209632 
11796  11990 
14097  14286 
16338  16522 

07411 
09831 
12184 
14475 
16706 

07616 
10029 
12377 
14663 
16889 

07819 
10227 
12570 
14850 
17072 

06023 
10425 
12762 
15038 
17255 

08225 
10622 
12954 
15225 
17437 

08428 
10819 
13146 
15411 
17619 

08629 
11015 
13337 
15597 

17800 

08831 
11211 
13527 
15783 
17982 

s 

s 
I 

30 
77 
116 

154 

40 
41 
42 
43 
44 

3.18162 
20301 
22389 
24427 
26418 

18343 
20477 
22560 
24594 
26581 

18522  18702 
20653  20828 
22732  22903 
2476224929 
26745  26908 

18881 
21003 
23073 
25095 
27071 

19060 
21177 
23244 
25262 
27234 

19238 
21351 
23414 
25428 
27396 

19417 
21525 
23583 
25594 
27558 

19594 
21699 
23753 
25759 
27720 

19771 
21872 
23922 
25924 
27881 

19949 

22044 
24090 
26089 
28042 

20125 
22217 
24259 
26253 
28203 

s 

1 

•2 
1! 

1 

34 

68 
102 
137 

45 
46 

47 
48 
49 

3.28363 
30266 
32128 
33950 
35734 

28524 
30423 
32281 
34100 
35881 

28683  28843 
30579  30735 
32434  32587 
34250  34400 
36028  36175 

2900229161 
30891  31047 
32739  32892 
3454934698 
36321  36467 

29320 
31202 
33044 
34847 
36613 

29478 
31357 
33195 
34995 
36758 

29637 
31512 
33347 
35144 
36903 

29i94 
31666 
33498 
35292 
37048 

29952 
31820 
33649 
35439 
37193 

30109 
31974 
33801 
35587 
37338 

I 
1 
•2 
3 

t 

31 

62 
92 
122 

50 
51 
52 
53 
54 

3  .  37482  37626  37770  37914 
39195  39336  39477  39618 
40875410134115241290 
42522426584279442929 
44138442724440544537 

36057138200 
3975939899 
41427  41565 
4306443199 
1467044803 

38343 
40039 
11702 
43334 
44935 

38486 
40179 
41839 
43469 
45067 

38628 
40319 
41976 
43603 
45199 

38770  38912 
4045840597 
1211342250 
43737  43871 
15331  45462 

39054 
40736 
42386 
44005 
45593 

a 
1 
2 
3 

1 

27 
55 

82 

no 

55 
56 
57 
58 
59 

3.45724 

47282 
48811 
50314 
51791 

45855  45986  46116 
474104753947667 
489381906449190 
504385056250686 
519135203552156 

46247,46377 
4779537923 
1931549441 
50809  50933 
5227852399 

46507 
48050 
1956G 
51056 
52520 

46636 
48177 
49691 
51179 
52641 

46766 
48305 
49816 
51301 
52761 

46895  47024 
4843248558 
49941  50066 
5142451547 
5288253002 

47153 
48685 
50190 
51669 
53122 

s 

1 
a 

3 

i 

25 
50 
75 
100 

278 

LOG  EISING  TO  FIND  THE 

TABLE  XVII. 

LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

1  Hour. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s.P.  P. 

U 
1 

2 
3 
4 

3  .  53243  533G2  c 
5467054788, 
5G074  56190, 
5745557569, 
58814  5892G 

>S48id 

54905 
5630G 
57683 
59038 

33602 
35023 
56421 
37797 
59150 

5372153840,53959 
55140o5258  55375 
56537  56652  56767 
57910  58024  58137 
59262  59374  59486 

54u7»  • 
35492, 
56S82  . 
58250 
59597 

54197  i 
55608  1 
56997  . 
38363  . 
59708, 

54^15:54434 
55725  55841 
5711257226 
5847G  58589 
59819,59930 

54552 
55958 
37341 
58702 
30041 

s 
1 

2 
3 

4 

23 
46 
70 
93 

5 

6 
7 
8 
9 

3.6015260202 
G1469  61578 
62766  62873 
6404364149 
65302  6540G 

30373 
31686 
32980 
34254 
35510 

130483 
J1795 
G3087 
64360 
65614 

60593  60703 
6190362012 
63194  63301 
6446564570 
6571765821 

130813 
52120 
63407 
64675 
65924 

3092D 
52228 
53513 
64780 
G6028 

31032 
32336 
33620 
34885 
36131 

3114361251 
3244362551 
3372G  63832 
3498965094 
36234  66337 

313uO 
32659 
33938 
35198 
56440 

s 
1 

a 
a 

4 

21 
42 
63 

85 

10 

11 
12 
13 
14 

3.6054266645 
67765  6786G 
689G9690G9 
7015870256 
71329  71426 

136747 
G7967 
G9169 
70354 
71523 

6'J849 
68067 
692G8 
70452 
71620 

6695-2 
68168 
G93G7 
70550 
71716 

37054  G715G 
38269  68369 
39467  695GG 
7064870745 
7181371909 

672-57 
G84G9 
69665 
70843 
72005 

37359 
38570 
59763 
70940 
72101 

37461  675G2 
3867068770 
398G2  G9961 
7103871135 
72197  72294 

57663 
68870 
70059 
71232 
72389 

s 

1 
2 
3 
4 

20 
40 
60 
80 

15 
16 
17 

18 
19 

3.7248572580J 
73G25  73719 
74750,74843 
75860  75952 
7695577046 

7267G 
73813 
7493G 
76043 
77137 

7277  1I728G7I 
73907:74001 
7502975121 
76135  76227 
77227  77318 

72962  73057  73152 
74095  74189  74283 
752147530775399 
763187640976501 
774087749877588 

73247 
7437G 
75491 
76592 
77678 

73341 

74470 
75584 
76683 
77768 

7343G 
74563 
75676 
76774 

77858 

73530 
74657 

75768 
76865 
77947 

s 
1 
9 
3 

4 

18 
37 
55 
74 

20 
21 
22 
23 
24 

3.78037|78127 
7919579193 
8015980247 
81201  81287 
82230  82315 

78210 
79282 
80331 
81373 
82400 

78305 
79370 
80421 

8145S 
82485 

:78395  78484 
79458  79546 
8050880595 
8154581631 
82570  82655 

78573 
79634 
80682 
81717 

82739 

78GG2 
79722 
80768 
81802 
82824 

78750J78839  78928|7901G 
79809798977998580072 
80855809428102881115 
81888819748205982144 
82908:829938307783162 

s 
1 
2 
3 

•1 

17 
35 
52 
70 

25 
26 

27 
28 
29 

3.8324G 
84250 
85242 
86223 
87192 

83330 
84333 
85325 
86304 
87272 

83414 
8441G 
8540G 
86385 
87352 

83498 
8449S 
85488 
8646C 
87432 

83582 
84582 
85570 
86547 
87513 

83G6G  83749  83833 
84G65  84748  84830 
85652  85734  8581G 
86628  86709  86790 
87593  87672  S7752 

83917  84000 
8491384995 
85897  85979 
8687086951 
8783287912 

84083 
85078 
86060 
87031 
87991 

841G7 
85160 
86111 
87112 

88071 

s 
1 
2 
3 
4 

16 
33 
49 
65 

30 
31 
32 
33 
34 

3.88150J88229 
8909789176 
90034  90112 
9096091037 
9187C;91952 

88309 
89254 
90189 
91114 
92028 

88388  88467 
8933389411 
90267  90344 
9119091267 
9210492179 

88540 
89489 
90421 
91343 
92255 

88G25  88704 
895G7  89645 
9049890576 
91420  9149G 
92331  J9240C 

88783 
89723 
90653 
9157z 

92482 

88862 
89801 
90730 
91648 
92557 

88940 
89879 
90807 
91724 
92632 

89019 
S9956 
90884 
91800 
92707 

» 
1 
2 
3 

•1 

15 
31 
46 

62 

35 
36 
37 
38 

39 

3.9278292858 
93679,93753 
94566J9463S 
9544395515 
96311J96383 

92933 
93827 
94712 
95588 
96455 

93007  93082 
9390193975 
94786  94859 
9566  1)95733 
96527  96599 

93157 
94043 
94932 
9580C 
96G7C 

93232 
94123 
95005 
95878 
96742 

9330G 
94197 
95078 
95950 
96813 

93381 
94271 
95152 
96023 

96885 

93456 
94345 
95224 
96095 
9G956 

93530  93G05 
9441894492 
95297  95370 
9016796239 
9702897099 

s 
1 
2 
3 

'i 

15 

29 
44 

58 

40 
41 
42 
43 
44 

3.97170,97242 
9802198091 

9886298932 
%99696  99765 
4.00521005SS 

9731c 
9816k 
9900: 
99834 
0065-i 

97384,97455 
9823298302 
9907299141 
9990399972 
0072G  00794 

97521 
98372 
99211 
0004C 
00862 

97597  97GG7 
9844398513 
9928099350 
0010900178 
0093000998 

j977ob 
98583 
99419 
00247 
010G6 

97809  9788(J 
98653  98723 
99488  99557 
0031500384 
0113401202 

,97950 
98793 
99627 
00452 
01270 

s 
1 
2 
3 

4 

14 

28 
42 
5G 

45 
46 
47 
48 
49 

4.0133701405 
02146  02212 
02947.0301S 
03740.0380C 
0452604591 

101471 
0228( 
0308C 
0387J 
0465( 

;01540  01608 
10234702414 
)  03146  03212 
03937,04003 
>  04721  0478C 

01075 
02481 
03278 
0406* 
04851 

01742 
02541; 
>  03344 
(04134 
049K 

01810 
02614 
03411 
0419S 
0498C 

01877 
02681 
03477 
04265 
0504i] 

01945 
02747 
0354i 
0433C 
05111 

02012 
02814 
03608 
04395 
05175 

0207  b 
0288C 
03674 
0446C 
05231 

s 
1 
2 
3 

4 

13 
26 
40 
53 

50 
51 
52 
53 
54 

4.053040536!: 
0607406138 
06838:06901 
07595,0765'i 
08344  0840( 

05433  05497  05561 
06202  06266  0633C 
06965  07028,07091 
077200778307845 
084680853008592 

05026  0509C 
06393  0645r 
07154  0721r 
0790807971 
08654  087K 

105754 
06521 
0728C 
108032 
)  08778 

U5S18 
06581 
07342 
08095 
0884C 

U5882!o594t 
0664806713 
07406  07461. 
081570822( 
0890208964 

0601C 
06775 
07532 
0828$ 
09025 

s 
1 
2 
3 

4 

13 
25 
38 
50 

55 
53 
57 

58 
59 

•i.  09087,0914* 
09823  098& 
10552  10611 
11275  1133; 
119921205- 

S092K 
t0994, 
iiOG7 
51139 
L  1211 

)  09272,0933311)9394  0945* 
3  10006  10067  10128  10181 
3  10734  10794  10854]  10U1, 
31145511515115751163 
L  12170'  1222912289  1234 

509517 
>  1024$ 
5  1097; 
1  1169^ 
5l240r 

09578 
1  103K 

iiioai 

1  11754 
HJ246( 

09640,0970] 
103711043] 
>  11095  1115( 
[1181311871 
.125251258- 

0976'. 
1049: 
511215 
$1193$ 
L  12641 

s 
!  1 

,  2 
\  3 

5  4 

12 
24 

36 

48 

TABLE  XVII.                279 

LOG  RISING  TO  FIND  THE  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

2  Hours. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.P. 

0 
1 
2 
3 
4 

4.1270212761 
13406  134G5 
14104  1416-2 
14797114854 
15483J15540 

12820 
13523 
14220 
14911 
15597 

12879 
13o81 
14278 
14969 
15652 

12938 
13640 
14336 
15026 
15710 

12996 
13696 
14394 
15083 
15767 

13055 
13750 
14451 
15140 
15824 

13114 
13814 
14508 
15198 

15880 

13172 
13872 
14567 
15255 
15937 

13231 
13931 
14625 
15312 
15994 

13283 
13989 
1468'2 
15369 
16050 

13348 

14047 
14739 
15420 
16107 

s 
1 
2 
3 
1 

11 

23 
34 
46 

5 

6 

7 
8 
9 

4.1610316220 
1683816894 
17507  17563 
18171  18226 
18829  18883 

16276 
16950 
17618 
18281 
18938 

1633-2 
17006 
17673 
18336 
18992 

16389 
17062 
17729 
18391 
19047 

16145 
17117 
17784 
18445 
19101 

16501 
17173 
17840 
18500 
19156 

16557 
17229 
17895 
18555 
19210 

16614 
17285 
17950 
18610 
19265 

16070 
17340 
18005 
18665 
19319 

107-20 
17396 
18060 
18719 
19373 

10782 
17451 
18116 
18774 
19427 

s 
1 
2 
3 

4 

11 

22 
33 
44 

10 
11 
12 
13 
14 

4.19482:19536 
201-29  20183 
20771120825 
'2140921461 
22041  22093 

19590 
20236 
20878 
21514 
22146 

19641 
20290 
20931 
21567 
22198 

19698 
20344 
20984 
21620 
22250 

19/52 
20397 
21037 
21673 
22303 

19806 
20451 
21091 
21725 
22355 

19800 
20505 
21144 
21778 
22407 

19914 
20558 
21197 
21831 
22459 

19968 
20611 
21250 
21883 
22511 

20022 
20665 
21303 
21936 
22564 

20075 
20718 
21356 
21988 
22610 

H 
] 

2 
3 

4 

11 
21 
32 
'42 

15 
16 
17 

18 
19 

4.22668 
23290 
23907 
24520 
25128 

2ii72u 
23342 
23959 
24571 
25178 

2277* 
23393 
24010 
24622 
25229 

22824 
23445 
24061 
24673 
25279 

22876 
23496 
24112 
24723 
25330 

22928 
23548 
24163 
24774 

25380 

2296'0 
23599 
24214 
24825 
25430 

23031 
23051 
24265 
24875 
25481 

23083 
23702 
24316 
24926 
25531 

23135 
23754 
24367 

24977 
25581 

23187 
23805 
24418 
25027 
25631 

23238 
23850 
24469 
25078 
25681 

B 
1 

2 
3 

4 

10 
20 
31 
41 

20 
21 
22 
23 
24 

4.  25731  25761 
2633026380 
2692426974 
27514  27563 
2803928148 

25831 
26429 
27023 
27612 
28197 

25881 
26479 
27072 
27661 
28245 

25931 
26529 
27121 
27710 
28294 

25981 
26578 
27171 
27759 
28342 

26031 
26628 
27220 
27807 
28391 

26031 
26677 
27269 
27856 
28439 

26131 
26727 
27318 
27905 
28487 

26181 
26776 
27367 
27954 
28536 

2u231 
26826 
27416 
28002 
28584 

26281 
26875 
27465 
28051 
28632 

s 
1 
2 
3 
4 

10 
20 
29 
39 

25 
26 
27 
28 
29 

4.2866128729 
29257  29305 
29830  29877 
3039830445 
30963  31009 

28777 
29353 
29925 
30493 
31050 

.:88Z5 
29401 
29973 
30540 
31103 

28873 
29449 
30020 
30587 
31150 

28921 
29496 
30067 
J0034 
31197 

2896U 
29544 
J0115 
JOG81 
31243 

^9017 
29592 
30162 
30728 
31290 

29060 
29639 
30209 
30775 
31337 

29114 
29687 
30257 
308-22 
31383 

29161 
29735 
30304 
30869 
31430 

29209 
29782 
30351 
30916 
31476 

s 
1 

2 

3 

•1 

10 

19 
29 
38 

30 
31 
32 
33 
34 

4.31523 
32079 
32631 
33180 
33724 

31569 
32125 
32677 
33225 
33770 

31610 
32171 
32723 
33271 
33815 

31602 
32217 
32769 
33316 
33800 

31709 
32264 
32815 
33362 
J3905 

31755 
32310 
32860 
33407 
33950 

31801 
32356 
32906 
33453 
33995 

31848 
32402 
32952 
33498 
34040 

31b91 
32448 
32997 
33543 
34085 

31940 
32491 
33043 
33589 
34130 

31987 
32540 
33089 
33634 
34175 

3203o 
32586 
33134 
33679 
34220 

a 
1 

'2 
1! 
•1 

9 

18 
28 
37 

35 
36 
37 
38 

39 

4.34205 
34802 
35335 
35865 
36391 

31310 
34847 
35380 
35909 
36435 

34355 
34891 
35424 
35953 
36476 

34400 
34936 
35468 
35997 
36522 

34444 

34980 
35512 
36041 
30565 

34489 
35025 
35556 
36085 
36609 

34534 
35069 
35601 
36128 
36053 

34579 
35114 
35645 
36172 
36696 

340.i3 
35158 
35689 
36216 
36740 

34008 
35202 
35733 
36260 
36783 

34713 
35247 
35777 
36303 
36827 

34757 
35291 
35821 
36347 
36870 

s 

1 
•2 
9 
•l 

9 

18 
27 
36 

40 
41 
42 
43 
44 

4.36913 
37432 

37948 
38460 
389G8 

369o7 
37475 
3799U 
38502 
3J010 

3700U 
37518 
38033 
38545 
39052 

37043 
37561 
38076 
38587 
39095 

37087 
37604 
38119 
38629 
39137 

37130 
37647 
38161 
38672 
39179 

37173 
37690 
38204 
38714 
39221 

37216 
37733 

38247 
38757 
39263 

37200 
37776 
38289 
38799 
39305 

37303 
37819 
38332 
38841 
39347 

37340 
37862 
38374 
38884 
39389 

37389 
37905 
38417 
38920 
39431 

s 

1 
•2 
3 
1 

9 
17 
26 
35 

45 
46 

47 
48 
49 

4.39473395io 
3997540017 
40474  40515 
4096941010 
41461  41502 

39557 
40058 
40550 
41051 
41543 

39599 
40100 
40593 
41092 
41583 

39641 
40142 
40639 
41133 
41624 

39683 
10183 
10680 
11174 
11065 

39725 
40225 
40722 
41215 
41706 

39700 
40260 
40763 
41256 
41746 

39ci08 
40308 
40804 
41297 
41787 

39850 
10349 
40845 
11338 
41828 

39892 
40391 
40887 
41379 
41868 

39930 
4043-2 
10928 
41420 
41909 

s 
1 
•1 

;; 

-i 

8 
17 
25 
34 

50 
51 
52 
53 
51 

4.41950'4199U 
4243542476 
4291842958 
4339843437 
4387443914 

42031 
42516 
42998 
43477 
43953 

42071 
42556 
43038 
43517 
43993 

421la 
42597 
43078 
43557 
44032 

42153 
42637 
43118 
43597 
44072 

42193 
42677 
43158 
43636 
44111 

42233 
12717 
43198 
43676 
14151 

42274 
42758 
43238 
43716 
44190 

42314 
42798 
43278 
43755 
44229 

42355 
42838 
43318 
43795 
44269 

42395 
42878 
43358 
43835 
44308 

s 

I 
a 

3 

i 

8 
If 
24 
32 

55 
56 

57 
58 
59 

4.4434»:44387 
4481844857 
4528645325 
45750  45789 
4621240250 

44426  44405 
4489644935 
453G3  45402 
45827  15860 
46289'46327 

44505 
14974 
15141 
45905 
46365 

44544  44583 
4501345052 
45480  45518 
4594345982 
4640i!46442 

44022 
45091 
45557 
46020 
16480 

44662 
45130 
1559G 
16058 
46518 

44701 
45169 
45634 
46097 

ior>r,i; 

44740 
15208 
45673 
46135 
46595 

44779 
45247 
45712 
46174 
46633 

s 

] 
•_' 

B 

-I 

8 
15 
23 
30 

280                TABLE  XVII. 

LOG  RISING  TO  FIND  THE  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

3  Hours. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s.  45s.  50s.  55s. 

P.P. 

0 
1 

2 
3 
4 

4.40671 
47127 

47580 
48031 

48479 

46709 
47165 
47618 
48068 
48516 

46747 
47203 
47656 
48106 
48553 

46785  46823  4686146899 
47241472784731647354 
47693477314776847806 
48143  4818048218  48255 
48590  48627  48664  48701 

40937 
47392 
47843 
48292 
48739 

40975  47013  47051  47089 
47430  47467^750547543 
47881479184795647993 
4833048367,4840448441 
48776488134885048887 

s 
] 
9 
:; 
4 

7 
15 
22 
30 

5 

6 

7 
8 
9 

4.48924 
49360 
49806 
50243 
50677 

43961 
49403 
49842 
50279 
50714 

4899S 
49440 
49879 
50316 
50750 

49035 
49476 
49915 
50352 
50786 

49071,4910849145 
495134955049586 
49952  49988  50025 
503885042450461 
50822  5085850894 

49182 
49623 
50061 
50197 
o0930 

4921949256  49293  49329 
49660  4969649733  497G9 
50098501345017050207 
50533  50569  50605  50641 
50966510025103851073 

s 

1 

2 
I 

•1 

7 
14 

22 
29 

10 
11 
12 
13 
14 

4.51109 
51539 
51966 
52390 
52812 

51145 
51574 
52001 
52425 
52847 

51181 
51610 
52037 
52461 

528S2 

31217 
51646 
52072 
52496 
52917 

5125351289,51324 
516815171751753 
521075214352178 
5253r52566'52601 
52952j5k987  53022 

513GO 
51788 
52213 
52636 
53057 

5139651432:5146751503 
51824  51859  51895'51930 
52249522845231952355 
52672  52707  52742  52777 
53092  53127  53162  53197 

8 

I 

2 
3 

4 

7 
14 
21 

28 

15 

1(3 
17 
18 
19 

4.53231 
53648 
54063 
54475 
54885 

53266 
53683 
54097 

53301 
53718 
54132 

53330 
53752 
54166 

533715340553440 
5378753821153856 

54201  54235,54269 

53475 
53891 
54304 

53510  53544  53579  53614 
53925  53960  53994  54029 
54338  54372;54407>54441 

8 
1 

2 
3 

4 

7 
14 

20 
27 

54509 
54919 

54544 
54953 

54578 
54987 

5461254646 
55021  55055 

o4680 
55089 

54715 
55123 

54749  54783,54817  54851 
55157551915522555259 

20 
21 
22 
23 

24 

4  .  55293 
55G98 
56101 
56501 
56900 

55327 
55732 
56134 
56534 
56933 

55360 
55765 
56168 
56568 
56966 

55394 
55799 
56201 
56G01 
56999 

55428 
55832 
56235 
56635 
57032 

55402  55496 
5586655900 
56268,56301 
56668'56701 
57065,57098 

55529 
55933 
56335 
56734 
57131 

55563  55597j55630,55664 
55967  56000  56034  56067 
56368  56401  56435  56468 
56767  56800,56834  56867 
57164571975723057263 

I 
j 

2 
3 

4 

7 
13 

20 
26 

25 

20 
27 
28 
29 

4.57296 
57690 
58082 
58471 
58859 

57329 
57723 
58114 
58504 
58891 

57362 
57755 
58147 
58536 
58923 

57395 

57788 
58179 
58568 
58955 

57428 
57821 
58212 
58601 
58988 

57460  57493 
57854  57886 
58244  58277 
58633  58665 
5902059052 

57526 
57919 
58309 
58698 
59084 

57559  57592jo7625  57057 
57951579845801758049 
58342583745840758439 
58730587625879458827 
59116591485918059212 

s 
1 
2 
3 

4 

6 

13 
19 

26 

30 
31 
32 
33 
34 

4.59244 
59627 
60008 
60388 
60764 

5927(j 
59659 
60040 
60419 
60796 

59308 
59691 
60072 
60450 
60827 

59340 
59723 
60103 
60482 
60858 

59372594045943(3 
597555978659818 
601356016760198 
60513  60545  G0576 
608906092160952 

59408 
59850 
60230 
6060-- 
60983 

59500  59532  59564  59596 
59882599135994559977 
60261  60293  60324J60356 
60639606706070160733 
61015610466107761108 

s 
1 
2 
3 

4 

6 
12 

18 
25 

35 
36 

37 
38 
39 

4.01139 
61512 
61883 
62252 
62619 

G1171 

61543 
61914 
62283 
62650 

61202 
61574 
61945 
62313 
62680 

61233 
61605 
61976 
62344 
62711 

61264 
6163G 
62006 
62375 
62741 

6129561326 
6166761698 
62037  62068 
6240562436 
62771  62802 

01357 
61729 
62099 
62466 
62832 

6138861419,6145061481 
61760617916182261852 
6212962160,6219162222 
62497  62528  62558  62589 
62863  62893  62923  62954 

s 
1 
2 
3 

4 

6 
12 
18 
24 

40 
41 
42 
43 
44 

4.62984 
63347 
63708 
640G8 
64425 

63014 
63377 
63738 
64097 
64455 

63045 
63407 
63768 
64127 
64484 

63075 
63438 
63798 
64157 
64514 

631056313663160 
63468  63498  63528 
638286385863888 
64187  64217  64246 
G4544  64573  64603 

63196  63226  G3257J63287jG3317 
J3558  63588  63618  63648  63678 
63918  63948  63978  64008  64038 
64276  64306  64336  64365!64395 
64632  64662  64692  64721  64751 

s 
1 
2 
3 

4 

6 
12 
18 
24 

45 
46 
47 

48 
49 

4.64780 
65134 
65486 
65836 
66184 

64810 
65163 
65515 
65865 
66213 

64839 
65193 
65544 
65894 
66242 

64869 
65222 
65573 
65923 
66270 

64898 
65251 
65603 
65952 
G6299 

6492864957 
65281  65310 
6563265661 
65981  '66010 
6632866357 

64987 
65339 
65690 
66039 
66386 

65016650456507565105 
65369653986542765456 
65719  65748  65777  65806 
66068660976612666155 
66415664446647266501 

s 
1 
2 
3 

4 

c 

12 
17 
23 

50 
51 
52 
53 
54 

4.66530 
66875 
67217 
67558 
67897 

66559 
66903 
67246 
67587 
67925 

66588 
66932 
67274 
67615 
67954 

66616 
66960 
67303 
67643 
67982 

66645 
66989 
67331 
67672 
68010 

G6674'66702 
6701867046 
6736067388 
6770067728 
6803868066 

66731 
67075 
67416 
67756 
68094 

66760  66789J66817  66846 
6710367132J6716067189 
6744567473:6750267530 
67785678136784167869 
68123681516817968207 

B 
1 

2 
3 

4 

6 

12 
17 
23 

55 
56 
57 

58 
59 

4.68235 
68571 
68905 
69237 
69568 

68283 
68599 
68933 
69265 
69595 

68291 
68627 
68960 
69292 
69623 

68319 
68654 
68988 
69320 
69650 

68347 
68682 
69016 
69348 
69678 

68375,68403  68431  68459  68487,68515  68543 
6871068738  68766  68794  68821  68849  68877 
69043  69071  69099  69127,69154  69182  69210 
69375  69403:69430  69458  69486,69513  69540 
69705  69733169760  69788  69815  69842  69870 

s 
1 

a 

3 
4 

6 

11 
17 

22 

TABLE  XVII. 

LOG  RISING  —  TO  FIND  THE  LATITUDE  BY  REDUCTION 

281 

TO  THE  MERIDIAN. 

4  Hours. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.P. 

0 

1 

2 
3 
4 

4.G9897 
70224 
70550 
70874 
71197 

6JW24 

70252 
70577 
70901 
71224 

G9952  69979 
7027970306 
70G04  70631 
70928'70955 
7125071277 

70000 
70333 
70658 
70932 
71304 

70031  70061  70U88  70115  70143 
70360  70387  70415  70442  70469 
70685  70712  70739  70766  70793 
71009  71036,71063  71089  71116 
7133l'71357,71384  71411  71438 

70170 
70496 
70820 
71143 
71464 

70197 
70523 
70847 
71170 
71491 

8 
1 

2 
3 

4 

5 
11 
16 

22 

5 
6 
7 
8 
9 

4.71518 
71837 
72155 
72471 

72785 

71544 
71864 
72181 

72497 
72812 

71571J71598 
7189071917 
7220872234 
7252372550 
72838  72864 

71624  71G51  71678 
719437197071996 
72260  7228772313 
7257C  72602  72628 
7289072916,72942 

7170417173171757 
7202372049,72075 
72339  723GG  72392 
726557268172707 
729687299473020 

71784 
72102 
72418 
72733 
7304C 

71810 
72128 
72445 
72759 
73072 

s 
1 
2 
3 
i 

5 
10 
16 
21 

10 
11 
12 
13 
14 

4  .  73099 
73410 
73720 
74028 
74335 

73125 
73436 
73746 
74054 
74361 

73151 
73462 
73772 
74080 
74386 

73177 
73438 
73797 
74105 
74412 

73203 
73514 
73823 
74131 
74437 

7322873254 
73539  73565 
73849  73874 
7415774182 
744G3  74488 

73280 
73591 
73900 
74208 
74514 

73306,7333* 
73G17  73643 
73926  73951 
7423374259 
7453974565 

73358 
73668 
73977 
74284 
74590 

73384 
73694 
74003 
74310 
7461G 

s 
1 
2 
3 

4 

5 
10 
15 

20 

15 

16 
17 
18 
19 

4.74041 
74945 
75247 
75549 

75S48 

74666 
74970 
75273 
75574 
75873 

74692 
74995 
75298 
75599 
75898 

74717 
75021 
75323 
75624 
75923 

74742 
75046 
75348 
75649 
75948 

74768 
75071 
75373 
75674 
75973 

74793 
75096 
75398 
75G99 
75997 

748181  74844  174869 
75122175147(75172 

754237544875473 
75723  7574875773 
76022  76047  76072 

74894 
75197 
75498 
75798 
76097 

74920 
75222 
75523 
75823 
76121 

s 

1 

2 
3 
4 

5 
10 
15 
20 

20 

21 

22 
23 
24 

4.76146 
76443 
76738 
77032 
77325 

76171 
76468 
76763 
77057 
77349 

761% 
76492 
76787 
77081 
77373 

76221 
76517 
76812 
77105 
77398 

76245 

76542 
7G83C 
77130 
77422 

70270170295 
76566  76591 
76861  76885 
77154  77179 

774-16,77470 

76320 
76615 
769K 
77203 
77495 

76344  763G9 
76640  76665 
76934  76959 
77227  77252 
7751977543 

76394 
76689 
76983 
77276 
77567 

76418 
76714 
77008 
77300 
77592 

s 

1 

2 
3 
4 

5 
10 
15 
20 

25 
26 
27 
28 
29 

4.77G16 
77906 
78194 
78481 
78767 

77640 
77930 
78218 
78505 
78790 

77604 
77954 
78242 
78529 
78814 

77088 
77978 
78266 
78552 

78838 

7771ci 
78002 
78290 
78576 
78861 

77737|77701I?7785 
780267805078074 
78314  78338  78361 
78600.7862478648 
78885;78909  78933 

77809 
78098 
78385 
78671 
78956 

77833 
78122 
78409 
78G95 
78980 

77857 
78146 
78433 
78719 
79004 

77882 
78170 
78457 
78743 
79027 

s 
1 
2 
3 

•4 

5 
10 
14 
19 

30 
31 
32 
33 
34 

4.79U51 
79334 
79615 
79896 
80175 

790747909879122 
79357  79381  79404 
796397966279686 
79919  79942  799G5 
80198  80221  S0244 

79145 
79428 
79709 
79989 
80267 

79109,79192 
79451  79475 
79732  7975G 
80012  80035 
8029080314 

79210 
79498 
79779 
80059 
80337 

7924079263 
79522  79545 
79802179826 
8008280105 
8036080383 

79287 
79568 
79849 
8012& 
80406 

79310 
79592 
79872 
80151 
80429 

s 

1 
2 
3 

-i 

5 
9 
14 
19 

35 
3G 
37 
38 
39 

4.80452 
80729 
81004 
81277 
81550 

80475 
30752 
81027 
31300 
81573 

80498,30521 
8077580797 
8104981072 
8132381346 
8159581618 

30545 
80820 
81095 
81368 
81641 

80508  80591  30014 
808438086680889 
811188114181163 
813918141481437 
816638168681708 

80637,80660180683 
80912  80935  80958 
811868120981232 
814598148281505 
81731  81754  81776 

80706 
80981 
81255 
81527 
81799 

s 
1 
2 
3 
4 

5 
9 
14 

18 

40 
41 

42 
43 
44 

4.81821 
82091 
82360 
82628 
82894 

31844 
82114 
82382 
82650 
82916 

8186681889 
8213682159 
3240582427 
8267282694 
8293882960 

81911819348195081979 
82181  82203  82226  82248 
82449  82472  82494  825  1C 
82716827398276182783 
82982830048302683049 

82001182024  820408.1069 
822711822938231582338 
82538  82561  82583  8260S 

82805828278285082872 
83071|83093  83115  83137 

s 

] 
a 

3 

1 

4 

9 
13 

18 

43 
46 
47 

48 
49 

4.83159 
83423 
83685 
83947 
84207 

83181 
83445 

8320383225 
83467  83488 

8324783269 
8351083532 

83291  83313 
8355483576 
8381683838 
84077  84099 
84337  84358 

83335:83357 
8359883620 
8386083881 
8412084142 
8438084401 

83379 
83642 
83903 
81164 
84423 

83401 
83663 
83925 
84185 
84444 

s 
1 
2 

a 

i 

4 
9 
13 

18 

837078372983751 
839688399084012 
842298425084272 

8377383794 
8403484055 
8429384315 

50 
51 
52 
53 

f>4 

4.84406 
84724 
81981 
85236 
85490 

84488 
84745 
85002 
85257 
85512 

8450984531 
8476784788 
8502385044 
8527885300 
8553385554 

8455284574,8459584617 
84810848318485284874 
8506G85087j85108,85130 
85321  85342,85363  85385 
85575855968561785638 

8463884659 
8489584916 
85151  85172 
8540685427 
85659  85680 

34081 
84938 
85194 
85448 
85701 

84702 
81959 
85215 
85469 
85722 

s 

1 

2 

:; 
•1 

4 
9 
13 
17 

55 
56 
57 
<•  58 
59 

4.85744 
85996 
86247 
86496 
86745 

85765 
86017 
86267 
86517 
86766 

8578685807 
8603886058 
8628886309 
86538  8655D 
8678686807 

85828  85849  85870  85891  85912:85933 
86079  86100  86121  86142lS6163  86184 
86330  8G35l'8G372  86392  8G413  86434 
86579  36600  8662  1  866  1  1  |S6GG2I8GG83 
86828  86848  86869  86889  86910  86931 

35954J85975 
86205  86226 
MM  .I.-.  36475 
8670486724 
86951  86972 

s 

1 
a 

:i 
i 

4 
8 
13 
17 

282                TABLE  XVII. 

LOG  RISING  PO  FIND  THE  LATITUDE  BY  REDUCTION 

TO  THE  MERIDIAN. 

5  Hours. 

M. 

Os. 

5s. 

10s. 

]5s 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.  P. 

0 

1 

2 
3 
4 

4  .  8b992  87013  87034  87054 
87239  87259  87280  87300 
87484875058752587545 
87728  87749  877G9  87789 
87971  87992  88012|88032 

87075 
87321 
87566 
87809 
88052 

87ulJiJ 
87341 
87586 
87830 
88072 

871Hi 
87362 
87606 
87850 
88093 

87136J8715787177 

873828740287423 
876278764787667 
878708789087911 
881138813388153 

87198 
87443 
87688 
87931 
88173 

87218 
87464 
87708 
67951 
88193 

s 

1 

4 

8; 

12 
16 

5 

r> 

7 
8 
9 

4.882138823488254 
88454  88474  88494 
886948871488734 
889338895388973 
891718919089210 

88274 
88514 
88754 
88992 
89230 

88^94 
88534 
83774 
89012 
89250 

88314 
88554 
88794 
89032 
89269 

88334 
88574 
88814 
89052 
89289 

88354 
88594 
88834 
89072 
88309 

88374  88394 
88614  88634 
8885388873 
89C91  89111 
8932889348 

88414 
88654 
88893 
89131 
89368 

88434 
88674 
88913 
89151 

89388 

8 
1 

2 
3 

4 

4 
8 
12 

16 

10 

11 

1'2 
13 

14 

4.89407(894^789447 
89G4389G62  89682 
898778989789916 
901119013090150 
90343,90363  90382 

89460 
89702 
89936 
901G9 
90401 

S9486 
89721 
S9955 
90188 
90421 

89500 
89741 
89975 
90208 
90440 

89525 
89760 
89994 
90227 
90459 

89545  89564:89584 
897808979989819 
900149003390053 
90247  90266  90285 
904789049890517 

89604 
89838 
90072 
90305 
90536 

896^3 
89858 
90091 
90324 
90555 

8 
1 

2 
3 

4 

4 
8 
12 
16 

15 

1G 
17 

18 
19 

4  .  90575  90594  90613  90632 
90805.9082419084390883 
91034  91051  91073J91092 
91263912829130191320 
91490915099152891517 

90u5_ 
90882 
91111 
91339 
91566 

90671 
90901 
91130 
91358 
91585 

90690 
90920 
91149 
91377 
91603 

90709 
90939 
91168 
91396 
91622 

9072890748 
90958,90977 
91187,91206 
9141491433 
9164191660 

90767 
90996 
91225 
91452 
91679 

90786 
91015 
91244 
91471 
91698 

s 
1 
2 
3 
4 

4 
S 
11 
15 

20 
21 
2-2 
23 
24 

4.917169173o 
9194291961 
9216692185 
92390  132408 
9261292630 

91754 
91979 
92203 
92427 
92649 

91773 
91998 
92222 
92145 
926G7 

31792 
92017 
92241 
92464 

9268G 

91811 
92035 
92259 
92483 
92704 

91829 
92054 
92278 
92501 
92723 

91848 
92073 
92297 
92519 
92741 

91867,91886 
9209292110 
9231592334 
9253892556 
92760,92778 

91904  91923 
9212992148 
9235292371 
92575  92593 
92796  92815 

S 
1 

2 
3 

•1 

4 
7 
11 
15 

25 
26 
27 
28 

29 

4.9.8339285J 
93054'93072 
93273  93291 
93492  93510 
93709  93727 

92870 
93090 
93310 
93528 
93745 

92888 
93109 
93328 
33546 
93763 

J2907 
93127 
93316 
93564 
93781 

92925 
93145 
93364 
93582 
93809 

92944 
93164 
93382 
93600 
93817 

92962 
93182 
93401 
93619 
93836 

92980,92999 
9320093218 
9341993437 
93637,93655 
93854!93872 

93017 
93237 
93455 
93673 
93890 

93035 
93255 
93473 
93691 
93908 

s 
1 
2 
3 

-i 

4 
7 
11 
15 

3J 
31 
32 
33 
34 

4.U3926 
94141 
94356 
91570 
94782 

93944 
94159 
94374 
91587 
94800 

939o293980 
94177  94195 
94392  94410 
91605  91623 
34818  94833 

93998 
94213 
94427 
34641 
94853 

'94016 
94231 
94445 
94658 
94871 

94034 
94249 
94463 
94G7G 
94888 

9405294069,94088 
94267  94284,94302 
94481  94498  94516 
946919471194729 
94906  94924^4941 

94105  94123 
94320  94338 
94534  94552 
94747  94765 
9495994976 

8 

1 

2 
3 

4 

4 
7 
11 
14 

35 

38 
37 
38 
39 

4.919949501^ 
95205  95223 
95415  95433 
95624  95642 
95832  95850 

95029 
95240 
95450 
95659 
95867 

95047 
95258 

J54GS 
95676 

95884 

35005 
95275 
95485 
35694 
95902 

35082 
95293 
95502 
95711 
95919 

95100 
95310 
95520 
95728 
95936 

95117i95135  95153 
95328,95315J95363 
95537  95555  95572 
95746  35763*95780 
959539597195988 

95170 
95380 
95589 
95798 
96005 

95188 
95398 
95607 
95815 
3.6022 

8 

1 

2 
3 
4 

3 

7 
1C 
14 

40 
41 
42 
43 
44 

4.96040'9G057 
96246  96263 
96451  93469 
96656  96673 
9686093877 

06074 
96280 
96486 
9G690 
96894 

96091 
96297 
96503 
96707 
9G910 

36109 
96315 
96520 

9G724 
9G927 

96126 
96332 
36537 
96741 
36944 

9614S 
96349 
96551 
96758 
96961 

36160 
96366 
96571 
96775 
96978 

96177,96195 
9638396400 
9658896605 
9679296809 
9G995  97012 

96212 
96417 
9G622 
96826 
97029 

96229 
96434 
9GG39 
96843 
37046 

s 
1 
2 
1! 
4 

3 

7 
10 
14 

4o 
4G 
47 

48 
49 

4.97002:37079 
9726497281 
9746597482 
97665  97682 
97865  97881 

97090  97113 
97298  97315 
9749997515 
9769997715 
9789897914 

37130 
97331 
97532 
97732 
97931 

97147 
97348 
97549 
97749 
37947 

37163 
97365 
97565 
97765 
97964 

97180 
97382 
97582 
97782 
97981 

9719797214 
9739897415 
97599,97615 
97798,97815 
97997|98014 

97231  97247 
97432  97449 
97G32  97649 
97832  97848 
9803098047 

s 
1 
2 
3 
4 

3 

7 
10 
13 

50 
51 
5-2 
53 
5t 

4  .  98063  98080  98096  98113 
98261982779829398310 
98457984749849098506 
98653986699868698702 

98848988649888098897 

9812998145 
9832698343 
9852398539 
9871898734 
3891398929 

9816z 
38359 
98555 
98751 
38945 

98178 
98375 
18572 
98767 
98961 

98195.9S211 
9.S39298408 
9858898G04 
9878398799 
9897798994 

98228 
98425 
38620 
38816 
39010' 

)8244 
)8441 
)8637 
)S832 
)902G 

s 
1 
2 
3 

4 

3 

7 
10 
13 

55 

5G 
57 
58 
59 

4  .  99042  9905S  99074^99090 
99235  9925l!99267|99284 
99423J99444  99460  99  476 
99G19  99635  99651  99667 
99310  99826  9984^99858 

39107199123 
3930099316 
39492  99508 
39683  99690 

3987399889! 

391399915599171199187 
99332  99348  993G4  99380 
99524995409955699572 
997159973199747,99763 
99905  9992  ll99937;99953 

9920399219 
3939699312 
39587  99603 
3977899794 
39968199984  1 

s 
1 

•2 

9 

4 

3 

6 
10 
13 

TABLE  XVII.                283 

LOG  RISING  TO  FIND  THE  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

6  Hours. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.P. 

0 
1 
2 
3 
4 

5.0000000010 
00189  00205 
00377100393 
0056500580 
00751  D0767 

00032 
00221 
00409 
J0596 
00782 

00047 
00236 
00424 
0061* 
00798 

00063  0007900095J00110 
00252  002G8  00283  00298 
00440004560047100487 
00627006430065800674 
00813008290084400860 

u01*G 
00315 
00502 
00689 
00875 

0014* 
00330 
00518 

00705 
0089J 

0015800173 
0034000362 
0053400549 
U0720  00730 
0090600922 

8 

1 

2 

8 

4 

3 
6 

9 
12 

5 
6 
7 
8 
9 

5.0093700953 
0112201138 
0130601322 
0149001505 
01672,01688 

009G8 
01153 
01337 
01520 
01703 

00984 
01168 
01352 
01536 
01718 

00999 
01184 
01368 
01551 
01733 

01014 
01199 
01383 
01566 
0174& 

0103001045 
01214  0123C 
0139801413 
01581  0159C 
0176301779 

01061 
01245 
01429 
01612 
01791 

01076 
01260 
01444 
01627 
01809 

01091 
01276 
01459 
dl642 
01824 

01107 
01291 
01474 
01657 
01839 

8 

1 

2 

;; 

3 

6 
9 
12 

10 
11 
12 
13 
14 

5.01854,01869 
0203502050 
02215  02230 
0239502410 
0257402588 

01884 
02065 
02245 
02425 
02603 

01900 
02080 
02260 
02440 
02618 

01915 
02095 
02275 
02455 
02633 

0193001945 
0211002125 
02-29002305 
0246902484 
0264802663 

01960 
02140 
02320 
02499 
02677 

01975 
02155 
02335 
02514 
02692 

01990 
02.1.70 
02350 
02529 
02707 

02005 
02185 
02365 
.'•2544 
02722 

02020 
022UO 
02380 
02559 
02737 

s 

1 

2 
3 

4 

3 

C 
9 
12 

15 
16 
17 
18 
19 

5.02751502766 
02928  02943 
0310503119 
0328003295 
03455  03470 

02781 
02958 
03134 
0331G 
03484 

H2796 
02973 
03149 
03324 
03499 

02811 
02987 
03163 
03339 
03513 

02825!0*840  02855 
03002  03017  03031 
031780319303207 
03353  03368  03382 
0352803542,03557 

02870 
03046 
03222 
03397 
03571 

02884 
03061 
03237 
03412 

03586 

02899 
03075 
03251 
03426 
03600 

0*914 
03090 
03266 
03441 
03615 

s 
1 
2 
3 
4 

3 
6 
9 

12 

20 
21 
22 
23 
24 

5.03629103644 
0380203817 
03975|03989 
04147  04161 
0431804332 

03658 
03831 
04004 
04175 
04346 

0367  z 
03846 
04018 
04190 
04360 

03687 
03860 
04032 
04204 
04375 

0370103710 
03874  03889 
04047  04061 
0421804232 
0438904403 

0373003745 
0390303918 
0407504090 
0424704261 
0441704431 

03759 
03932 
04104 
04275 
04445 

03774 
03946 
04118 
0428t 
04460 

03788 
03961 
04132 
04303 
04474 

s 
1 
2 
3 

4 

3 

6 
9 
12 

25 
26 
27 
28 
29 

5.04488:04502 
04657  04672 
0482604840 
0499405008 
0516205175 

04516 
04686 
04854 
05022 
05189 

04530 
04700 
04868 
05036 
05203 

04545 
04714 
0488* 
05050 
05217 

045590457301587 
047280474204756 
048960491004924 
050640507805092 
052310524505259 

04601 
04770 
04938 
05106 
05273 

04615 
04784 
04952 
05120 
05286 

04629 
04798 
04966 
05134 
05300 

04G43 
04812 
04980 
05148 
05314 

s 
1 
2 
3 

4 

3 
5 
8 
11 

30 
31 
32 
33 
34 

5.0532805342 
0549405508 
0565905673 
0582305837 
05987J06001 

05356 
05521 
05686 
05851 
06014 

05370 
05535 
05700 
05864 
06028 

05383 
05549 
05714 
05878 
06041 

05397J0541  105425  05439 
05563055770559005604 
05728057410575505769 
05892  05905  05919  05933 
06055060690608206096 

05452 
05618 
05782 
05946 
06109 

05460 
05632 
05796 
05960 
06123 

05480 
05645 
05810 
05973 
06136 

s 
1 
2 
3 

4 

3 
5 
8 
10 

35 
36 
37 
38 
39 

5.061500616306177 
C6312  06326  06339 
06474,06487  06500 
066340664806661 
067940680806821 

06191 
03353 
06514 
06674 
06834 

06204 
06368 
06527 
06688 
06848 

06218 
06379 
06541 
06701 
06861 

06231J06245  06258 
063930640606420 
06554065670G581 
067140672806741 
068740688706901 

06272 
06433 
06594 
06754 
06914 

06285 
06447 
06608 
067G8 
OG927 

06299 
06460 
06621 
06781 
06941 

K 
1 

2 
3 

4 

3 
5 

8 
10 

40 
41 
42 
43 
44 

5.0695406967 
0711207126 
0727007284 
07428:07441 
07584  07597 

OH980 
07139 
07297 
07454 
07610 

06994 
07152 
07310 
07467 
07623 

U7007 
07165 
07323 
07480 
07636 

07020 
07178 
0733G 
07493 
07649 

07033  0704G  07060 
071920720507218 
073490736207375 
07506.0751907532 
076620767507688 

07073 
07231 
07388 
07545 
07701 

07086 
07244 
07401 
07558 
07714 

07099 
07257 
07415 
07571 
07727 

s 

\ 

3 

5 
8 
10 

45 
46 
47 
48 
49 

5.077400775307766 
078950790807921 
080500806308075 
08204  08216,03229 
083570836908382 

0777907792 
07934  07947 
0808808101 
0824208255 
0839508408 

07805  07818|07831  0784407857 
07960  07973j07985j07998  08011 
081  14  08127  08140  081  52  08165 
08267  08280  08293  0830G  08318 
08420  08433  08446  08458,08471 

07869 
08024 
08178 
08331 
08484 

07882 
08037 
08191 
08344 
08496 

s 

1 

2 

;s 
i 

3 
5 

8 

10 

50 
51 
52 
53 
54 

5.085090852208534 
086610867308686 
088120882408837 
089620897508987 
091120912409137 

08547  08560 
0869908711 
0385008862 
0900009012 
0914909162 

085720858508598,08610 
087240873608749,08762 
08875088870890008912 
09025  09037  09050  09062 
09174091870919909211 

08623 
08774 
08925 
09075 
09224 

08636 
08787 
08937 
09087 
09236 

08648 
08799 
08950 
09100 
09249 

s 

1 

2 
3 

4 

2 
5 

7 
10 

55 
56 

57 
58 
59 

5  .  09261  09273  09286  09298  0931  1  09323'09335  09348  09360  09372  09385  09397 
0940909422,09434  09446  09459  09471  09483  09496  09508  09520  09533  09545 
09557  095C9  09582  095D4  09606  09618  09631  0964309655  09667  091580  09692 
09704  09716  09729  09741  09753  09765  09777  09790(09802  09814  09826  09838 
09851  09863  09875  09887  09899  0991  1  0992  109936  099  48  099C.O  09972  09984 

s 
1 
2 
3 

4 

2 

*- 
7 
10 

284                TABLE  XVII. 

LOG  RISING  TO  FIND  THE  LATITUDE  BY  REDUCTION  TO  THE  MERIDIAN. 

7  Hours. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.P. 

0 
1 

2 
3 
4 

5.09996 
10141 
1028C 
10430 
1057S 

0006 
015L 
029, 
0441 
0585 

oo^j 

0166 
0310 
0454 
0597 

0033 
0178 
032i 
0465 
060!: 

L0045 
10190 
L0334 
L0477 
10620 

10057 
L0202 
1034C 
10489 
10632 

10069 

L0214 
L0358' 
10501 
10644 

10081 
10226 
10370 
10513 
1065C 

10093 
10238 
10382 
10525 
10G68 

L0105 
10250 
10394 
L0537 
L0680 

10117 
10262 
10400 
10549 
10691 

L0129 
10274 
10418 
L05G1 
10703 

s 
1 

2 
3 

4 

2 

5 

7 
9 

5 

6 
7 
8 
9 

5.10715 
10S57 
10998 
1113^ 
11271; 

1072. 
08GL 
1101C 
11150 

11290 

0739 
0881 
1022 
116i 
1302 

0751 
089L 
103. 
1174 
1314 

LO/03 
L0904 
11045 
11185 
11325 

10774 
1091C 
11057 
11197 
11337 

10786 
10928 
11069 
11209 
11348 

10798 
10941, 
11080 
11220 

1136C 

10810 
10951 
11092 
11232 
11372 

10822 
10963 
11104 
11244 
11383 

10833 
10975 
11115 
11255 
11395 

10845 
10986 
11127 
11267 
11406 

S 
1 

2 
3 

4 

2 
5 
7 
9 

10 
11 
12 
13 
14 

5.1141b 
11557 
11G95 
1183i 
11969 

11429 
11568 
1170C 
11843 

11980 

1411 
1580 
1717 
1855 
1991 

1453 
1591 
1729 
11866 
2003 

11464 
11603 
11740 
11878 
12014 

11476 
11614 
11752 
11889 
12025 

11467|114'J9 
1162611637 
1176311775 
1190011912 
12037|12048 

11510 
11649 
1178G 
11923 
12059 

11522 
11660 
11793 
11934 
12071 

11533 
11672 
11809 
11946 

12082 

11545 
11683 
11820 
11957 
12093 

s 
1 
2 
3 
4 

2 
5 

7 
9 

15 

16 
17 
18 
19 

5.12100 
12240 
12375 
1-2500 
12643 

12110 
12251 
1238G 
12520 
12654 

2127 

2263 
2397 
2532 
2665 

12139 
12274 
12409 
12543 
12676 

12150 
12285 
12420 
12554 

12687 

12161 
12296 
12431 
12565 
12698 

12173  12184 
12308  1231& 
1244212453 
12576  12587 
12709  12721 

12195 
12330 
12465 
12598 
12732 

1220G 
12341 
1247G 
12610 
12743 

12218 
12353 
12487 
12621 
12754 

122-^9 
12364 
12498 
12632 
12765 

s 
1 

2 
3 
4 

2 

4 
7 
9 

20 
21 
22 
23 
24 

5.12770 
12908 
13040 
13171 
13302 

12787 
12919 
13051 
13182 
13313 

2796 
2930 
3062 
3193 
3323 

12809 
12941 
13073 
13204 
13334 

12820 
12952 
13084 
13215 
13345 

12831 
12963 
13095 
13226 
13356 

1284212853 
1297412985 
1310613117 
13237  13248 
13367,13378 

12864 
12996 
13128 
13258 
13388 

12875  128SG 
13007  13018 
13139  13149 
132G9  13280 
13399  13410 

12897 
13029 
13160 
13291 
13421 

s 
1 
2 
3 

4 

2 
4 

7 
9 

25 
26 

27 
28 
29 

5.1343. 
13561 
13690 
13818 
13945 

1344. 
13572 
13701 
1382& 
13956 

345b 
3582 
13711 
13839 
13967 

13464 
13593 
13722 
13850 
13977 

13475 
13604 
13732 
13860 
13988 

13486 
13615 
13743 
13871 
13998 

1349o  13507 
13625I13G36 
1375413765 
13882'  13892 
14009  14019 

13518 
13647 
13775 
13903 
14030 

13529 
13658 
13786 
13914 
14041 

13539 
136G8 
13797 
13924 
14051 

13550 
13679 
13807 
13935 
14062 

s 

1 
2 
3 
4 

2 
4 

7 
9 

30 
31 
32 
33 
34 

5.1407. 
1419G 
14324 

14449 
14574 

I408b 
14209 
14330 
14460 
14584 

14093 
14220 
14345 
14470 
14595 

14104 
14230 
14356 
14481 
14605 

14114 
14241 
14366 
14491 
14615 

14125 
14251 
14377 
14501 
14626 

14136 
14262 
14387 
14512 
14636 

14146  14157 
14272  14282 
14397  14408 
1452214533 
14646'  14657 

14167 
14293 
14418 
14543 
14667 

14178 
14303 
14429 
14553 
14677 

14186 
14314 
14439 
14564 
146S8 

s 
1 
2 
3 

4 

2 
4 

6 

8 

35 
36 
37 

38 
39 

5  .  14096 
1482 
14944 
1506C 
15188 

14708 
14832 
14954 
15076 
1519& 

14719 

14842 
149G4 
1508" 
15208 

14729 
14852 
14975 
15097 
15218 

14739 
14862 
14985 
15107 
15228 

14750 
14872 
14995 
15117 
15238 

14760  14771 
1488314893 
15005  1501E 
15127  15137 
15248  15258 

14780 
14903 
15026 
15147 
15269 

14790 
14913 
1503G 
15157 

15279 

14801 
14924 
15016 
15168 
15289 

14811 
14934 
15056 
15178 
15299 

s 
1 
2 
3 
4 

2 

4 
6 
8 

40 
41 
42 
43 
44 

5.15309 
1542C 
15549 

1566 
1578 

15319 
15439 
15559 
15678 
1579 

1532U 
15449 
15569 
15G88 
1580" 

15339 
15459 
15579 
15698 
15817 

15349 
15469 
15583 
15708 

15827 

15359 
15479 
15599 
15718 
15837 

153691537915389 
15489  15499  15509 
15609  15619  15629 
15728  15738  15748 
15846  15856  15866 

15399  15409 
15519  15529 
15639  1564S 
15758  15767 
15876  1588C 

154  li 
15539 
15659 
15771" 
15896 

• 
1 
2 
3 

4 

2 
4 

6 

8 

45 
46 
47 
48 
49 

5.1590c 
1602c 
1614C 
1625t 
1637$ 

1591 
1603 
1614 
1626 
1638 

1592 
1604 
1615 
1627 
1639 

15935 
16052 
16169 
16285 
16401 

15944 
1606$ 
1617£ 
1629i 
164K 

15954 
1607$ 
16188 
16304 
1642C 

1596^ 
1608" 
16191 
1631' 
16481 

1  15974  15984 
1  16091116101 
*  16208  13217 
[  16324  16332 
)  16439  1644C 

15991 
1611] 
1622r 
1634; 
16451 

(  16002 
1612C 
16237 
i  16352 
)  16468 

16013 
16130 
16246 
163G2 
16478 

s 
1 

2 

3 
4 

2 
4 

6 
8 

50 
51 
52 
53 
54 

5.  1648  < 
16605 
167H 
16831 
1694J 

1649 
.1661 
J1672 
J1683 
51695 

16501 
16621 
1673c 
1684£ 
16961 

16516 
16631 
1674c 

16856 
16971 

1652t 
1664( 
1675^ 
1686r 
1698( 

1653c 
1665C 
1  1676^ 
'  1687r 
)  1699( 

165451655416564 
16659  16G69  16676 
16773167821679$ 
'  16886  16896  1690t 
)  16999  17008  1701* 

1657; 
16685 
1680 
1691; 
1  1702' 

5'16582 
J  16697 
1  16813 
5  16924 
•  1703( 

16592 
16707 
16820 
1693 
>1704 

s 
1 
2 
3 
4 

2 
4 
6 

8 

55 
56 
57 
.  58 
59 

5.1705; 
1716' 
1727* 
1738! 
17495 

>1706 

ri7i7 

S  1728 
)1739 
)1750 

1707^ 
1718( 
1729r 
1740* 
1751  f 

1708; 
>  1719c 
'  1730C 
}  1741P 
j  1752r 

!  1709; 
.  1720' 
>  1731, 
'  17421 
"1753 

5  1710; 
1  1721^ 
5  1732J 
J  1743; 
5  1754, 

!  17111  17121  1713( 
U7223  17232  1724] 
517334173431735'. 
517444174541746; 
5117554175631757; 

>1713' 
1725 
>  1736! 
]  1747- 
]  1758- 

)  1714* 
1726( 

21737] 
2  1748] 
217591 

51715 
)172G 
1738C 
L1749 
L1760 

s 
1 
2 
3 
4 

2 
4 
6 

8 

TABLE  XVIII.               285 

LOGARITHMS  FOR  FINDING  THE  APPARENT  TIME  OR  HORARY  ANGLE. 

0  Hour. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s.  55s. 

P.P. 

0 
1 
2 
3 

4 

%  .     51921 
5.6775774710 
5.2796331509 
6318165561 

6.8816889959 

12127  47345  72333;91715 
81147,871399274598011 
34916381944135244400 
6787770133  72332  74477 
91714934349512196775 

07551 
02976 
46345 
76570 
98399 

20941 
07672 
50193 
78614 
99992 

32539 
12127 
52951 
80611 
01557 

42770:5192160200 
16365  20406  24267 
5562358216,60734 
8256384172.86340 
03095  0460S|OC090 

5 

6 
7 
8 
9 

6.0755008985 
23385  24583 
3G774  37802 
48372  49271 
58600  59401 

10398  11787  13155 
257652693128081 
38817  3982W0814 
50162  5104J  51916 
601946098061759 

14502 
29217 
41795 
52780 
62531 

15828 
30337 
4276C 
53636 
6329G 

17134 
31444 
43726 
54484 
64054 

18421 
32536 
44675 
55323 
64806 

19689 
33615 
45614 
56154 
65552 

2093822170 
3468135734 
4654347462 
56977  57792 
66291  J67024 

10 
11 
12 
13 
14 

6.67751JG847.L 
7602876683 
8358484185 
9053591089 

".  96970  97485 

69186  69895  70598 
773347797978620 
847828537485963 
91641  92189,92733 
979979850699013 

71296 
79256 
86548 
93274 
99516 

7  1988 
79888 
87129 
93812 
00017 

72674 
80515 
87706 
94346 
00514 

73355 
81137 

88279 
94877 
01009 

74031 
81756 
88848 
95405 
01501 

7470275367 
8236982979 
89414*89976 
9593096451 
01990'02476 

8 
1 

2 
3 

1 

119 
238 
358 
476 

15 
16 
17 

18 
19 

7.02960 
08564 
13827 
18790 
23483 

03441 
09015 
14252 
19191 
23863 

03920  04395 
0946409910 
1467415095 
19590  19987 
24241  24618 

04S69 
10354 
15513 
20383 
24993 

05339 
10796 
15930 
20776 
25366 

05807 
11236 
16344 
21168 

25738 

06273 
11673 
16756 
21558 
26108 

06736 
12108 
17167 
21947 
26477 

07196 
12541 
17575 
22333 
26844 

0765508110 
12972113401 
1798218387 
2271923102 

2721027573 

3 
1 

2 
3 

1 

84 
168 
25',: 
336 

20 

21 
22 
23 
24 

7.27986 

32171 
36209 
40067 
43760 

28297 
32515 
36537 
40380 
44061 

28656 
32857 
36864 
40693 
44361 

2901429371  29726 
331983353833876 
371893751437837 
410054131541625 
44659,44957(45254 

30079 
34213 
38159 
41933 
45549 

30431 
34519 

38480 
42240 
45844 

30782 
34884 
3880d 
42546 
46138 

31131 
35217 
39118 
42851 
46430 

3147931826 
3554935879 
3943539752 
4315543458 
46722  47013 

B 

\ 

''I 

65 
130 
195 

200 

25 

26 
27 
2* 
29 

7.47302 
50706 
53980 
57135 
60179 

47591 
50983 
54247 
57393 
60428 

47879 
51260 
54514 
57650 
60676 

4816(5 
51536 
54780 
57906 
60924 

48452 
51811 
55045 
58162 
61170 

48737 
52085 
55308 
58416 
61417 

49021 
52358 
55572 
58670 
61662 

49304 
52631 
55834 
58924 
61907 

4958(5 
52902 
56096 
59176 
62151 

49867 
53173 
56357 
59428 
62394 

5014850427 
5344353712 
56617  56870 
59679,59929 
6263662878 

s 
1 
•2 

3 
4 

53 

106 
159 

212 

3U 
31 
32 
33 

34 

7.63120 
65964 
68717 
71385 
73974 

633(50 
66196 
68942 
71604 
74186 

63600  63839,64078 
G6429  66660  66891 
69167  69392  69616 
71822  72040J72257 
7439874609,74819 

64310 
67121 
69839 
72473 
75030 

64553 
67351 
70061 
72689 
75239 

61790 
67580 
70283 
72904 
75448 

65026 
67809 
70505 
73119 
75657 

65261 
68037 
70726 
73334 
75865 

65490  65730 
6826468491 
70946i71166 
7354873760 
7607376280 

s 
1 
2 
3 

1 

45 
90 
134 

178 

35 
36 
37 
38 
39 

7  .  76487  76693 
7892979129 
8130381498 
8361583804 
85866  86050 

76898  77104|77308|77513 
79329  79529f79728  79926 
8169381887,8208182274 
83994841838437281560 
86235864198660386786 

77716  7792(JJ78122 
801248032280519 
824678265982851 
847478493585122 
869698715287334 

78325  78526  7»72b 
807168091281108 
83043  83234  83424 
853088549485680 
8751C  87697,87876 

8 

1 

2 

a 

4 

39 
77 
116 
154 

40 
41 
42 
43 
44 

7.8805988240 
90198J90374 
9228692457 
9432494491 
9G315  96478 

88419:88599^877888957 
90550  90725  90900  91074 
92629928009297093141 
94659948269499295159 
96642968059696897131 

8913589314 
9124891422 
9331193480 
95325  95491 
97293  97455 

89491 
91596 
93650 
95656 
97617 

89668,89846  90022 
917699194192114 
9381993987,94156 
958219598696150 
977789793998100 

s 
1 

2 
3 

! 

34 
68 
102 
137 

45 
46 
47 

48 
49 

-/a  .  98260,98421  98580  98740  98899  99058 
8  .  00163100320  00476  00632  00788  00944 
02025:02178  02331  02484  02636  02789 
03847  03997  04147  04297  04446  04595 
05631:05778  0592506072  06218  06364 

99217 
01099 
02941 
04744 
06510 

99375 
01254 
03092 
04892 
06655 

99534 
01409 
03244 
05041 
06800 

99^91  99849  00000 
015630171701871 
03395  03546,03697 
051890533605484 
0694507090,07235 

s 

1 
2 

3 

! 

31 

62 
92 
122 

50 
51 
52 
53 
54 

8.07379,07523 
09092  09233 
10772  10910 
12419  12555 
14035  14169 

07G67  0781  107934  08097 
09374  09515  09656  09796 
11048111871132411462 
12691  12826  12961  13096 
14302  14434  14567  14700 

08240 
09936 
11599 
13231 
14832 

08383 
10076 
11736 
13366 
14964 

08525 
10216 
11873 
13500 
15096 

08667 
10355 
12010 
13634 

15228 

0880908951 
1049410633 
12147  12283 
13768  1390  i 
15359  15490 

s 
1 
2 
3 
1 

27 
55 
82 
110 

55 
56 
57 

58 
59 

8.15621  15752 
17179  173)7 
1870818835 

20211J20335 
21(588  21810 

15883il6013il0144  16274  16404110533 
17436  17564'  1769217820  17947  18074 
1  8961  19087:  19212'  1  9338  19463  19588 
20459  20583  20706  20830  20953  21076 
21932  22053  22175  22296122417(22538 

16603 
18202 
19713 
21198 

22<;r,;- 

1679216921  17i>5< 
18329  18455:1858-2 
19838  199G3  20087 
21321  21444  21560 
22779122899:23019 

s 
1 
•2 

r; 
i 

25 
K< 

75 
10 

286                TABLE  XVIII. 

LOGARITHMS  FOR  FINDING  THE  APPARENT  TIME  OR  HORARY  ANGLE. 

1  Hour. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.  P. 

0 

1 

2 
3 
4 

8.23140 
245G7 
25971 
27352 
28711 

23259 
24685 
26087 
•27466 

28823 

23379 
24802 
26203 
27580 
28935 

23499 
24920 
26318 
27691 
29047 

23618 
25037 
26434 
27607 
29159 

.^3737 
25155 
26549 
27921 
29271 

23856  23975  24094 
25272  25389  25505 
26664  26779  26894 
280342814728260 
293S3'29494|29605 

24212j24331 
2562225738 

-7009  27123 
28373  28486 
29716  29827 

24449 
25855 
27238 
28599 
29938 

s 
1 
2 
3 
4 

28 

46 
70 
93 

5 

6 
7 
8 
9 

8  .  30049 
31366 
32G63 
33940 
35199 

3015930270 
3147531583 
3277032877 
3404631151 
35303,35407 

30380 
31692 
32984 
34257 
35511 

•30490 
31800 
33091 
34362 
35614 

30GOO  .30710 
3190932016 
33198  33304 
3446731572 
3571835821 

30820  309-9 
3212532233 
3341033517 
34677  34782 
35925  36028 

31039 
32340 
33623 
34886 
36131 

31148 
32448 
33729 
34991 
36234 

31257 
32556 
33835 
35095 
36337 

s 
1 
2 
3 

4 

21 
42 
63 

85 

10 
11 
12 
13 
14 

8.3(3439 
37062 
38866 
40055 
41226 

36542 

377(53 
3896(5 
10153 
11323 

36044 
37864 
39066 
40251 
4J420 

36746 
37964 
39165 
10349 
41517 

36849  36951J37053  37154 
38065  38166  38266  3836C 
39261  39364  39463  39562 
10447405454064240740 
41613117101180611902 

37256 
38467 
39660 
10837 
41998 

37358 
38567 
39759 
40935 
12094 

37459 
386G7 
39858 
41032 
12191 

37560 
38767 
39956 
41129 
12286 

s 
1 
2 
3 
4 

20 
40 
60 

80 

15 
16 

17 
18 
19 

8.4-2382 
43522 
44647 
45757 
46852 

42177 
1361C 
14740 
15849 
16943 

12573 
437K 
14833 
15940 
17031 

12668 
13804 
14926 
4G032 
47124 

12764  42859  42954 
138984399244086 
450184511145204 
16124  46215  16306 
172154730547395 

43049 
44180 
45296 
46398 
47485 

43144 
4427C 
15388 
16489 
47575 

13236 
44367 
15481 
16580 
17665 

43333 
44460 
15573 
16671 
17755 

13427 
44554 
45665 
46762 
47844 

s 

1 

2 
3 

4 

18 
37 
55 

74 

20 
21 
22 
23 
24 

8.47934 
4900-2 
5005G 
51098 
52127 

18024 
19090 
30144 

5118:1 

52212 

18113 
19179 
50231 
31270 
32297 

48202 
19267 
30318 
51356 
52382 

18292 
19355 
30405 
51442 
32467 

18381 
49443 
50492 
51528 
52552 

.48470 
49531 
50579 
51614 
52636 

48559 
19619 
50G65 
51699 
52721 

18647 
19706 
50752 
51785 

52805 

1873G 
19791 
50839 
51871 
52890 

48825 
19882 
50925 
51950 
32974 

48913 
19969 
51012 
52041 
53059 

B 
1 
2 
3 

4 

17 
35 

52 
70 

25 
26 
27 
28 
29 

8.5314b 
54147 
55139 
56120 
57089 

53227 

53311 

33395 

33479,53563  53646 

53730 

53814 

53897 

53981 

54064 

s 
1 

2 
3 

-1 

16 
33 
49 
65 

34230 
35221 

54313 
55303 

54396 
35385 

34479  54562  54645 
554675554955631 

54727 
•55713 

54810 
55794 

54892 
5587C 

54975 
55957 

55057 
56038 

36201 

06282 

56363 

36144  56525 

a6G06 

36687 

•56707 

56848 

56928 

•57009 

37169 

o'/249 

•57330 

37410  57490  57569 

57619 

57729 

57809 

jV88b 

57968 

30 
31 
32 
33 
34 

8.58047 
53991 
59931 
60857 
6177^ 

J812GI  58206 
•39078  59151 
50009  30086 
30934  31011 
31849  31925 

38285 
59230 
30164 
31087 
62001 

38364 
59308 
60241 
31164 
32076 

5841358522 
5938359464 
6031860395 
6124061317 
62152  62228 

58601 
•39542 
60473 
31393 
32303 

58680 
59620 
60550 
61469 
62379 

38759 
59698 
G0627 
61545 
62451 

58837 
5977( 
6070J 
61621 
62529 

58916 
59853 
60781 
G1697 
32G04 

s 
1 
2 

3 
4 

15 
31 

46 
62 

35 
36 
37 

33 
39 

8.62671 
6357G 
64463 
65340 
66208 

32755 
33650 
34536 
65412 

6G280 

G2830 
63724 
64609 
G5485 
66352 

32901 
G3798 
34G83 
35558 
66424 

6-979 
63872 
34756 
65630 
.36496 

63054 
63946 
G4829 
65703 
66567 

63129 
61020 
61902 
65775 
66639 

J3203 
64094 
G4975 
65817 
6G710 

63278 
64168 
G5048 
65920 
66782 

63353 
64242 
65121 
35992 
66853 

63427 
G4315 
65194 
66064 

G6925 

63502 
64389 
65267 
66136 
6699G 

3 
1 

2 
3 
4 

15 
29 
44 

58 

40 
41 
42 
43 
44 

8.07067 
67918 
6S759 
G9593 
70418 

(5713967209 
3798868059 
3882968899 
G9362  69731 
70486,70554 

67*81 
68129 
6S969 
G9SOO 
70623 

07352 
68199 
39038 
39869 
70691 

67423 
68269 
69108 
G9937 
70759 

67491 
G8340 
69177 
70006 
70827 

67561 
68110 
69247 
70075 
70895 

67635 
68480 
69316 
70141 
70963 

67706 
68550 
G9385 
7021-2 
71031 

68620 
G9154 
7028] 
71099 

67847 
68690 
69524 
70349 
71167 

• 
1 
2 

3 
4 

14 

28 
42 
56 

45 
46 
47 

48 
49 

8.71234 
72043 
72814 
73637 
74123 

713u2  71370 
7211072177 
72910,72977 
73703  73768 
74488,74553 

71437 
72244 
73043 
73834 
74618 

7150571572 
72311  72378 
7310973175 
73900739G5 
74683,74748 

71640 
72444 
73241 
74031 
74813 

71707 
72511 
73308 
7J096 
74877 

71774 
72578 
73374 
74162 
74942 

71812 
72644 
73439 
74227 
75007 

71909 
72711 
73505 
74292 
75072 

71976 
72777 
73571 
74357 
75136 

s 

1 
o 

3 
4 

13 

26 
40 
53 

50 
51 
52 
53 
51 

8.75201 
75971 
76735 
7749- 
78241 

752657533075391 
760357609976163 
767987686276925 

77551  77617|77680 
78303  78365  78427 

75458  75523 
76227.76290 
76988:77051 
7774277805 
7848978551 

75587 
76354 
77114 
77867 
78613 

75651 
76418 
77177 
77930 

78675 

75715 
76481 
77240 

77992 
78737 

75779 
76545 
77303 

78054 
78799 

75843 
76608 
77366 
78117 
78861 

75907 
76672 
77429 
78179 
78922 

K 
1 

2 

a 

4 

13 
25 
38 

50 

55 
56 
57 
58 
59 

8.78984 
79720 
80149 
81172 
81889 

79015  79107  79109,79230  79291 
79781  79842  79903179964  80025 
8051C'80570  80631  80691  80751 
31232  31292  81352  81412  81472 
81948  82008  82067  32126  82186 

79353 
80085 
80812 
81531 
82245 

79114 
80146 
8087-2 
81591 
82304 

79475179537 
8020780268 
8093280992 
8165181710 
82363182422 

79598 
80328 
81052 
81770 

824811 

79659 
80389 
81112 
81829 
82540 

s 

1 

•2 
3 
4 

12 

21 
36 

48 

LOGARITHMS 

TABLE  XVIII.               287 

FOR  FINDING  THE  APPARENT  TIME  OR  HORARY  ANGLE. 

2  Hours. 

M. 

Os. 

5s. 

10s. 

15s 

Ms 

35s 

80s 

85s 

40s 

45s 

50s 

55s. 

P.P. 

0 

1 

2 
3 

4 

8.8259i) 
83303 
84001 
84G94 
8538(1 

82658  32  1  17 
3336:;  83420 
8405984117 
84751  84808 
8543785194 

82770 
83478 
84175 
84866 
85550 

8J835 
83537 
84233 
34923 
85607 

3289L 
5359J 
84291 
8493C 
85664 

(82952 
83653 
84348 
85037 
85721 

83011 
83711 

84406 

331  109 
33769 
44464 

,831^ft 
83828 
84521 

83187 

'3388L 
S457S 
8526G 
35947 

83245 
83944 
84636 
85323 
86004 

s 
1 
2 
3 

4 

11 
23 
34 

46 

85095 
85777 

35152 
35834 

85*09 
85891 

5 
6 
7 

8 
9 

8.860GU 
83735 
87404 
830G8 
8872G 

86117 

36791 
87460 
88123 

•S8780 

36173 
86347 
87515 

88178 
S8835 

86229 
86903 
37570 
88233 

38889 

8628d 
86959 
87626 
88288 
88944 

86342 
87014 
87681 
88342 

88938 

8639s 
87070 
37730 
88397 
8905. 

86454 

37126 
37792 
88452 
39107 

36511 

87182 
37847 
88507 
89162 

86567  8662; 
87237  87293 
8790287957 
88562*38616 
89216*89270 

86679 
87348 
88013 
88671 
89324 

1 
2 
3 

1 

11 
22 
33 
44 

10 
11 
.12 
13 
14 

8.89J79 
9002G 
90668 
91306 
91938 

8943.J 
90080 
30722 
91358 
91991- 

89487 
90133 
9077C 
91411 
92043 

89541 
90187 
J0328 
31464 
92095 

89595 
90241 
90881 
91517 
92147 

89649 
90294 
30934 
9157( 
92200 

39/03 
90348 
90988 
91622 
92252 

89757 
90401 
91041 
91675 
92304 

89811 
90455 
91094 
91728 
92356 

89865,89918 
9050890562 
91147  91200 
9178091833 
9240892461 

89972 
90615 
91253 
91885 
92513 

s 
1 
2 
3 

•1 

11 
21 
32 

42 

lo 
16 
17 
18 
19 

«  .  92-j6o 
93187 
93804 
94417 
93025 

J261V 
93239 
93856 
34488 

95075 

9266J 
93290 
93907 
94519 
9512G 

92721 
93342 
93958 
94570 
35176 

927  /a 
93393 
94009 
94620 
95227 

9282u 
93445 
9406C 
94671 
95277 

928/7 
9349G 
94111 
91722 
93327 

92928 
93548 
94162 
94772 
95378 

92980 
93599 
94213 
94823 
95428 

93032  93084 
9365193702 
9426494315 
94874  94924 
9547895528 

9313.3 
93753 
94366 
94975 
95578 

s 
1 
2 
3 

1 

10 
20 
31 
41 

'20 
21 
22 
23 
21 

8  .  95628 
96227 
93821 
97411 
9799G 

95678 
9G277 
96871 
974GO 
980  45 

957^8 
96326 
93920 
97503 
98091 

93/78 
96376 
96969 
97558 
98142 

95828 
96426 
97018 
97607 
98191 

95878 
9G475 
97038 
97656 
98239 

95928 
9G525 
37117 
97701 

38288 

95978 
93574 
97166 
97753 
9833G 

36028 
9GG24 
97215 
97802 
98384 

9607896128 
9667396723 
9726497313 
37851  97893 
98433  38481 

93178 
96772 
97362 
97948 
98529 

R 
1 

2 
3 

4 

10 
20 
29 
39 

25 
26 
27 
28 
29 

8  .  9857s 
99154 
9.99727 
9.00295 
008GO 

98626:98674 
99201  93250 
99774  09822 
00342  00390 
00906  00953 

3872v 
99298 
99869 
00437 
01000 

9877U 
993  1C 
99917 
00481 
01017 

98816 
99393 
9996  1 
00331 
01094 

98806 
93441 
00012 
00578 
01140 

98914 
99489 
00059 
00825 
01187 

98903 
9933G 
00108 
00672 
01234 

99011J99058 
9958439332 
0015400201 
0071900766 
01280J01327 

991U6 
99G7G 
00248 
00813 
01373 

s 
1 

2 
3 
i 

10 
19 
29 
38 

30 
31 
32 
33 
34 

9.014UO 
01976 
02528 
03077 
03G21 

0146601513 
0202202065 
0257402620 
0312203168 
03667  0371-2 

J1559 
02114 
02366 
03213 
03757 

01606 
02161 
02712 
03259 
03802 

01G52 
02207 
02757 
03304 
03847 

01693 
02253 
02803 
03350 
03892 

0174501791 
02299  02345 
02849  02894 
03395  03140 
0393703982 

01837101884 
0239102437 
0294002986 
03486:03531 
04027,04072 

01930 
02483 
03031 
03576 
04117 

s 
1 
2 
3 

4 

9 

18 
28 
37 

35 
33 
37 
38 
39 

9.  04162 
04G99 

04207,04252 
0474404788 

0429  i 
04833 

04341 

04877 

04386 
04922 

04431 
34936 

04476 
05011 

0452004565,04610 
0505505099,05144 

04651 
05188 

s 
1 
2 
9 
4 

9 

18 

27 
36 

05232 
05762 
06288 

05277,05321 
0580605850 
06332'OG375 

05365 
05894 
06419 

05409 
05938 
06462 

03453 
05982 
03506 

05493 
06025 
06550 

05542 
060G9 
06593 

05586 
06113 
06637 

0,j630,05674 
06157,06200 
0668006724 

05718 
08244 
067G7 

40 
41 
42 
43 
44 

9.0381U 
07329 
07845 

08357 
08865 

OG854  00897 
0737207415 
07887  07930 
0839908442 
08907  08949 

06940 
07458 
07973 
03484 
08992 

05934 
07501 
08016 
08526 
09034 

07027 
07544 
08058 
03569 
0907G 

070/0 
07587 
08101 
03611 
09118 

07113 
07630 
08141 
08654 
09160 

0715707200,07243 
G7673  077  16  07759 
081860822908271 
086960873808781 
0923209244:09236 

07286 
07802 
08314 
08823 
09328 

s 

1 

2 

a 

i 

9 
17 

26 
35 

45 

46 
47 
48 
49 

9.09370 
09872 
10371 
10866 
11338 

09412;09454 
0991409955 
1041210453 
10907|  10948 
11399,11440 

09496 
09997 
10495 
10989 
11480 

09538 
10039 
1053G 
11030 
11521 

09580 
10030 
10577 
11071 
11562 

09G22 
10122 
10319 
11112 
11603 

09363. 
10163 
10630 
11153 
11643 

09705 
10205 
10701 
11194 
11684 

09747  09789 
10246  10288 
10742  10784 
1123511276 
1172511765 

09830 
10329 
10825 
11317 
11806 

s 

1 

2 
9 

1 

8 
17 
25 
34 

50 
51 
52 
53 
54 

9.11847 
12332 
12815 
13295 
13771 

118871192811968 
12373,12113  12453 
12855  12895  12935 
13334,13374113414 
13811  13850  13S90 

12009 
12494 
12975 
13454 
13929 

12050 
12534 
13015 
13491 
13969 

12090 
12574 
13055 
13533 
MOOS 

12130 
12614 
13095 
13373 
14048 

12171! 
12655 
13135 
13613 
14037 

1221112252 
12695  12735 
13175  13215 
13652  13692 
14126  141G6 

12292 
12775 
13255 
13732 
14205 

s 

1 
•1 

I! 
1 

8 
16 
24 
32 

55 
56 
57 
53 
59 

9.14215 
14715 
15183 
15647 
16109 

14284 
1  1754 
15221 
15686 
16147 

11323 
14793 
15260 
15724 
16186 

14362 
14832 
15299 
15763 
16224 

14102 
14871 

15338 
15802 
16262 

14441 
14910 
15377 
15840 
16301 

14430 
14919 
15415 
1587S) 
16339 

14519 
14988 
15151 
15917 

10377 

11559J  14593 
15027  15066 
15193  15531 
15935  15994 
16415116453 

14637 
15105 
15570 
16032 
16492! 

14676 
15144 
15609 
16071 
16530 

s 

1 
•J 

3 
•1 

8 
15 
23 
30 

288 

LOGABITHMS 

TABLE  XVIII. 

FOE  FINDING  THE  APPAEENT  TIME  OB  HOEAEY  ANGLE. 

3  Hours. 

M.     OS. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.P. 

0 
1 
2 
3 

4 

9  .  16568 
17024 
17477 
17928 
18376 

16GU8  16644 
1706217100 
17515,17553 
17963  18003 
18413  18450 

16682 
17138 
17590 
18040 
18487 

167ZOJ1G758  16796 
171751721317251 
17628  17665  17703 
18077|18115  18152 

18524  18561  18598 

1G834 
17289 
17740 
18189 
18636 

16872 
17326 
17778 
18227 
18G73 

16J10 
17364 
17815 
18264 
18710 

1694816986 
17402  17440 
17853  17890 
1830118338 
18747  18784 

s 
1 
2 

3 
4 

7 
15 

22 
30 

5 
6 

7 
8 
9 

9.18821 
19263 
19703 
20140 
2057J 

18858  18o'95 
19300  19337 
19739,19776 
20176:20213 
2061120647 

189Jz 
19373 
19812 
20249 
20683 

189G8irJOUO  19042 
19410  19447  19483 
198491988519922 
2028520321^0358 
207192075520791 

19079 
19520 
19958 
20394 

20827 

19116 
19557 
19995 
20430 
20863 

19153 
19593 
20031 
2046G 
20899 

1919U  19226 
19630  19666 
20067  20104 
20502  20538 
20935  20970 

s 
1 

2 
3 
4 

7 
14 
22 
29 

10 
11 
12 
13 
14 

9.2100G 
21436 
21863 
22287 
22709 

2104221078 
2147121507 
21898  21934 
22322  22358 
22744  22779 

21513 
219G9 
22393 

22814 

2115021186,212^1 
21578'21G14  21650 
22001)2204022075 
2242822463  22498 
228492288422919 

21257 
21685 
22111 
22533 
22934 

21293 
21721 
22146 
22569 
22989 

21329 
21756 
22181 
22604 
23024 

213G4;21400 
21792)21827 
2221622252 
22639  22674 
2305923094 

s 
1 

2 
3 
•1 

7 
14 
21 

28 

15 

16 
17 
18 
19 

9.23128 
23345 
23960 
24372 

24782 

2316323198 
2358023615 
23994  24029 
2440G  24441 
2481G  24850 

23233 
23649 
24063 
24475 

24884 

23268 
23684 
24098 
24509 
2i918 

23302  23337 
2371823753 
24132124166 
24543  24577 
24952  2498G 

23372 
23788 
24201 
24612 
25020 

23407 
23822 
24235 
24646 
25054 

23441 
23857 
2426C 
24680 
25088 

23470 
23891 
24304 
24714 
25122 

23511 
23926 
24338 
24748 
25156 

8 
1 

2 

,1 

20 

27 

20 
21 
22 
23 

24 

9.25190 
25595 
25998 
2G398 

26797 

25224 
25629 
26031 
26432 
26830 

25257 
256G2 
2GOG5 
26465 
26863 

25291 
25696 
26098 
26498 

2G89G 

25325  25359  25393 
25729:25763  2579C 
261322616526198 
265322656526598 
26929  2G9G2  26995 

25420 
25830 
26232 
26631 

27028 

25460 
25864 
26265 
26664 
27061 

25494 
25897 
26298 
26697 
27094 

25527 
25931 
26332 
26731 
27127 

25561 
25964 
26365 
26764 
27160 

s 

I 

I 

7 
13 
20 
26 

25 
'26 
27 

28 
29 

9.27193 
27587 
27979 
28368 

28756 

27226 
27620 
28011 
28401 

28788 

27259 
27652 
28044 
28433 

28820 

27292 
27685 
28076 
28465 

28852 

^7325)27357 
27718)27751 
2810928141 
2819828530 

2888528917 

27390 
-.7783 
28174 
28562 
28949 

27-423 
27816 
28206 
28595 
28981 

27456 
27848 
28239 
28627 
29018 

27489 
27881 
28271 
28659 
29045 

27521 
27914 
28304 
28691 
29077 

27554 
27946 
2833G 
28724 
29109 

s 

I 

3 
4 

6 
13 

19 
26 

30 
31 
32 
33 
34 

9.29141 
29524 
29905 
30285 
30661 

2917329205 
29550  29588 
29937  29969 
30316  30347 
3069330721 

29237 
29620 
30000 
30379 
30755 

29269 
29652 
30032 
30410 
30787 

29301 
29683 
30064 
30442 
30818 

29333 
29715 
30095 
30173 
30849 

29365 
29747 
30127 
30505 

30880 

29397 
29779 
30158 
30536 
30912 

29429 
29810 
30190 
30567 
30913 

29461  29493 
29842  29874 
30221  30253 
30599:30630 
30974J31005 

s 
1 
2 
3 
4 

6 
12 
18 
25 

35 
36 
37 
38 
39 

9.31036 
31409 
31780 
32149 
32516 

31068  31099 
3144031471 
31811  31842 
3218032210 
32547  32577 

31130 
31502 
31873 
32241 
3260S 

311613119231223 
315333156431595 
319033193431965 
32272  32302  32333 
32638  32668  32699 

31254 
31626 
31996 
32363 
32729 

34285 
31657 
32020 
32394 
32760 

31310 

31688 
32057 
32425 
32790 

31347  31378 
3171931749 
3208832119 
32455  32486 
3282032851 

s 
1 
2 
3 

4 

6 
12 

18 
24 

40 
41 
42 
43 
44 

9.32881 
33244 
33603 
33965 
34322 

32911132942 
33274  33304 
33635,33665 
33994  34024 
34352  34381 

329  /•/  33002  33033  33063 
33335333653339533425 
33695  33725  33755  33785 
34054340843411434143 
34411  34441  34470  34500 

33093 
33455 
33815 
34173 
34529 

33123 
33485 
33845 
34203 
34559 

33154 
33515 
33875 
34233 
34589 

3318433214 
33545J33575 
33905133935 
3426234292 
3461834648 

s 
1 

2 
3 

•i 

6 
12 

18 
24 

45 
46 
47 
48 
49 

9.34677 
35031 
3538C 
35733 
36081 

34707  34736 
35060  35090 
3541235441 
35762:35791 
3G110|36139 

34766 
35119 
35470 
35820 
36167 

347953482534854 
351483517835207 
35499  35529  35S58 
3584935878:35907 
36196|36225|36254 

31884 
35236 
35587 
3593G 
36283 

34913 
3526C 
35616 
35965 
36312 

349433497235002 
35295  35324  35353 
?5645  35674  35703 
35994  36023  36052 
3634136369,36398 

s 
1 
2 
3 
4 

6 
12 
17 
23 

50 
51 
52 
53 
54 

9.36427 
36771 
37114 
37455 
37794 

36456)36485 
3680036829 
37143:37171 
3748437512 
3782337851 

36513 
36857 
37200 
37540 
37879 

3G542 
36886 
37228 
37568 
37907 

j3657Jj36599 
3691536943 
37257:37285 
37597J37625 
3793537963 

36628  36657136686  36714.36743 
36972  37000  37029  37057  37086 
37313  37342  37370  37C99  37427 
37653  37682  37710  37738,37766 
37991  38020  38048  38076  38104 

s 
1 
2 
3 
4 

6 
11 
17 
23 

55 
66 
57 

58 
59 

9.38132 
38468 
38802 
39134 
39465 

38100J38188I38216 
38496  38524'38551 
38830,38857  38885 
391623918939217 
39492'39520'39547 

38244I38272I38300  38328 
38579  38607|38635  38663 
38913389403896838996 
39245392723930039327 
39575  39602t39630l39657 

3835(j 
38691 
39024 
39355 
39684 

38384  38412:38440 
3871838746)38774 
390513907939107 
393823941039437 
I39712I39739'39767 

s 
1 
2 
3 

4 

(i 
1 

22 

TABLE  XVIII.               289 

LOGARITHMS  FOB  FINDING  THE  APPARENT  TIME  OR  HORARY  ANGLE. 

4  Hours. 

M. 

Os. 

5s 

10s 

15s 

90s 

9,5s 

80s 

35s 

40s 

45s 

50s 

55s 

P.P. 

u 
1 

2 
3 
4 

y  39794'3962  1  M6-i\)  3957(3.39903  39931  39958  39985  40012  40040  40007 
40121  40149  10176  40203  40230  40257  40281  40312  10339  40366  40393 
40447:40474  10501  40528  40555  40582  4060'J  10636  40663  40690|40717 
40771  40798  10825  40852J40879  40906  40933  4096040986  4101341041 
41094411214114741174:41201412281125441281413084133541361 

40094 
40420 
10741 
41067 
41388 

s 
1 
2 
3 
4 

5 
11 
16 

22 

5 
6 

7 
8 
9 

9.4141511411 
4173441761 
4205242078 
42368  12394 
42682  42709 

41468  4149-3  41521  41048 
41787  J  1814  41840  41867 
42105421311215742181 

424-2042447  1247342499 
12735  4276  1  1427»7  428  1  3 

41575 
41893 
42210 
42525 
42839 

1160141628 
41920  4194G 
4223642263 
42562^2578 

42865  42891 

11654 
41972 

1228'J 
12604 
42917 

41681 
41999 
42315 
42630 
12943 

41707 
42020 
42312 
12606 
42969 

s 

1 

2 

3 

i 

5 
10 
16 
21 

10 

11 

ia 

13 
14 

9.  42996 
43307 
43617 
43925 
44232 

13022 
43333 
43643 
43951 
44258 

430184307443100 
43359  43385!13111 
4366943691  1372( 
33977  44002  44028 
442834430944334 

43125 
13436 
43746 
44054 
14360 

43151 
43462 
43771 

44079 
4438.3 

4317743203 
4348843514 
43797  43823 
1410544130 
4441144436 

13229 
43540 
43848 
44156 

41462 

43255 
43565 
43874 
44181 
44487 

43-81 
43591 
43900 
44207 
44513 

s 
1 
2 

3 

•1 

5 
10 
15 

20 

lo 
16 
17 
18 
19 

9.4403S 
44842 
45144 
45416 
45745 

44563 
14867 
45m 
15471 

45770 

14-J8944614 
4489244918 
1519545220 
4519845.321 
457954.3820 

1463'J 
41943 
45245 
1554G 
45845 

146uO 
44968 
4-3270 
15571 
15870 

11690 
14993 
15295 
15595 
45894 

14715  14741 
4501945011 
45320  45340 
45620  45645 
40919  15944 

41760 
45069 
45370 
45670 
45969 

44791 
45094 
45395 
45695 
45994 

44817 
15119 
15420 
45720 
46018 

s 
1 
2 
3 
i 

5 
10 
15 
20 

20 
21 
22 
23 
24 

9.4G043 
46340 
4G635 
46929 
47222 

4G006 
46360 
46660 
46954 
1724G 

160934611S 
4638946414 
16G84  46709 
1697847002 
172704729.3 

16142 
46439 
4.J733 
17027 
47319 

46167 
16163 
16758 
17051 
47343 

4619- 
46488 
16782 
47076 
47367 

4621746241 
46512  46537 
4G807  46831 
4710047124 
47392  474  1C 

46266  46-^91 
46562  46586 
4685G  46880 
47149  47173 
47440  47464 

46315 
46611 
46905 
47197 
47489 

s 

1 

•2 
3 

1 

5 
10 
15 
20 

26 
26 
27 
28 
89 

9.4751317537 

47803  17827 
48091  18115 
48378  4S10L 
4866448687 

4756147585 
1785147875 
1813918163 
1812648449 
1871l'48735 

47610 
47899 
48187 
48473 
48758 

17634 
1792o 
18211 
48497 

48782 

47658 
47947 
48235 
18521 
18806 

17682  47706 
47971  17995 
4825848282 
48540  485G8 
4883018853 

47/30 
48019 
48306 
48592 
48877 

47754 
48043 
48330 
48616 
48900 

17779 
18067 
48351 
48640 
48924 

s 
1 

2 
3 

1 

5 
10 

11 

19: 

30 
31 

32 
33 
34 

9.4894848971 

49231  4925J 
49512!  19536 
4979349816 
50071|50095 

18995  19019 
19278'493Q1 
19-359  19583 
1983919862 
5011850141 

19042 
19325 
19GOU 
19S8G 
50164 

49066 
49348 
49629 
19909 
30187 

49089 
19372 
49653 
49932 
50211 

19113,49137 
49395.49419 
1967G'49699 
49956149979 

0023450257 

49160 
19442 
49723 
50002 
50280 

19181 
49465 
49746 
00025 
50303 

19_07 
49489 
497G9 
50048 
50326 

a 

I 

3 

•i 

5 
9 
14 
19 

35 

36 
37 
38 
39 

9.50349 
50626 
50901 
51174 
51447 

50372 
•30649 
50924 
31197 
31470 

5039550418 
3067250391 
•30916  50969 
•3122051243 
3149251515 

50441 

50717 
30992 
51265 

•31538 

50465 
30740 
51015 
51288 
31560 

50188 
50763 
51038 
51311 
51583 

0001150531 
50786  00809 
•3106051083 
5133451356 
5160551628 

50057 
50832 
51106 
51379 
51651 

00580 
50855 
51129 
51402 
51673 

50603 
50878 
51102 
51424 
51696 

s 
1 
2 

3 

•! 

J 

18 

4U 
41 
42 
43 
44 

9.51718 
51988 
52257 
52525 
52791 

31741 
52011 

•32279 
52547 
52813 

•31763  51766 
•32033  5205G 
32302  52324 
52569,52591 
52835;52857 

31808 
52078 
52346 
52G13 
52879 

31831 
52100 
32369 
52636 
32901 

51853 

52123 
52391 
52658 
52923 

51876,51898 
52145,52168 
5241352435 
5268052702 
52946  02968 

31921 
52190 
52458 
52724 
52990 

51943 
52212 
52480 
52747 
53012 

519G6 
52235 
52502 
52769 
53034 

s 
I 
•2 

3 

l 

4 
9 
13 

18 

45 

46 

47 
48 
49 

9.5305653078 
5332053342 
5358253604 
5384453865 
54104  54126 

53100,53122 
533154  53385 
5362653648 
.3388753909 
54147  541G9 

53144 
.33107 
53670 
•33931 
54190 

33166 
33429 
53691 
53952 
54212 

331885321053232 
.334515347353195 
53713  53735  33757 
339745399654017 
54234  54255)54277 

53254 
33517 
53778 
54039 
54298 

53276 
53539 
53800 
54061 
54320 

33298 
53560 
53822 
54082 
54341 

a 

1 

•2 
3 

i 

4 
9 
13 
18 

4 
9 
13 
17 

50 
51 
52 
53 
54 

9  .  54363  54385|54406  54428  54449 
54621  54642  54GG4o4685  54707 
5487854899  5492054941  549G3 
5513355154551755519755218 
55387  55409,55430  55151  55472 

34471 
54728 
54984 
35239 
55493 

544925451454535 
547495477154792 

54556 
54813 

54578 
54835 

34599 
54856 

s 

1 
•2 
:; 
i 

35005  55027  55048  55069 
55260  -55282  55303(55324 
35514155535  55-5.5i;  ">.">.  >77 

55091 
55345 

55598 

55112 
35366 
55619 

55 
56 
57 
58 
59 

9.55641 
55893 
56144 
56393 
56642 

55662155683 
55914  -3.3934 
56164B6185 
5641456435 
56663!56683 

3.370  1:  35725  5574(5 
35955  55976  55997 
3620056227  56248 

55767J55788  55809 
56018  56039  56060 
562695628956310 

55830 

56081 
56331 

55851 
56102 
56352 
5GG01 
56818! 

55872 
3612;) 
36372 
56621 

56Sr,'.) 

s 

1 

9 
3 

1 

4 
8 
13 
17 

36156.36476 
5670156725 

66497 

56745 

565185653856559:56080 
56766156786  56807  56828 

290               .  TABLE  XVIII. 

LOGARITHMS  FOR  FINDING  THE  APPARENT  TIME  OR  HORARY  ANGLE. 

5  Hours. 

1C. 

Os. 

5s 

10s 

15s 

20s. 

35s 

80s 

35s 

40s 

45s 

50s. 

55s 

P.  P. 

0 

1 

2 
3 
4 

(J.  5(5889 
5713G 
573S1 
57G25 
578G8 

36910 
57156 
37402 
57646 

37889 

56931 
37177 
57422 
57666 
37909 

56951 
57197 
57442 
57686 
57929 

56972  56992 
5721857238 
574G3  57483 
57706  57727 
57949  57969 

57013 
57259 
57503 
57747 

37990 

57033 
37279 
57524 
57767 
58010 

57054 
57299 
57544 
57787 
38030 

57074 
57320 
57564 
57808 
58050 

5709557115 
57340  57361 
57585  57605 
57828  57848 
58070  58090 

a 
l 
2 
3 
4 

4 
8 
12 
16 

5 
6 

7 
8 
9 

9.58110 
5835J 
58591 
58830 
590G8 

38131 
58371 
58611 
38850 
39087 

38151 
58391 
58631 
58870 
59107 

38171 
3$411 
38651 
38889 
59127 

58191 
58431 
58671 
58909 
59147 

58211 
58451 
38691 
58929 
39166 

18231 
38471 
58711 
38949 
39186 

58251 
58491 
58731 
58969 
59206 

38271 
58511 
58750 
38988 
39225 

38291 
58531 
58770 
59008 
59245 

5831158331 
58551  58571 
5879058810 
5902859048 
59265  59285 

s 

1 

2 
3 

4 

4 
8 
12 
16 

10 
11 
12 
13 
14 

9.59304 
59540 
59774 
G0008 
G0240 

59324 
59559 
59794 
30027 
30260 

59344 
59579 
59813 
60017 
60279 

393G3 
59599 
59833 
30066 
(50298 

59383 
59618 
59852 
60085 
30318 

59403 
59638 
59872 
60105 
G0337 

59422 
39657 
59891 
30124 
6035C 

59442 
59677 
59911 
60144 
G0375 

39461 
5969G 
39930 
60163 
60395 

594S1 
59716 
59950 
60182 
60414 

59501-59520 
5973559755 
59969  59988 
6020260221 
60433,60452 

s 
1 
•2 
3 
4 

4 
8 
12 
16 

15 

1G 
17 
18 
19 

9.60472 
G0702 
60931 
61160 
G1387 

6049  J 
30721 
30951 
31179 
3140G 

3051U 
60740 
G0370 
31198 
G1425 

60529 
60760 
60989 
61217 
151444 

60549 
30779 
61008 
G123G 
61463 

60568 
60798 
61027 
61255 

G1482 

U0j&7 
60817 
31046 
61274 
61500 

GOG06 
60833 
G1065 
G1293 
61519 

60625 
60855 
61084 
61311 
31538 

G0645 
60874 
61103 
61330 
61557 

6066460083 
6089360912 
6112261141 
6134961368 
6157G  61595 

s 

1 

2 
3 
4 

4 
8 
11 

15 

20 
21 
22 
23 
24 

9.61013 
61839 
62063 
62287 
62509 

G103- 
31858 
G2082 
G2305 
32527 

61651 
G1876 
62100 
62324 
G2546 

31670 
131895 
62119 

G2342 
G2564 

G1G89 
61914 

32138 
62361 
32583 

61708 
61932 
62156 
62379 
62601 

G172G 
31951 
G2175 
32398 
62620 

61745 
G1970 
G2194 
G2416 

G2G38 

131764 
6198& 
62212 
62435 
62657 

61783 
62007 
62231 
62453 
62675 

G1801  61820 
62026  62045 
62249  62268 
6247262490 
6269362712 

s 
1 
2 
3 

4 

4 
7 
11 
15 

25 
26 
27 
28 
29 

9.62730 
62951 
63170 
G3389 
63606 

J2749 
62969 
.33188 
G3407 
63624 

32767 
32987 
63207 
63425 
63G42 

32785 
33006 
33225 
63443 
33660 

32804 
33024 
33243 
33461 

G3C78 

62822 
63042 
63261 
33479 
63696 

G2841 
63061 
63279 
63497 
63715 

G2859 
63079 
63298 
63516 
63733 

G2877 
63097 
63316 
63534 
G3751 

62896 
63115 
63334 
63552 
63769 

62914;62932 
G3134  63152 
6335263370 
63570  63588 
63787  63805 

s 
1 
2 
3 

4 

4 
7 
11 

1C 
0 

30 
31 
32 
33 
34 

9.63823 
64038 
64253 
64467 
64G79 

63841 
3405G 
34271 
34484 
64G97 

G3859 
64074 
64289 
64502 
61715 

G3877 
84092 
64307 
64520 
64732 

(3389563913 
6411064128 
3432464342 
G4538  64555 
3475064768 

G3931 
64146 
64360 
G4573 

G4785 

63949 
64164 
64378 
64591 
64803 

639GG 
64181 
64395 
64609 
64821 

639856400264020 
641996421764235 
64413  64431  64449 
G4G26  64644  64662 
64838  G485G  64873 

s 
1 
2 
3 
4 

4 
7 
11 
14 

35 
3G 
37 
38 
39 

9.64891 
65102 
65312 
65521 
65729 

34909 
65120 
65330 
65539 
G5747 

G492G 
65137 
65347 
G555G 
65764 

G4944 
65155 
35365 
65573 
65781 

64962 
35172 
65382 
65591 
S5799 

64979 
65190 
65399 
65608 
65816 

64997 
65207 
65417 
65625 
65834 

65014 
65225 
65434 
65643 

65850 

65032 
G5242 
65452 
65660 

65868 

65050 
65260 
654G9 
G5677 
65885 

65067  G5085 
6527765295 

6548G!G5504 
6569565712 
65902  G5919 

s 
1 
2 
3 
4 

7 
10 
14 

40 
41 
42 
43 
44 

9.65937 
6G143 
66348 
66553 
G6757 

35954 
G6160 
66366 
66570 
66774 

65971 
66177 
66383 
6G587 
GG791 

65986 
36194 

66400 
66604 
36807 

66000 
GG212 
66417 
66621 
6G824 

66023 
G6229 
66434 
66638 
66841 

GG040 
66246 
66451 
66655 
G685S 

GG057 
66263 
66468 
66672 
66875 

G6074 
66280 
66485 
66689 
6G892 

66092 
66297 
66502 
66706 
66909 

06109.66126 
66314G633J 
6651966536 
6672366740 
6692666943 

s 
1 
2 
3 

4 

7 
10 
14 

45 
4G 
47 
48 
49 

9.66959 
67161 
67362 
67562 
67762 

66976 
67178 
67379 
67579 
67778 

66993 
67195 
67396 
G759G 
67795 

67010  G7027G7044 
G72  12  67228  67245 
G7412'G7429  G7446 
67612  67629  G7646 
678116782867844 

67060 
67262 
67462 
67662 
67861 

67077 
G7279 
G7479 
67679 

67878 

67094 
67295 
67496 
67G95 
67894 

67111 
67312 
67512 
67712 
67911 

67  128  67  144 
6732967346 
67529;67546 
6772967745 
67927,67944 

8 
1 

2 
3 

4 

1 
1 

50 
51 
52 
53 
54 

9.67960 
68158 
68354 
68550 
68745 

67977 
68174 
68371 
68566 
68761 

67993 
68190 
68387 
68583 
68777 

680106802668042 
G8207  68223  68240 
684036842068436 
685996861568631 
68794  G8810  68826 

68059 
6825G 
68452 
68648 
68842 

G8075 
68272 
G84G9 
686G4 
G8858 

0809L 
68289 
68485 
68680 
68874 

681U8 
68305 
68501 
68696 
68891 

68125,68141 
6832268338 

68517|G8534 
68713,68729 
6890768923 

s 
1 
2 
3 
4 

1 
1 

55 
56 
57 

58 
59 

9.68939 
69132 
69325 
69516 
69707 

68955 
G9148 
G9341 
G9532 
69723 

68971 
69164 
69357 
69548 
69739 

168987  69004  69020 
6918169197  G9213 
G9373  69389  69405 
69564  G9580G9596 
IG9755G9770G9786 

69036  69052 
6922969245 
69421  G9437 
69G12  G9C28 
!69802l6981b 

69068 
69261 
69453 
69614 
69834 

69084 
69277 
69469 
69G60 
169850 

69100,69116 
6929369309 
6948169500 
6967569691 
69866169881 

8 
1 

2 
3 
4 

6 
10 
18 

TABLE  XVIII.               291 

LOGARITHMS  FOR  FINDING  THE  APPARENT  TEME  OR  HORARY  ANGLE. 

6  Hours. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.P. 

0 
1 

2 
3 

4 

9.098976991369929 
7008670102,70118 
70274  70-29070306 
70462:7047770193 
70618170664  70G80 

69944 
70133 
70321 
70539 
70695 

69960 
70149 
70337 
70524 
70710 

69976 
70165 
70353 
70540 
70726 

69992  70007 
7018070196 
7036870384 
70555  70571 
7074170757 

70023 
70211 
70399 
70586 
70772 

700397005570070 
702277024370259 
70415,7043170446 
70602j706  17  70633 
707887080370819 

s 
1 
2 
3 
4 

3 

6 
9 
12 

5 
6 
7 
8 
9 

9.7U8347085070865 
710197103571050 
712037121971234 
713877140271417 

715697158.J71GOO 

70881 
71065 
71249 
71433 
71615 

70896 
71081 
71265 
7  1448 
7163J 

70911 
71096 
71280 
71463 
71645 

70927  70942 
7111171127 
7129571310 
7147871493 
7166071676 

78958 

71142 
71326 
71509 
71691 

709737098871004 
711577117371188 
713417135671371 
715247153971554 
7170671721  71736 

B 
1 
2 

a 

4 

3 
6 
9 
12 

10 
11 
12 
13 
14 

9.717517176671781 
719327194771962 
721127212772142 
72292  72307:72322 

72471  7248572500 

71797 
71977 
72157 
72337 
72515 

71812 
71992 
72172 
72352 
72530 

71827 
72007 
72187 
72366 
72545 

71842 
72022 
72202 
72381 
72560 

71857 
72037 
72217 
72396 
72574 

71872 
72052 
72232 
72411 
72589 

71887  7190271917 
720677208272097 
7224772262^72277 
72426,72441  72456 
72604,7261972634 

s 
1 
2 
3 

4 

3 
6 
9 
12 

15 
16 
17 
18 
ia 

9.  72648  72663/2678 
728257284072855 
730027301673031 
731777319273207 
73352  73367  73381 

72693 
72870 
73046 
73221 
73396 

72708 
72881 
73060 
73236 
73410 

72722 
72899 
73075 
73250 
73425 

7273772752 
72914  72928 
73090  73104 
73265  73279 
73439  73454 

72767 
72943 
73119 
73294 
73468 

72781  7279672811 
729587297272987 
731347314873163 
733097332373338 
734837349773512 

s 

r 

2 
3 

4 

3 

6 
9 
12 

20 
21 
22 
23 
24 

9  .73526  73541  73555 
73699  73714  73728 
738727388673901 
74044  74058i7-4072 
74215  74229,74243 

73569 
73743 
73915 
74087 
74257 

73584 
73757 
73929 
74101 

74272 

73598 
73771 
73944 
74115 
74286 

7361373627 
73786  73800 
7395S  73972 
7412974144 
7430074314 

73642  73656  73671  73685 
73815738297384373858 
73987  74001  74015  74029 
74158741727418674200 
74328  74342,74357  74371 

s 

1 
2 
3 

4 

3 
6 
9 
12 

25 
26 

27 
28 
29 

9.74385 
74554 
74723 
74891 
75059 

74399  74413 
7456974583 
74737  74751 
7490574919 
75072  75086 

74427 
74597 
74765 
74933 
75100 

74442 
74611 
74779 
74947 
75114 

74456 
74625 
74793 
74961 
75128 

74470 
74639 
74807 
74975 
75142 

74484 
74653 
74821 
74989 
75156 

74498 
74667 
74835 
75003 
75170 

74512  74526)74540 
74681J74695  74709 
74849,74863174877 
75017  75031  75045 
75183  75197J75211 

s 
1 
2 

3 
4 

3 

5 
8 
11 

30 
31 
32 
33 
34 

y.  75225  75239  75253 
753917540575418 
7555G  75570,75583 
75720  75734  75748 
75884  7589S  75911 

75267 
75432 
75597 
75761 
75925 

7528U 
75446 
75611 
75775 
7593S 

75294 
75160 
75625 
75789 
75952 

75308  75322 
7547475487 
75638  75652 
7580275816 
75966  75979 

75336 
75501 
75666 
75830 
75993 

75349,7536,; 
7551575528 
75679  75693 
75843  75857 
76006  76020 

753V7 
75542 
75707 
75870 
76033 

B 

J 

9 

-1 

3 
5 
8 
10 

35 
36 
37 
38 
39 

9.76047 
76209 
76371 
76531 
76691 

7606076074 
76223  76236 
7638476397 
76545  76558 
76705  76718 

76088 
76250 
76411 
76571 
76731 

76101 
76263 
76424 
76585 
76745 

76115 

76276 
76438 
76598 
76758 

76128 
76290 
76451 
76611 
76771 

76142 
76303 
76464 
76625 
76784 

76155 
76317 
76478 
76638 
76798 

761697618276196 
763307634476357 
7649l'76505  76518 
760517666576678 
768117682476838 

s 
1 
2 
3 
4 

3 
5 
8 
10 

40 
41 
42 
43 
44 

9.76851 
77009 
77167 
77325 
77481 

76864  76877 
7702377036 
7718177194 
7733877351 
77494  77507 

76891 
77049 
77207 
77364 
77520 

76904 
77062 
77220 
77377 
77533 

76917 
77075 
77233 
77390 
77546 

7693076943 
7708977102 
77246  77259 
7740377416 
7755977572 

76957 
77115 

77272 
77429 
77585 

76970 
77128 
77285 
77442 
77598 

76983 
77141 
77298 
77455 
77611 

76996 
77154 
77312 
77468 
77624 

s 
1 
2 
3 

-1 

3 
5 

8 
10 

45 
4G 
47 
48 
49 

9.776377765077663 
77792  77805  77s  is 
779477796077972 
781017811378126 
782547826678279 

77676 
77831 
77985 
78139 
78292 

77689 
77844 
77998 
78152 
78305 

77702 
77857 
78011 
78164 
78317 

77715J77728 
7787077882 
7802478037 
78177J78190 
7833078343 

77741 

77895 
78019 
78203 
78355 

7775477766 
7790877921 
7806278075 
78215,78228 
7836878381 

77779 
77934 
78088 
78241 
78393 

s 

1 

a 

3 

•! 

3 

5 
8 
10 

50 
51 
52 
63 
54 

y.  78406:78419  78431 
78558,7857078583 
787097872178734 
78859  78872J78884 
79009  7902  1J79034 

78444 
7859G 
78747 
78897 
79046 

78457 
78608 
78759 
78909 
79059 

78469 
78621 
78772 
78922 
79071 

78482  78495 
7863378646 
7878478797 
7893478947 
7908479096 

78507 
78659 
78809 
78959 
79108 

78520  78533 
78671  78684 
78822,78834 
78972  78984 
79121J79133 

78545 
78696 
78S47 
78997 
79146 

s 
1 

a 

3 

•1 

2 
5 
7 
10 

55 
56 
57 

58 
59 

9.791587917079183 
79306,7931979331 
794547946679179 
79601  79613  7962G 
79748  79760^79772 

79195 
79343 
79491 
79638 
79784 

79^08 
79356 
79503 
79650 
79796 

79220 
79368 
79515 
796G2 

7:  (SO* 

7923279245 
79380,79393 
795287954(1 
79674  79687 
7982179833 

79257 
79405 
79552 
79699 
79845 

792697928279294 
794177943079442 
79564,7937779589 
797117972379735 
798577986979881 

8 

1 

9 

3 
•1 

2 
5 
7 
10. 

7  .  _  ,  .  

292                TABLE  XVIII. 

LOGARITHMS  FOR  FINDING  THE  APPARENT  TIME  OR  HOEAEY  ANGLE. 

7  Hours. 

M. 

Os. 

5s. 

10s. 

15s., 

.20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s. 

P.P. 

0 
1 
2 
3 
4 

9.7989379905 
800C8  30050 
80183  80195 
80327  80338 
8047080482 

79918 
80063 
80207 
80350 
30494 

(9930*9942 
8007580087 
302,1980231 
8036288874 
30505  80J17 

7'J954 
80099 
80243 
S0386 
S0529 

79966 
30111 
80255 
S0398 
80541 

79978 
80123 
80267 
30410 
80553 

79990 
80135 
30279 
80422 
80565 

80602 
80147 
80291 
30434 
80577 

80014 
80159 
30303 
30446 
30588 

80J-^6 
80171 
30315 
30453 
30600 

s 
1 
2 

3 

4 

2 
5 

7 
9 

5 

6 

7 
8 
9 

9.80612 
80754 
80895 
81036 
81176 

80624 
80766 
S0907 
8L047 
81187 

80636 
80778 
30910 
81059 
31199 

S0648 
307S9 
80930 
31071 
31211 

80660 
30801 
80942 
31082 
81222 

30671 
80813 
80954 
31094 
31234 

30633  30695 
8082580836 
8096C  80977 
8110681117 
3124531257 

30707 
80848 
80989 
81129 
81269 

30719 
80860 
81001 
31141 
31280 

30730 
30872 
81012 
31152 
31292 

8UV42 
30883 
81024 
81161 
81303 

s 
1 
2 
3 
4 

2 
5 

7 
9 

10 
11 
12 
13 
14 

9.81315 
81454 
81592 
81729 
818% 

31326 
31465 
81600 
81740 
31877 

J133S 
81477 
81614 
81752 
31888 

31350 
31488 
31626 
31763 
31900 

81361 
31500 
31637 
31775 
81911 

81373 
31511 
31649 
31786 
31922 

8138431396 
3152331534 
3166081672 
31797  31809 
8193^81945 

81407 
31546 
8168S 
8182C 
81956 

31419 
31557 
31695 
31831 
31968 

81430 
81569 
3170C 
31843 
81979 

3144-2 
31580 
31717 
31854 
319CO 

s 
1 

a 

3 

4 

2 
5 

7 
9 

15 

16 
17 
18 
19 

9.82002 
82137 
8-2272 
82406 
82540 

82013 
32148 
82283 
32417 
32551 

82024 
321GC 
32294 
82429 
32562 

32036 
82171 
32306 
32440 
32573 

82047 
82182 
32317 
32451 
8258] 

32058 
82193 
82328 
32462 
32595 

32070 
32205 
82339 
82473 
82606 

32081 
82216 
32350 
82484 
32618 

82092 
$2227 
82362 
82495 
82629 

32103 
82238 
32373 
32507 
32640 

82115 
82250 
82334 
82518 
32651 

32126 
82261 
32395 
32529 
32662 

s 
1 
•2 
3 
4 

2 
4 

7 
9 

20 
21 
22 
23 

24 

9.82673 
82805 
82937 
83068 
83199 

82G84 
32810 
82948 
83079 
33210 

32695 
82827 
82959 
33090 
83220 

8-706 
82838 
32970 
33101 
83231 

82717 
82849 
32981 
83112 
33242 

82728 
82860 
32992 
83123 
83253 

32739 
32871 
33003 
83134 
83264 

82750 
32882 
330W 
83144 
83275 

32761 
82893 
83025 
83155 
83285 

3-772 
82901 
83035 
83166 
33296 

32785 
82915 
83046 
83177 
33307 

82794 
32926 
33057 
83188 
83318 

s 

! 
| 

2 
4 
7 
9 

25 
26 
27 
28 
29 

9.83329 
83458 
83587 
83715 
83842 

83339 
83469 
S3597 
33725 
33853 

33350 
33179 
3360S 
83736 
33863 

33361 
33490 
33619 
33747 

33874 

83372 
83501 
836-29 
83757 
3388Z 

33383 
83512 
33640 
33768 
83895 

33393 
33522 
83651 
83779 
83906 
34031 
84159 
34284 
84409 
84533 

83101 
33533 

83662 
83789 
83916 

83415 
83544 
83672 
83800 
33927 

8342683436 
8355583565 
8368383691 
33811  53821 
33938  83948 

33447 
83576 
33704 
83832 
33959 

B 

I 
I 

2 
4 

7 
9 

30 
31 
32 
33 

34 

9.83969 

8409G 
84221 
84346 
84471 

<3980 
81106 
34232 
84357 
34481 

3399U 
34117 
34242 
34367 
84492 

84001 
84127 
84253 
84378 
84502 

34011 
8413& 
84:163 

34388 
84512 

34022 
34148 
34274 
84398 
84523 

84013 
84169 
34294 
84419 
34543 

84054 
84179 
84305 
34430 
84554 

34064  84075 
34190  34200 
84315  8432C 
84440  84450 
J4564  84574 

84U85 
84211 
34336 
34461 
84585 

S 
1 

2 
3 

-i 

2 
4 

6 

8 

35 
36 
37 
38 
39 

9.84595 
84718 
84841 
84983 
85085 

3400.: 

J4729 
84851 
84973 
35095 

34616 
31739 
318G1 
84984 
85105 

84626  34636 
3474984759 
8187234882 
34994'85004 
8511585125 

84646 
84769 
34891 
35014 
35135 

34657 
34780 
81902 
35024 
35145 

84667 
84790 
84912 
85034 
85155 

84677 
84800 
84923 
85044 
85166 

31687 
34810 
34933 
85051 
85176 

84696 
34821 
84943 
85065 
85186 

84708 
84S31 
84953 
85075 

35196 

s 
1 
2 
3 

4 

2 
4 
6 
8 

40 
41 
42 
43 
44 

9.  155206 

85216J85226 

35236  85246 

85256 

85266 

85276 

85286 

35296  85306 

65316 

s 
] 
2 
3 
4 

2 
4 
6 

8 

85326185336I35346 
8544G  83456  85466 
85565  85575  85585 
85684  8569-185704 

85356  35366 
8547685486 
8559585605 
8571485724 

85376 
85496 
85615 
85733 

8538C  85396 
8550G  85516 
85625  85635 
8574b  85753 

85406 
8552C 
85645 
85763 

35416  85426 
8553685546 
8565485661 
8577385783 

85436 
85555 
85674 
85792 

45 
46 
'  47 
t  48 
49 

9.85802 

85920 
86037 
86153 
8G269 

35812  85822 
85930  35939 
3604686056 
861633617k 
86279  86288 

8583285841 
85949  35959 
86066  8G07C 
861823619; 
8629886307 

35851 
85969 
86085 
86201 
36317 

8-38(51  85871 
85978  85988 
8609586105 
86211  86221 
8632786336 

85881 
85998 
86114 
86230 
86346 

85890  85900 
8600886017 
8612486134 
8624086250 
8635686365 

85910 
86027 
86143 
86259 
86375 

s 
1 
2 
3 

4 

2 
4 
6 

8 

50 
51 

53 
53 

54 

9.86384 
86499 
86613 
86727 
86840 

86394'3G403 
8650986518 
86623  86632 
8673686746 
8684986858 

86413*6423 
8652*6537 

8664S86651 
8675586764 
86868,86877 

86432 
S6547 
86661 
86774 
86887 

8644286451 
8655686566 
8667086679 
8678386793 
8689686905 

86461 

86575 
86689 
86802 
86915 

86470|36480 
86585,86594 
8669886708 
8681286821 
8692486933 

86439 
86604 
86717 
86830 
86943 

s 
1 
2 
3 

4 

2 
4 
6 
8 

55 
56 
57 

58 
59 

9.869528696286971 
87064  3707387083 
871758718587194 
87286  37295  87305 
8739G8740G  87415 

3698086990 
8709287101 
8720337212 
87314  87323 
37424:87433 

86999  87008  87018  87027 
37111871208712987138 
87222  87231  87240  87249 
87332873113735187360 
87442874518746087470 

87036  87045  87055 
871488715787166 
87259,8726887277 
873698737887387 
874798748887497 

s 
1 
2 
3 
4 

! 
2 
4 
6 
8 

-I 

TABLE  XVIII.               293 

fJARITHMS  FOR  FINDING  THE  APPARENT  TIME  OR  HORARY  ANGLE. 

8  Hours. 

M. 

Os. 

5s. 

10s. 

15s. 

20s. 

25s. 

30s. 

35s. 

40s. 

45s. 

50s. 

55s.  P.  P. 

0 
1 
2 
3 
4 

9.8750687515 
87G15  87624 
8772487733 
8783287841 
87939,87948 

87524 
87633 
87742 
87850 
87957 

87534 

87643 
87751 
87859 
8796G 

87543 

87652 
8776C 
87868 
87975 

;87552,»75G1 
87661  187670 
877G9  37778 
87877,87886 
87984  3799.3 

87570 
87679 
87787 
37895 
38002 

87579 
37688 
3779G 
87904 
88011 

87588 
87697 
87805 
87913 
8802C 

87597 
8770G 
87814 
37921 
88029 

87606 
87715 
87823 
87930 
88038 

8 
1 

2 

3 
1 

2 
4 
5 
7 

5 

G 
7 
8 
9 

9.86046 
88153 
83259 
88364 
884G9 

88055 
8316-2 
88268 
38373 
88478 

88064 
88170 
38270 
88381 
88486 

88073 
38179 
38285 
38390 
88495 

88082 
38188 
38294 
38399 
38503 

38091 
88197 
88303 
38408 
88512 

88100 
38206 
88311 
3841G 
38521 

88109 
88215 
38320 
38425 
88530 

38117 

88223 
38329 
38434 
88538 

8812li 
88232 
88338 
38443 
88547 

88135 
38241 
38346 
88451 
38556 

88144 
38250 
88355 
88460 
88565 

s 
1 
2 
3 

4 

2 
4 
5 

7 

10 
11 
12 
13 
14 

9.88o73 
83677 
88780 
83882 
83984 

88582 
8868( 
88789 
38891 
8899S 

88590 
3809.1 
33797 
3389D 
89001 

33591 
88703 
3880G 
38908 
3901C 

88GO< 
38711 
88814 
88910 
=9018 

586  It 
38720 
88823 
38925 
39027 

88025 
387-28 
38831 
38933 
89035 

38634 
38737 
88840 
38942 
39044 

j864k 
88745 
88848 
88950 
J905-2 

38651 
88754 
88857 
83959 
39061 

3865'J 
38763 
38865 
38967 
89069 

38068 
88772 
38874 
38976 
39078 

8 
1 

2 
3 
4 

2 
4 
5 

7 

15 
16 
17 
18 
19 

9.83080 
89187 
89287 
89387 
80487 

3909. 
89196 
39296 
89396 
89495 

39lOo 
39204 
8930J 
39401 
89503 

39112 

89213 
39313 
3941S 
39512 

3912CJ 
89221 
39321 
39421 
89520 

39129 
39229 
39330 
39429 
89528 

39137 
89237 
39338 
89437 
39536 

39145 
39246 
8934C 
39446 
89545 

39l5o 
39254 
39354 
89454 
39553 

39102 
3926S 
39363 
39462 
89561 

39170 
89271 
39371 
89470 
39569 

3917U 
33279 
89379 
39479 
39577 

s 
1 
2 
3 
4 

2 

4 

5 
7 

20 
21 
22 
23 
24 

9.89580 
89684 
89782 
89879 
8997G 

39o96 
89693 
39790 
89888 
3998J 

39602 
39701 
J979S 
39S9G 
3999-1 

39611 
3970C 
89807 
80904 
9000C 

39019 
39717 
39815 
399K 
9000S 

89o27 
89725 
39823 
39920 
9001C 

j9G35 
39733 
89831 
,9926 
90024 

39643 
89741 
39839 
89936 
90032 

89651 
89749 
39847 
39944 
9004( 

396GC 
89758 
8985C 
8995-2 
9004!- 

89GGb 
3976G 
898G3 
89960 
90056 

89676 
39774 
89871 
89968 
90064 

s 
1 
2 

a 

4 

2 
3 
5 
6 

25 
26 
27 
28 
29 

9.9iJ072 
90168 
90263 
90358 
90452 

30080 
90176 
90271 
9036C 
90460 

JUOob 
9018J 
90279 
J037,! 
901G8 

900% 
3019- 
30287 
90382 
3017( 

90104 
30200 
30295 
90390 
90484 

90112 
30208 

30303 
30398 
9049. 

90120 
90216 
90311 
30405 
30499 

30128 
30224 
90319 
90413 
90507 

3013G 
30232 
90327 
90421 
90515 

90144 
30240 
90335 
9042C 
3052E 

90152 
90248 
90342 
30437 
30531 

90160 
90256 
90350 
90445 
90539 

s 

1 

2 
3 

1 

2 
3 

5 
6 

3'J 
31 
32 
33 
34 

9.90546 

90639 
90732 
90824 
90916 

90551 
90647 
90740 
90832 
90921 

90562 
90655 
90747 
90840 
J0331 

30570 
90663 
30755 
90848 
30939 

J0577 
30670 
.30763 
30855 
30946 

90585 
90678 
90771 
90863 
90954 

90593 
90686 
90778 
30870 
90962 

30G01 
30694 
90786 
30878 
90970 

30G08 
90701 
90794 
90885 
90977 

90610 
.30708 
90802 
90893 
)0985 

90624 
90717 
90809 
90901 
30992 

30032 
90725 
90817 
90909 
91000 

s 
1 
2 
3 
1 

2 
3 
5 
6 

35 
36 
37 
38 
39 

9.  9  1007 
91098 
91188 
91277 
913G7 

31015 
31106 
9119G 
31285 
91374 

9102:; 
91113 
91203 
31292 
31331 

31030 
31121 
91211 
31300 
91389 

91037 
31128 
91218 
31307 
9139G 

31015 
91136 
31226 
31315 
91104 

9105291060 
9114331151 
9123391241 
3132291330 
9141191419 

31067 
91158 
91248 
91337 
9142G 

31075 
9116C 
91255 
91345 
91433 

31083 
91173 
91262 
91352 

31440 

91091 
91181 
91270 
91360 
91448 

s 
1 

a 

3 

i 

2 
3 
5 
6 

40 
41 
4-2 
43 
44 

9.91455jt>14'J3 
9154391531 
91631I91638 
91718^91725 
91805,91812 

3147U 
31558 
91645 
91732 
91819 

31478 
91566 

91653 
31740 
9182G 

3148u 
31573 
91660 
91747 
31833 

91492 
91580 
91667 
91754 
91841 

91499 
E)1587 
31674 
31761 
31848 

31507 
91595 
31682 
31769 
31855 

91514 
91602 
91689 
91776 
31862 

91522 
91609 
91696 
31783 
91869 

3152y 
91616 
31703 
91790 
91870 

91536 
91624 
91711 
31798 
31884 

s 
1 

a 

a 

4 

2 
3 

5 
6 

4j 
46 
47 
48 
49 

9.9189191898 

91976  91984 
92061  92069 
9214692153 
3^80,92237 

91900 
31991 
92076 
92160 
92244 

91912 
91938 
92083 
92167 
92251 

31919 
92005 
92090 
32174 
92258 

31927  91934  919411 
920129201992026 
920979210492111 
92181  9218892195 

922G5  92272  92279 

31948 
32033 
32118 
32202 
32286 

91955 
92040 
92125 
92209 

92293 

31962 
92047 
92132 
92216 
92300 

31969 
32054 
32139 
32223 
92307 

s 
1 
2 
3 
4 

1 

3 
4 
6 

50 
51 
52 
53 
54 

9.  92314  923-21 
92397  92404 
9248092487 
9256292569 
9264392650 

92328 
92411 
92493 
92575 
9265? 

32335 
92418 
32500 
92582 
92664 

32342 
32425 
92507 

325.N9 

12070 

92349  92355  92302 
924329243892445 
925149252192528 
9259G92G03  92610 
92677,92684  92691 

32369 
32452 
32534 
32616 
32698 

92370 
92459 
92541 
92623 
32705 

32383 
92466 
92548 
92630 
32711 

32390 
32473 
32555 
J2637 

32718 

s 
1 

9 

:i 
•I 

1 
3 

4 

6 

55 
56 
57 
58 
59 

9  .  92725  92732  92738  92745 
92805928129281992826 
92885928929289992906 
929G5  92972  92978  92985 
93041;93051  93057193064 

32751 
92832 
92912 
92992 
93071! 

327589-276592772 
928399284592852 
929199292592932 
929999300593012 
930789308493091 

32778 
32859 
32939 
33018 
33097 

32785 
32866 
32j)46 
33025 
(3101 

32792 
92872 
32952 
33031 
93110 

32799 
32879 
32959 
33038 
33117 

s 

1 

•2 

a 

4 

1  1 
3 
4 
6 

294 

TABLE  XIX.                                    ^ 

TO    FIND   THE   LATITUDE   BY   AN    ALTITUDE    OF   THE    POLE   STAB.- 

Subtracted  if  the  R.  A.  is  found 
in  this  column. 

Correction. 

Added  if  the  R.  A.  is  found  in 
this  column. 

H.      M. 

H.        M. 

° 

H.       M. 

H.       M. 

7     10 

19     10 

0        0 

7     10 

19    10 

7    00 

19    20 

0        3 

7    20 

19    00 

G    50 

19    30 

0       7 

7    30 

18    50 

6    40 

19    40 

1      11 

7    40 

18    40 

G    30 

19     50 

0      15 

7     50 

18    30 

G    20 

20    00. 

0      18 

8    00 

18     20 

G    10 

20    10 

0      21 

8    10 

18    10 

6    00 

20     20 

0      25 

8    20 

18    00 

5     50 

20    30 

0      29 

8    30 

17    50 

5    40 

20    40 

0      32 

8    40 

17    40 

5     30 

20    50 

0      36 

8    50 

17    30 

5     20 

21     00 

0      39 

9    00 

17    20 

5    10 

21     10 

0      42 

9    10 

17    10 

5     00 

21     20 

0      45 

.  9     20 

17    00 

4    50 

21     30 

0      48 

9    30 

16    50 

4    40 

21    40 

0      51 

9    40 

16    40 

4    30 

21     50 

0      54 

9    50 

16    30 

4    20 

22    00 

0      56 

10    00 

16     20 

4    10 

22    10 

0      59 

10     10 

16    10 

4    00 

22    20 

1      02 

10     20 

16    00 

3    50 

22    30 

1      04 

10    30 

15    50 

3    40 

22    40 

1      06 

10    40 

15    40 

3    30. 

22    50 

1      08 

10    50 

15    30 

3    20 

23    00 

1      10 

11    00 

15    20 

3     10 

23    10 

1      13 

11     10 

^-    10 

2    50 

23    30 

1      17 

11     30 

14    50 

2    30 

23    50 

1      19 

11    50 

14    30 

2    10 

0    10 

1      21 

12    10 

14    10 

1    40 

0    40 

1      23 

12    40 

13    40 

1     10 

1     10 

1      24 

13     10 

13    10 

TABLE  XX.                295 

AMPLITUDES. 

DECLINATION. 

Lat. 

1 

2° 

3° 

4° 

5° 

6° 

70 

8° 

9° 

1<P 

11° 

12° 

13°  14- 

1 

3 

5 
7 
9 
10 
11 
12 

1  0 
1  0 
1  0 
1  0 
1  1 
1  1 
1  1 
1  1 

2  0 
2  0 
2  0 
2  1 
2  1 
2  2 
2  2 
2  3 

3  0 
3  0 
3  1 
3  1 
3  2 
3  3 
3  3 
3  4 

4  0 
4  0 
4  1 
4  2 
4  3 
4  4 
4  4 
4  C 

5  0 
5  0 
5  1 
5  2 
5  4 
5  5 
5  6 
5  7 

6  0 
6  0 
6  1 
6  3 
6  5 
6  6 
6  7 
6  8 

7  0 
7  1 
7  2 
7  3 

7  5 
7  6 
7  7 
7  9 

8  0 
8  1 
8  2 
8  4 
8  6 
8  8 
8  9 
8  11 

9  0 
9  1 

9  2 
9  4 
9  7 
9  9 
9  10 
9  12 

10  0 
10  1 
10  2 
10  5 
10  8 
10  10 
10  11 
10  13 

11  0 
11  1 
11  3 
11  5 
11  8 
11  11 
11  13 
11  15 

12  0 
12  1 
12  3 
12  5 
12  9 
12  11 
12  13 
12  10 

13  0 
13  1 
13  3 
13  6 
13  10 
13  12 
13  15 
13  18 

14  0 
14  1 
14  3 
14  G 
14  11 
14  13 
14  16 
!4  19 

]3 
14 

15 
16 
17 

18 
19 
20 
21 

1  i 
1  2 
1  2 
1  2 
1  3 
1  3 
1  3 
1  4 
1  4 

•2  3 
2  4 
2  4 

2  5 
2  5 
2  6 
2  7 
2  8 
2  9 

3  5 
3  6 
3  6 
3  7 
3  8 
3  9 
3  10 
3  12 
3  13 

4  b 
4  7 
4  8 
4  10 
4  11 
4  12 
4  14 
4  15 
4  17 

5  8 
5  9 
5  11 
5  12 
5  14 
5  15 
5  17 
5  19 
5  21 

0  lu 
6  11 
6  13 
6  15 
6  17 
6  19 
6  21 
G  23 
6  26 

7  11 
7  13 
7  15 
7  17 
7  19 
7  22 
7  24 
7  27 
7  30 

8  13 
8  15 
8  17 

8  19 
8  22 
8  25 
8  28 
8  3) 
8  34 

9  14 
9  17 
9  19 
9  22 
9  25 
9  28 
9  31 
9  35 
9  39 

10  10 
10  19 
10  21 
10  24 
10  28 
10  31 
10  35 
10  39 
10  43 

11  18 
11  20 
11  21 
11  27 
11  31 
11  34 
11  39 
11  43 
11  48 

12  19 
12  22 
12  2G 
12  29 
12  33 
12  38 
12  42 
12  47 
12  52 

13  21 
13  24 
13  28 
13  32 
13  3G 
13  41 
13  4G 
13  51 
13  57 

14  73 
14  26 
14  30 
14  35 
14  39 
14  41 
14  49 
14  55 
15  1 

22 
23 
24 
25 
26 
27 
.28 
29 
30 

1  5 
1  5 
1  6 
1  6 
1  7 
1  7 
1  8 
1  9 
1  9 

2  9 
2  10 
2  11 
2  12 
2  14 
2  15 
2  16 
2  17 
2  19 

3  11 
3  16 
3  17 

3  19 
3  20 
3  22 
3  24 
3  26 
3  25 

4  19 
4  2] 
4  23 
4  25 
4  27 
4  29 
4  32 
4  31 
4  37 

o  21 
5  2G 
5  28 
5  31 
5  34 
5  37 
5  40 
5  43 
5  47 

0  28 
6  31 
G  34 
6  37 
6  41 
6  44 
6  48 
6  52 
G  5f 

7  33 
7  36 

7  40 
7  44 
7  48 
7  52 
7  5G 
8  1 
8'  5 

8  38 
8  4i 
8  4C 
8  5C 
8  51 
8  59 
9  4 
9  9 
9  1C 

9  4^ 
9  47 
9  52 
9  56 
10  1 
10  7 
10  12 
10  18 
10  24 

10  48 
10  52 
10  57 
11  3 
11  8 
11  14 
11  21 
11  27 
11  34 

11  53 

11  58 
12  3 
12  9 
12  15 
12  22 
12  29 
12  30 
12  44 

12  57 
13  3 
13  9 
13  16 
13  22 
13  30 
13  37 
13  45 
13  53 

14  2 
14  9 
14  15 
14  22 
14  30 
14  37 
14  4G 
14  54 
15  3 

15  7 
15  14 
15  21 
15  29 
15  37 
15  45 
15  54 
16  3 
1C  13 

31 
32 
33 
34 
35 
36 
37 
38 
39 

1  10 
1  11 
1  12 
1  12 
1  13 
1  14 
1  15 
1  16 
1  17 

2  20 
2  22 
2  23 
2  25 
2  27 
2  28 
2  30 
2  32 
2  31 

3  30 
3  32 
3  35 
3  37 
3  40 
3  43 
3  45 
3  48 
3  52 

4  4U 
4  43 
4  40 
4  50 
4  5o 
4  57 
5  1 
5  5 
5  9 

5  50 
5  54 
5  58 
6  2 
6  6 
6  11 
6  10 
6  21 
6  26 

7  0 

7  5 
7  10 
7  15 
7  20 
7  25 
7  3J 
7  37 
7  44 

8  JO 
8  1C 
8  21 
8  27 
8  33 
8  40 
8  47 
8  51 
9  1 

9  21 
9  27 
9  3L 
9  4C 
9  47 
9  54 
10  2 
10  10 
10  19 

10  31 
10  3b 
10  45 
10  5£ 
11  1 
11  9 
11  18 
11  27 
11  37 

11  41 

11  49 
11  57 
12  5 
12  14 
12  24 
12  33 
12  44 
12  55 

12  52 
13  0 
13  9 
13  18 
13  28 
13  39 
13  49 
14  1 
14  13 

14  2 
14  11 
14  21 
14  31 
14  42 
14  54 
15  5 
15  18 
15  31 

15  13 
15  23 
15  34 
15  45 
15  5G 
16  9 
16  22 
16  35 
70  61- 

10  24 
16  34 
1G  46 
16  58 
17  11 
17  21 
17  38 
17  53 
18  8 

40 
41 
42 
43 
44 
45 
46 
47 
48 

1  18 
1  20 
1  21 
1  22 
1  23 
1  25 
1  26 
1  28 
1  30 

2  37 
2  30 
2  42 
2  41 
2  47 
2  50 
2  53 
2  5C 
2  59 

3  55 
3  59 
4  2 
4  6 
4  10 
4  15 
4  19 
4  24 
4  29 

5  13 
5  18 
5  23 
5  28 
5  34 
5  40 
5  4C 
5  52 
5  59 

0  32 
6  38 
6  44 
6  51 

6  58 
7  5 
7  12 
7  21 

7  29 

7  51 
7  58 
8  5 
8  13 
8  21 
8  30 
8  39 
8  49 
8  59 

9  d 
9  18 
9  26 
9  3C 
9  45 
9  55 
10  6 
10  18 
10  30 

10  26 
10  36 
10  48 
10  58 
11  9 
11  21 
11  33 
11  46 
12  0 

11  4V 
11  58 
12  9 
12  21 
12  34 
12  47 
13  1 
13  16 
13  31 

13  G 
13  18 
13  31 
13  41 
13  58 
14  13 
14  29 
14  45 
15  2 

14  25 
14  39 
14  53 
15  7 
15  23 
15  39 
15  57 
16  15 
1G  31 

15  45 
15  59 
16  15 
16  31 
16  48 
17  6 
17  25 
17  45 
18  G 

17  5 
17  20 
17  37 
17  55 
18  13 
18  33 
18  54 
19  1'j 
19  39 

18  25 
18  4? 
19  0 
19  19 
19  39 
20  0 
20  23 
20  47 
21  12 

4'J 
50 
51 
52 
53 
54 
55 
56 
57 

1  31 
1  33 
1  35 
1  37 
1  40 
1  42 
1  45 
1  47 
1  50 

3  3 
3  7 
3  11 
3  15 
3  19 
3  24 
3  29 
'3  35 
3  40 

4  35 
4  40 
4  46 
4  53 
4  59 
5  7 
5  14 
5  22 
5  31 

6  6 
6  14 
6  22 
6  30 
6  39 
6  49 
6  59 
7  10 
7  22 

7  3S 
7  48 
7  58 
8  8 
8  20 
8  32 
8  44 
8  58 
9  13 

9  lu 
9  22 
9  31 
9  47 
10  0 
10  15 
10  30 
10  46 
11  4 

10  4i 
10  56 
11  10 
11  25 
11  41 
11  58 
12  16 
12  35 
12  56 

12  lo 
12  3( 
12  47 
13  4 
13  22 
13  42 
14  3 
14  25 
14  48 

13  4b 
14  5 
14  24 
14  43 
15  4 
15  26 
15  50 
16  15 
16  42 

15  21 
15  40 
16  1 
16  23 
16  46 
17  11 
17  37 
18  5 
18  36 

10  54 
17  16 
17  39 
18  3 
18  29 
18  57 
19  26 
19  57 
20  30 

18  29 
18  52 
19  17 
19  44 
20  13 
20  43 
21  15 
21  50 
22  26 

20  321  38 
20  2922  7 
20  5722  36 
21  2623  8 
21  5723  42 
22  3024  18 
23  524  57 
23  4325  38 
24  2420  22 

58 
59 
60 
61 
62 
63 
64 
65 
60 

1  53 
1  57 
2  C 
2  4 
2  8 
2  12 
2  17 
2  22 
2  28 

3  47 
3  53 
4  0 
4  8 
4  16 
4  25 
4  34 
4  44 
4  55 

5  40 
5  50 
6  0 
6  12 
6  21 
6  37 
0  51 
7  7 
7  24 

7  34 
7  47 
8  1 
8  16 
8  33 
8  50 
9  9 
9  30 
9  53 

9  28 
9  45 
10  2 
10  21 
10  42 
11  4 
11  28 
11  54 
12  22 

11  23 
11  43 
12  4 
12  27 
12  52 
13  19 
13  48 
14  19 
14  51 

13  18 
13  41 
14  6 
14  34 
15  3 
15  34 
16  8 
16  4C 
17  2C 

15  14 
15  41 
16  10 
16  41 
17  15 
17  51 
18  31 
19  14 
20  1 

17  10 
17  41 
18  14 
18  49 
19  28 
20  9 
20  51 
21  44 
22  37 

19  8 
19  4'2 
20  19 
20  59 
21  42 
22  29 
23  20 
24  16 
25  1C 

21  6 
21  45 
22  26 
23  11 

23  59 
24  51 
25  48 
26  50 
27  59 

23  G 
23  49 
24  34 
25  24 

26  17 
27  15 
28  19 
29  28 

ID  -i;, 

&  727  10 
25  54  28  1 
26  4428  56 
27  3929  56 
28  3831  1 
29  4232  12 
ii)  .VJ:53  30 
32  1031  55 
33  35'30  30 

296                TABLE  XX. 

AMPLITUDES. 

DECLINATION. 

Lat. 

15° 

16° 

17°  18= 

19° 

20° 

21° 

21°  30' 

22° 

•22°  30' 

23° 

23°  28' 

1 

15  0 

16  0 

17  0 

18  019  6 

20  0 

21  0 

21  30 

22  0 

22  30 

23  0 

23  28 

3 

15  1 

16  1 

17  118  2'19  2 

20  221  2 

21  32 

22  2 

22  32 

23  2 

23  30 

5 

15  4 

16  4 

17  4 

18  419  5 

20  521  5 

21  35 

22  5 

22  35 

23  6 

23  34 

7 

15  7 

16  7 

17  8 

18  819  9 

20  921  10 

21  40 

22  10 

22  41 

23  11 

23  39 

9 

15  11 

16  12 

17  1318  1419  15 

20  1621  16 

21  47 

22  17 

22  48 

23  18 

23  47 

10 

15  14 

16  15 

17  16 

18  17 

19  18 

20  1921  20 

21  51 

22  21 

22  52 

23  23 

23  51 

11 

15  17 

16  18 

17  20 

18  21 

19  22 

20  2421  25 

21  55 

22  26 

22  57 

23  28 

23  50 

12 

15  21 

16  22 

17  23 

18  25 

19  26 

20  2821  30 

22  0 

22  3) 

23  2 

23  33 

24  1 

13 

15  24J16  26 

17  '2818  '2919  3l|20  3321  35 

22  6 

22  37 

z3  8 

23  38 

'24  7 

14 

15  28 

16  30 

17  32 

18  34:19  36 

20  3821  40 

22  11 

22  43 

23  14 

23  45 

24  14 

15 

15  33 

16  35 

17  37 

18  39  19  42 

20  44 

21  47 

22  18 

22  49 

23  20 

23  52 

24  21 

16 

15  37 

16  40 

17  42  18  45  19  48 

20  51 

21  53 

22  25 

22  56 

23  28 

23  59 

24  28 

17 

15  42 

16  45 

17  4818  5119  54 

20  57 

22  1 

22  32 

23  4 

23  35 

24  7 

24  36 

18 

15  47 

16  51 

17  54 

18  5820  1 

21  5 

22  8 

22  40 

23  12 

23  44 

24  15 

24  45 

19 

15  53 

16  57 

18  1 

19  5 

20  8 

21  12 

22  16 

22  49 

23  20 

23  52 

24  25 

24  54 

20 

15  59 

17  3 

18  8 

19  12 

20  16 

21  21 

22  25 

22  57 

23  30 

24  2 

24  34 

25  4 

21 

16  6 

17  10 

18  15 

19  2020  25 

21  29 

22  34 

23  7 

23  39 

24  12 

24  45 

25  15 

22 

16  13 

17  18 

18  23 

19  '2820  33 

21  39 

22  44 

23  17 

23  50 

24  23 

24  55 

•25  2(i 

23 

16  20 

17  25 

18  31 

19  3720  43 

21  49 

22  55 

23  28 

24  1 

24  34 

25  7 

25  38 

24 

16  27 

17  34 

18  40 

19  4620  53 

21  59 

23  6 

23  39 

24  13 

24  46 

25  19 

25  51 

23 

16  36 

17  42 

18  49 

19  5621  3 

22  10 

23  18 

23  51 

24  25 

24  59 

25  32 

26  4 

26 

16  44 

17  52 

18  59 

20  721  14 

22  22 

23  30 

24  4 

24  38 

25  12 

25  46 

26  18 

27 

16  53 

18  1 

19  9 

20  1821  26 

22  34 

23  43 

24  17 

24  52 

25  26 

26  1 

26  33 

23 

17  3 

18  11 

19  20 

20  2921  38 

22  47 

23  57 

24  31 

25  6 

25  41 

26  16 

26  49 

29 

17  13 

18  22 

19  32 

20  4121  51 

23  1 

24  11 

24  46 

25  22 

25  57 

26  32 

27  5 

30 

17  23 

18  34 

19  44 

20  5422  5 

23  16 

24  27 

25  2 

25  38 

26  13 

26  49 

27  23 

31 

17  34 

18  45 

19  57 

21  822  19 

23  3l|24.  43 

25  19 

•25  55 

26  31 

27  7 

27  41 

32 

17  46 

18  58 

20  10 

21  2222  35 

23  4725  0 

25  36 

26  13 

26  49 

27  26 

28  0 

33 

17  59 

19  11 

20  24 

21  37 

22  51 

24  425  18 

25  55 

26  32 

27  9 

27  46 

28  21 

34 

18  11 

19  25 

20  39 

21  53 

23  7 

24  2225  37 

26  14 

26  52 

27  29 

28  7 

28  42 

35 

18  25 

19  40 

20  55 

22  10 

23  25 

24  41  25  57 

26  35 

27  13 

27  51 

28  29 

29  5 

36 

18  39 

19  55 

21  11 

22  27 

23  44 

25  126  18 

26  56 

27  35 

28  14 

28  53 

29  30 

37 

18  55 

20  11 

21  28 

22  46 

24  3 

25  2126  40 

27  19 

27  58 

28  38 

29  17 

29  55 

38 

19  10 

20  28 

21  47 

23  5 

24  24 

25  43  27  3 

27  43 

28  23 

29  3 

29  44 

30  21 

39 

19  27 

20  46 

22  6 

23  26 

24  46 

26  727  28 

28  8 

28  49 

29  30 

30  11 

30  49 

40 

19  45 

21  5 

2'2  26 

23  47 

25  9 

26  3127  54 

'28  35 

29  17 

29  58 

30  40 

31  19 

41 

20  3 

21  25 

22  48 

24  10 

25  33 

26  57 

28  21 

29  3 

29  46 

30  '28 

31  11 

31  51 

42 

20  23 

21  46 

•23  10 

24  34 

25  59 

27  24 

28  50 

29  33 

30  16 

31  0 

31  43 

32  24 

43 

'20  44 

22  823  34 

25  0 

26  26 

•27  5329  20 

30  5 

30  49 

31  33 

32  18 

32  59 

44 

•21  5 

22  32 

23  59 

25  26 

26  55 

28  2329  53 

30  38 

31  23 

32  8 

32  54 

33  37 

45 

21  28 

22  57 

24  25 

25  55 

27  25 

28  5630  27 

31  13 

31  59 

32  46 

33  33 

34  17 

46 

21  53 

23  23 

24  53 

26  25 

27  57 

29  3031  3 

31  51 

32  38 

33  26 

34  ]4 

34  59 

47 

22  18 

23  50 

25  23 

26  57 

28  31 

30  631  42 

32  30 

33  19 

34  8 

34  57 

35  44 

48 

2-2  45 

24  20 

25  55 

27  30 

29  7 

30  4432  23 

33  13 

34  3 

34  58 

35  44 

36  31 

49 

•23  14 

24  51 

26  28 

28  6 

29  45 

.il  2533  7 

33  58 

34  49 

35  41 

36  33 

37  2? 

50 

23  45 

25  24 

27  2 

28  44 

30  26 

32  933  53 

34  46 

35  39 

36  32 

37  26 

38  17 

51 

24  17 

25  59 

27  41 

29  25 

31  9 

32  55 

34  43 

35  37 

36  32 

37  27 

38  23 

39  15 

52 

24  52 

26  36 

28  21 

30  8 

31  56 

33  45 

35  36 

36  32 

37  29 

38  26 

39  24 

40  18 

53 

25  28 

27  16 

29  4 

30  54 

32  45 

34  38 

36  33 

37  31 

38  30 

39  29 

40  29 

41  26 

54 

26  7 

27  58 

29  50 

31  43 

33  38 

35  35 

37  34 

38  34 

39  36 

40  37 

41  40 

42  39 

55 

26  49 

28  43 

30  39 

32  36 

34  35 

36  36 

38  40 

39  43 

40  47 

41  51 

42  56 

43  58 

56 

27  34 

23  32 

31  31 

33  33 

35  3G 

37  42 

39  51 

40  57 

42  4 

43  11 

44  20 

45  24 

57 

28  22 

30  24 

32  28 

34  34 

36  43 

38  54 

41  9 

42  18 

43  27 

44  38 

45  50 

46  59 

58 

29  14 

31  21 

33  2935  4U 

:J7  54 

40  I'J 

42  33 

43  45 

44  59 

46  14 

47  30 

48  43 

59 

30  10 

32  21 

34  35 

36  52 

39  12 

41  37 

14  6 

45  22 

46  40 

47  59 

49  21 

50  38 

60 

31  10 

33  27 

35  41 

38  10 

40  38 

43  10 

45  47 

47  8 

48  31 

49  56 

51  24 

52  47 

61 

32  16 

34  39 

37  5 

39  36 

42  11 

14  52 

47  40 

49  7 

50  36 

52  7 

53  42 

55  13 

62 

33  27 

35  57 

38  31 

41  10 

13  54 

46  46 

49  4G 

51  19 

52  56 

54  36 

56  20 

58  1 

63 

34  45 

37  23 

40  5 

42  54 

45  49 

48  53 

52  8 

53  50 

55  36 

57  27 

59  23 

61  18 

04 

36  11 

38  58 

11  5( 

44  49 

17  58 

51  17 

54  50 

56  44 

58  43 

60  48 

63  2 

65  17 

C5 

37  4( 

40  43'43  4G 

46  59 

50  23 

54  2 

57  59 

60  8 

62  25 

64  53 

67  36 

70  26 

66 

39  31 

12  40'l5  57149  2753  K, 

57  1-1 

61  46 

64  18 

(17  4 

70  12 

73  52 

78  15 

CALENDAR  FOR  1878. 


298 

TABLE  XXI. 

JANUARY,  1878.—  Page  1. 

AT  APPARENT  NOON. 

^ 

y 

£ 

« 
•3 

*o 

* 

ft 

Pay  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
added 
to 
Apparent 
Time. 

Var.    in 
1  hour. 

Apparent 
Right  Ascension 

Var.  in 
1  hour 

Apparent 
Declination. 

Var.  in 
1  hour 

Tuesday  . 
Wednes'y 
Thursday 

1 

2 
3 

h.  m.      s. 
18  47  53.62 
18  52  18.53 
18  56  43.08 

8. 

11.045 
11.030 
11.015 

S.23  0  2'l 
22  54  45.0 
22  49  0.5 

12.64 
13.78 
14.92 

m.      s. 
3  52.25 
4  20.52 
4  48.44 

S. 

1.185 
1.171 
1.155 

Friday.  .. 
Saturday  . 
Sunday  .  . 

4 
5 
6 

19    1    7.24 
19    5  30.97 
19    9  54.23 

10.998 
10.979 
10.959 

22  42  48.7 
22  36  9.9 
22  29  4.2 

16.05 
17.18 
18.29 

5  15.96 
5  43.06 
6    9.69 

1.138 
1.119 
1.100 

Monday  . 
Tuesday  . 
Wedues'y 

7 
8 
9 

19  14  17.01 
19  18  39.26 
19  23    0.96 

10.938 
10.916 
10.892 

22  21  31.9 
22  13  33.2 
22  5  8.4 

19.40 
20.49 
21.57 

6  35.84 

7     1.46 
7  26.54 

1.079 
1.056 
1.033 

Thursday 
Friday  .  .  . 
Saturday  . 

10 
11 
12 

19  27  22.09 
19  31  42.63 
19  36    2.54 

10.868 
10.843 
10.816 

21  56  17.7 
21  47  1.4 
21  37  19.7 

22.65 
23.71 
24.76 

7  51.05 
8  14.95 
8  38.24 

1.009 
0.983 
0.957 

Sunday  .  . 
Monday  . 
Tuesday  . 

13 
14 
15 

19  40*21.81 
19  44^40.41 
19  48  58.34 

10.789 
10.761 
10.732 

21  27  13.0 
21  16  41.5 
21  5  45.6 

25.80 
26.83 
27.83 

9    0.89 
9  22.88 
9  44.19 

0.930 
0.902 
0.873 

Wednes'y 
Thursday 
Friday.  .  . 

1G 
17 
18 

19  53  15.57 
19  57  32.08 
20    1  47.87 

10.703 
10.67b 
10.643 

20  54  25.6 
20  42  41.7 
20  30  34.4 

28.83 
29.82 
30.79 

10    4.80 
10  24.71 
10  43.89 

0.844 
0.814 
0.784 

Saturday  . 
Sunday  .  . 
Monday  . 

19 
20 
21 

20    6    2.93 
20  10  17.24 
20  14  30.80 

10.612 
10.581 
10.549 

20  18  3.9 
20  5  10.5 
19  51  54.6 

31.75 

32.69 
33.62 

11     2.33 
11  20.04 
11  36.99 

0.753 
0.722 
0.690 

Tuesday  . 
Wednes'y 
Thursday 

22 

23 
24 

20  18  43.59 
20  22  55.62 
20  27    6.88 

10.517 
10.485 
10.453 

19  38  16.6 
19  24  16.6 
19  9  55.0 

34.54 
35.45 
36.34 

11  53.18 

12    8.61 
i2  23.28 

0.659 
0.627 
0.595 

Friday.  .  . 
Saturday  . 
Sunday  .  . 

25 
20 

27 

20  31  17.37 

20  35  27.07 
20  39  35.98 

10.421 

10.388 
10.355 

18  55  12.3 

18  40  8.7 
18  24  44.7 

37.21 
38.07 
38.92 

12  37.17 
12  50.2V 
13    2.59 

0.562 
0.5^0 
0.497 

Monday  . 
Tuesday  . 
Wednes'y 
Thursday 

28 
21) 
JU 
31 

20  43  44.10 
20  47  51.41 
20  51  57.91 
20  56     3.59 

10.321 

10.288 
10.254 
10.220 

18  9  0.6 
17  52  56.9 
17  36  34.1 
17  19  52.4 

39.75 
40.55 
41.34 
42.12 

13  14.12 
13  24.85 
13  34.  It 
13  43.87 

0.464 
0.430 
0.396 
0.362 

299 
TABLE  XXI. 

JANUARY,   1878.—  Page  2, 

AT  MEAN  NOON. 

J 

a 

V 

* 

9 
-** 

•M 
o 

* 

O 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equal  ion 
of  Time, 
to  be 
subtracted 
from 
Mean  Time* 

Apparent 
Llight  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

Tuesday  .... 
Wednesday  . 
Thursday  ;  .  . 

Friday  

1 

2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 

18 

19 
20 
21 

22 
23 
24 

25 
26 
27 

28 
29 
30 
31 

h.    m.      s. 
18  47  52.91 
18  52  17.73 
18  56  42.20 

19    1     6.27 
19    5  29.92 
19    9  53.11 

19  14  15.81 
19  18  37.98 
19  22  59,61 

19  27  20.67 
19  31  41.14 
19  36    0.98 

19  40  20.19 
19  44  38.73 
19  48  56.60 

19  63  13.77 

19  57  30.23 
20    1  45.97 

20    6    0.98 
20  10  15.24 
20  14  28.76 

20  18  41.51 
20  22  53.50 
20  27    4.72 

20  31  15.17 

20  35  24.84 
20  39  33.73 

20  43  41.82 
20  47  49.11 
20  51  55.59 
20  56    1.26 

S.23    0'    2".  9 
22  54  46.0 
22  49    1.7 

22  42  50.1 
22  36  11.5 
22  29    6.1 

22  21  34.1 
22  13  35.6 
22    5  11.1 

21  56  20.7 
21  47    4.6 
21  37  23.3 

21  27  16.9 
21  16  45.7 
21     5  5*0.1 

20  54  30.4 
20  42  46.9 
20  30  39.9 

20  18    9.8 
20    5  16.7 
19  52    1.1 

19  38  23.4 
19  24  23.8 
19  10    2.5 

18  55  20.1 
18  40  16.8 
18  24  53.1 

18    9    9.4 
17  53    6.0 
17  36  43.5 
17  20    2.1 

16  18~2 
16  18.2 
16  18.2 

16  18.2 
16  18.2 
16  18.1 

16  18.1 
16  18.1 
16  18.0 

16  18.0 
16  18.0 
16  17.9 

16  17.9 
16  17.8 
16  17.8 

16  17.7 
16  17.6 
16  17.5 

16  17.4 
16  17.3 
16  17.2 

16  17.1 
16  17.0 
16  16.9 

16  16.8 
16  16.6 
16  16.5 

16  16.4 
16  16.2 
16  16.1 
16  15.9 

m.      s. 
3  52.17 
4  20.44 
4  48.35 

5  15.86 
5  42.95 
6    9.58 

6  35.72 
7     1.34 
7  26.41 

7  50.91 
8  14.82 
8  38.10 

9    0.75 
9  22.73 
9  44.04 

10    4  66 
10  24  56 
10  43.75 

11     2.20 
11  19.90 
11  36.85 

11  53.05 
12    8  49 
12  23.16 

12  37.05 
12  50.16 
13    2.49 

13  14.02 
13  24.75 
13  34.68 
13  43.79 

Saturday  .... 
Sunday  

Monday  .... 
Tuesday 
Wednesday  . 

Thursday  .  .  . 
Friday  

Saturday  .... 
Sunday  

Monday  .... 
Tuesday  .... 

Wednesday 
Thursday  .  .  . 
Friday  

Saturday  .... 
Sunday  

Monday  .... 

Tuesday  
Wednesday  . 
Thursday  .  .  . 

Friday.  . 

Saturday  .... 
Sunddy  

Monday  .... 
Tuesday  .... 
Wednesday  . 
Thursday  .  .  . 

300 

TABLE  XXI. 

FEBEUARY,  1878.—  Page  1, 

AT  APPARENT  NOON. 

1 

c 

THE  SUN'S  RIGHT  ASCENSION  AND 

Equation 

£ 

= 

k!-l 

DECLINATION. 

of  Time 

* 

?Z 

O 

to  be 

"*3 

<+-< 
o 
j-^ 

U;. 
^ 

Apparent 

Var.  ii 

Apparent 

Var.  in 

added 
to 
Apparent 

Var.   in 

V 

Right  Ascension 

1   hour 

Declination. 

1  hour 

Time. 

1   hour. 

ft 

ft 

h.    m.       s. 

s. 

O          <         // 

m.       s. 

s. 

Friday.  .  . 

1 

21     0     8.46 

10-186 

S.17     2  52.3 

42.88 

13  52.16 

0.328 

Saturday  . 

o 

/ 

21     4  12.50 

10.151 

16  45  34.4 

43.61 

13  59.62 

0.294 

Sunday  .  . 

r 
O 

21    8  15.71 

10.116 

16  27  58.9 

44.34 

14    6.26 

0.259 

Monday  . 

4 

21  12  18.09 

10.082 

16  10    6.2 

45.04 

14  12.07 

0.225 

Tuesday  . 

^ 

21  16  19.65 

10.048 

15  51  56.9 

45.73 

14  17.06 

0.191 

Wednes'y 

G 

21  20  20.38 

10.013 

15  33  31.3 

46.39 

14  21.22 

0.156 

Thursday 

7 

21  24  20.29 

9.979 

15  14  50.0 

47.04 

14  24.56 

0.122 

Friday.  .  . 

8 

21  28  19.38 

9.945 

14  55  53.3 

47.68 

14  27.09 

0.089 

Saturday  . 

r 

21  32  17.66 

9.912 

14  36  41.6 

48.69 

14  28.82 

0.055 

Sunday  ,  , 

IQ 

21  36  15.14 

9.879 

14  17  15.4 

48.88 

14  29.74 

0.022 

Monday  . 

11 

21  40  11.83 

9.846 

13  57  35.0 

49.47 

14  29.87 

0.011 

Tuesday  . 

12 

21  44    7.73 

9.813 

13  37  41.0 

50.03 

14  29.21 

0.044 

Wednes'y 

13 

21  48    2.85 

9.781 

13  17  33.8 

50.57 

14  27.78 

0.076 

Thursday 

14 

21  51  57.20 

9.749 

12  57  13.8 

51.09 

14  25.58 

0.107 

Friday.  .  . 

15 

21  55  50.80 

9.718 

12  36  41.3 

51.60 

14  22.63 

0.138 

Saturday. 

1C) 

21  59  43.66 

9.688 

12  15  56.8 

52.10 

14  18  95 

0168 

Sunday  .  . 

17 

22    3  35.81 

9.658 

11  55    0.7 

52.58 

14  14.55 

0.198 

Monday  . 

18 

22    7  27.25 

9.629 

11  33  53.2 

53.04 

14    9.45 

0.227 

Tuesday  . 

19 

22  11  18.00 

9.601 

11  12  34.9 

53.48 

14    3.67 

0.225 

Wednes'y 

20 

22  15    8.09 

9.574 

10  51     6.1 

53.91 

13  57.22 

0.282 

Thursday 

21 

22  18  57.53 

9.547 

10  29  27.0 

54.33 

13  50.13 

0.308 

Friday  .  .  . 

22 

22  22  46.35 

9.521 

10    7  38.2 

54.73 

13  42.42 

0.334 

Saturday  . 

23 

22  26  34.57 

9.496 

9  45  39.9 

55.11 

13  34.10 

0.359 

Sunday  .  . 

24 

22  30  22.19 

9.472 

9  23  32.7 

55.48 

13  25.19 

0.383 

Monday  . 

25 

22  34    9.24 

9.449 

9    1  16.9 

55.83 

13  15.71 

0.407 

Tuesday  . 

26 

22  37  55.72 

9.425 

8  38  53.0 

56.16 

13    5.67 

0.430 

Wedues'y 

27 

22  41  41.66 

9.403 

8  16  21.3 

56.47 

12  55.08 

0.452 

Thursday 

28 

22  45  27.07 

9.381 

7  53  42.3 

56.77 

12  43.96 

0.474 

301 

TABLE  XXI. 

FEBRUARY,  1878.—  Page  2. 

AT  MEAN  NOON. 

4J 

"c 

THE  SUN'S  EIGHT  ASCENSION  AND 

$• 

o 

— 

DECLINATION. 

Equation 

0 

0 

of  Time, 

•3 

— 

to  be 

"*^ 

sit  Jjt  TO,  ctcd 

"o 

"o 

Apparent 

Apparent 

Semi- 

from 

c3 

C3 
Q 

Right  Ascension 

Declination. 

diameter. 

Mean  Time. 

h.    m.     s. 

o        /     // 

rn.      s. 

1 

21     0     6.10 

S.17    3    2.3 

16  15''8 

13  52  08 

Saturday  .... 

2 

21     4  10.13 

16  45  44.5 

16  15.6 

13  59.55 

Sunday  

3 

21     8  13.33 

16  28    9.3 

16  15.5 

14     6.19 

Monday  .... 

4 

21  12  15.71 

16  10  16.9 

16  15.3 

14  12.01 

Tuesday  .... 

5 

21  16  17.26 

15  52    7.8 

16  15.2 

14  17.01 

Wednesday  . 

6 

21  20  17.99 

15  33  42.4 

16  15.0 

14  21.18 

Thursday  .  .  . 

7 

21  24  17.90 

15  15     1.3 

16  14.8 

14  24.53 

Friday  .... 

8 

21  28  16.99 

14  56    4.7 

16  14.7 

14  27.07 

Saturday  .... 

9 

21  32  15.27 

14  36  53.2 

16  14.5 

14  28.80 

Sunday  

10 

21  36  12.76 

14  17  27.2 

16  14.3 

14  29.73 

Monday  .... 

11 

21  40    9.45 

13  57  47.0 

16  14.1 

14  29.87 

Tuesday  .... 

12 

21  44    5.36 

13  37  53.1 

16  13.9 

14  29.92 

Wednesday  . 

13 

21  48    0.49 

13  17  46.0 

16  13.7 

14  27.80 

Thursday  .  .  . 

14 

21  51  54.86 

12  57  26.0 

16  13.6 

14  25.61 

Friday  . 

15 

21  55  48.47 

12  36  53.6 

16  13.4 

14  22.67 

Saturday  

16 

21  59  41.35 

12  16    9.2 

16  13.2 

14  18.99 

Sunday  

17 

22     3  33.51 

11  55  13.2 

16  13.0 

14  14.60 

Monday  

18 

22    7  24.97 

11  34    5.8 

16  12.7 

14    9.50 

Tuesday  .... 

19 

22  11  15.75 

11  12  47.5 

16  12.5 

14    3.72 

Wednesday  . 

20 

22  15    5.86 

10  51  18.6 

16  12.3 

13  57.28 

Thursday  .  .  . 

21 

22  18  55.33 

10  29  39.5 

16  12.1 

13  50.20 

Friday   

22 

22  22  44.18 

10    7  50.7 

16  11.8 

13  42.49 

Saturday   .  . 

23 

22  26  32.42 

9  45  52.4 

16  11.6 

13  34.18 

Sunday  

24 

22  30  20.07 

9  23  45.1 

16  11.4 

13  25.28 

Monday  

25 

22  34    7.15 

9    1  29.2 

16  11.1 

13  15.80 

Tuesday  .... 

26 

22  37  53.67 

8  39    5.2 

16  10.9 

13    5.76 

'Wednesday  . 

27 

22  41  39.64 

8  16  33.5 

16  10.6 

12  55.18 

Thursday  .  .  . 

28 

22  45  25.08 

7  53  54.4 

16  10.4 

12  44.07 

302 

TABLE  XXI. 

MARCH,   1878.—  Page  1. 

AT  APPARENT  NOON. 

2 
*o 
P 

1= 

<; 
o 

> 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
added 
to 
Apparent 
Time. 

Var.  in 
1  hour. 

Apparent 
Right  Ascension 

Var.  in 
1  hour 

Apparent 
Declination. 

Var.  in 
1  hour 

Friday  .  .  . 

1 

h.   in.       s. 
22  49  11.96 

S. 

9.360 

S.  7  30  56'  4 

57.05 

m.      s. 
12  32.33 

s. 
0.495 

Saturday  . 
Sunday  .  . 

2 

O 

22  52  56.35 
22  56  40.25 

9.339 
9.319 

7     8    4.0 
6  45     5.6 

57.31 
57.55 

12  20.20 
12    7.58 

0.516 
0.536 

Monday  . 
Tuesday  . 
Wednes'y 

4 

r\ 

G 

23    0  23.68 
23    4    6.66 
23    7  49.20 

9.300 
9.282 
9.264 

6  22    1.5 

5  58  52.2 
5  35  38.0 

57.78 
57.99 
58.18 

11  54.49 
11  40.95 
11  26.98 

0.555 
0.573 
0.591 

Thursday 
Friday  .  .  . 
Saturday  . 

7 

8 

23  11  31.32 
23  15  13.04 
23  18  54.37 

9.247 
9.230 
9.215 

5  12  19.4 
4  48  56.8 
4  25  30.5 

58.36 
58.52 
58.66 

11  12.58 
10  57.79 
10  42.61 

0.608 
0.624 
0.640 

Sunday  .  . 
Monday  . 
Tuesday  . 

10 
11 
1-2 

23  22  35.34 
23  26  15.97 
23  29  56.26 

9.200 
9.18G 
9.172 

4    2    1.0 
3  38  28.7 
3  14  53.9 

58.79 
58.90 
58.99 

10  27.07 
10  11.19 
9  54.97 

0.655 
0.669 
0.682 

Wednes'y 
Thursday 
Friday  .  .  . 

13 
14 

23  33  36.24 
23  37  15.94 
23  40  55.36 

9.160 
9.148 
9.137 

2  51  17.0 
2  27  38.4 
2    3  58.6 

59.07 
5913 
59.18 

9  38.45 
9  21.63 
9     4.55 

0.695 
0.706 
0.717  I 

Saturday  . 
Sunday  .  . 
Monday  . 

1C 
17 

18 

23  44  34.53 
23  48  13  48 
23  51  52.23 

9.127 
9.119 
9.111 

1  40  17.7 
1  16  36.2 
0  52  54.4 

59.22 
5924 
59.24 

8  47.22 
8  29.66 
8  11.90 

0.727 
0.736 
0.744 

Tuesday  . 
Wednes'y 
Thursday 

19 
20 
21 

23  55  30.80 
23  59    9.23 
0    2  47.54 

9.104 

9.099 
9.094 

0  29  12.6 
S.   0    5  31.2 
N.  0  18    9.6 

59.23 
59.21 
59.18 

7  53.97 
7  35.89 
7  17.70 

0.750 
0.756 
0.760 

Friday  .  .  . 
Saturday  . 
Sunday  .  . 

22 
23 
24 

0    6  25.75 
0  10    3.89 
0  13  41.99 

9.091 
9.088 
9.087 

0  41  49.5 
1     5  28.1 
1  29    5.1 

59.14 

59.08 
59.00 

6  59.41 
6  41.05 
6  22.64 

0.764 
0.766 
0.768 

Monday  . 
Tuesday  . 
Wednes'y 

25 

2(5 
27 

0  17  20.05 
0  20  58.10 
0  24  36.16 

9.086 
9.086 
9.086 

1  52  40.0 
216  12.5 
2  39  42.3 

58.90 
58.80 
58.68 

6    4.20 
5  45.75 
5  27.31 

0.769 
0.769 
0.768 

Thursday 
Friday  .  .  . 
Saturday  . 

Sunday  . 

28 
21) 
JO 
Jl 

0  28  14.25 
0  31  52.38 
0  35  30.58 
0  39     8.85 

9.088 
9.090 
9.093 
9.097 

3    3    9.0 
3  26  32.2 
3  49  51.6 
4  13     6.7 

58.54 
58.39 
58.22 
58.03 

5    8.89 
4  50.52 
4  32.21 
4  13.98 

0.766 
0.764 
0.7C1 
0.757 

303 
TABLE  XXI. 

MARCH,   1878.—  Page  2. 

AT  MEAN  NOON. 

* 

o 

•M 

O 

1 

o 
o 

o 

p 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
ot  Time, 
to  be 
subtracted 
from 
Mean  Time. 

Apparent 
light  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

Friday  ..... 

1 

2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
1*7 
18 

19 
20 
21 

22 
23 
24 

25 
26 
27 

28 
29 
30 
31 

h.    m.      s. 
22  49  10.00 
22  52  54.43 
22  56  38.37 

23    0  21.83 
23    4    4.85 
23    7  47.43 

23  11  29.59 
23  15  11.35 
23  18  52.73 

23  22  33.74 
23  26  14.41 
23  29  54.74 

23  33  34.77 
23  37  14.51 
23  40  53.98 

23  44  33.20 
23  48  12.19 
23  51  50.98 

23  55  29.60 
23  59    8.08 
0    2  46.43 

0    6  24.69 
0  10    2.88 
0  13  41.02 

0  17  19.13 
0  20  57.23 
0  24  35.34 

0  28  13.47 
0  31  51.65 
0  35  29.89 
0  39    8.21 

S.  °7  3l'    8.3 
7     8  15.8 
6  45  17.2 

6  22  13.0 
5  69    3.5 
5  35  49.1 

5  12  30.3 
4  49    7.5 
4  25  41.0 

4    2  11.3 
3  38  38.7 
3  15    3.6 

2  51  26.5 
2  27  47.7 
2    4    7.5 

1  40  26.4 
1  16  44.6 
0  53    2.5 

0  29  20.4 
S.   0    5  38.7 
N.  0  18    2.4 

0  41  42.6 
1     5  21.5 
1  28  58.8 

1  52  34.1 
2  16    6.9 
2  39  37.0 

3    3    4.0 
3  26  27.5 
3  49  47.2 
4  13     2.6 

16  I0''l 
16    9.9 
16    9.6 

16    9.4 
16    9.1 
16    8.9 

16    8.6 
16    8.4 
16    8.1 

16    7.9 
16    7.6 
16    7.3 

16    7.1 
16    6.8 
16     6.5 

16    6.3 
16    6.0 
16    5.7 

16    5.5 
16    5.2 
16    4.9 

16    4.7 
16    4.4 
16    4.1 

16    3.8 
16    3.5 
16    3.2 

16    3.0 
16    2.7 
16    2.4 
16    2.1 

in.      s. 
12  32.44 
12  20.31 
12    7.69 

11  54.60 
11  41.06 
11  27.09 

11  12.69 
10  57.90 
10  42.73 

10  27.19 
10  11  30 

9  55.08 

9  38.56 
9  21.74 
9    4.66 

8  47  32 
8  29.76 
8  12.00 

7  54.07 
7  35.99 
7  17.79 

6  59.50 
6  41  13 
6  22.72 

6    4.27 
5  45  82 
5  27.38 

5    8.96 
4  50.58 
4  32.27 
4  14.04 

Saturday  .... 

Monday  
Tuesday 
Wednesday  . 

Thursday  .  .  . 
Friday  

Saturday  .... 
Sunday  

Monday  .... 
Tuesday  .... 

Wednesday 
Thursday  .  .  . 
Friday  

Saturday  
Sunday  

Monday  

Tuesday  
Wednesday  . 
Thursday  .  .  . 

Friday  
Saturday  
Sunday  

Monday  .... 
Tuesday  .... 
Wednesday  . 

Thursday  .  . 
Friday  .  . 

Saturday  .  .  . 
Sunday  

304 

TABLE  XXI. 

APRIL,   1878.—  Page  1. 

AT  APPARENT  NOON. 

« 

i 

o 

o 

!>> 

c5 

ft 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time 
.     to  be 
added  to 

Var.  in 
1  hour. 

Apparent 
Right  Ascension 

Var.  in 
1  hour. 

Apparent 
Declination. 

Var.  in 
1  hour. 

subt.  from 
Apparent 
Time. 

Monday  . 
Tuesday  . 
Wednes'y 

1 

2 
8 

h.    in.       s. 
0  42  47.23 
0  46  25.72 
0  50    4.34 

8. 

9-101 
9.106 
9.112 

N.  4  36  17  '2 
4  59  22.8 
5  22  23.1 

57.84 
57.62 
57.39 

m.      s. 
3  55.85 
3  37.84 
3  19.95 

8. 

0.753 
0.748 
0.742 

Thursday 
Friday  .  .  . 

4 
5 

0  53  43.11 
0  57  22.04 

9.119 
9.126 

5  45  17.7 
6    8    6.2 

57.15 

56.89 

3     2.22 
2  44.65 

0.735 

0.728 

Saturday  . 

e 

1     1    1.16 

9.134 

6  30  48.3 

56.61 

2  27.26 

0.720 

Sunday  .  . 
Monday  . 
Tuesday  . 

7 
8 
9 

1    4  40.47 
1     8  20.00 
1  11  59.75 

9.143 
9.152 
9.161 

6  53  23.7 

7  15  52.0 
7  38  12.8 

56.33 
56.02 
55.70 

2  10.07 
1  53.08 
1  36.33 

0.712 
0.703 
0.693 

Wednes'y 
Thursday 
Friday.  .  . 

to 

11 
12 

1  15  39.74 
1  19  19.99 
1  23    0.50 

9.172 
9.182 
9.194 

8    0  25.7 
8  22  30.'4 
8  44  26.7 

55.36 
55.02 
54.66 

1  19.81 
1     3.55 
0  47.55 

0.683 
0.672 
0.661 

Saturday. 
Sunday  .  . 
Monday  . 

Tuesday  . 
Wednes'y 
Thursday 

13 

14 
15 

1G 
17 

18 

1  26  41.30 
1  30  22.41 
1  34    3.84 

1  37  45.62 
1  41  27.77 
1  45  10.30 

9.206 
9.220 
9.234 

9.249 
9.264 
9.281 

9    6  14.1 
9  27  52.4 
9  49  21.2 

10  10  40  2 
10  31  49.2 
10  52  47.8 

54.29 
53.90 
53.50 

53.08 
52.66' 
52.22 

0  31.84 
0  16.44 
0    1.36 

0.648 
0.635 
0.621 

0606 
0.591 
0.574 

0  13  38 
0  27.75 
0  41.73 

Friday  .  .  . 
Saturday  . 

19 

20 

1  48  53.24 
1  52  36.61 

9.298 
9.316 

11  13  35.9 
11  34  13.0 

51.77 
51.31 

0  55.31 
1     8.46 

0.557 
0.539 

Sunday  .  . 

21 

1  56  20.42 

9.335 

11  54  38  8 

50.84 

1  21.17 

0.520 

Monday  . 
Tuesday  . 
Wedues'y 

22 
23 
24 

2    0    4.69 
2    3  49.42 
2    7  34.63 

9.354 
9.374 
9.394 

12  14  53.1 
12  34  55.4 
12  54  45.5 

50.35 
49.85 
49.33 

1  33  43 
1  45.22 
1  56.53 

0.501 

0.481 
0.461 

Thursday 
Friday  .  .  . 
Saturday  . 

25 

20 
27 

2  11  20.34 
2  15    6.55 
2  18  53.26 

9.415 
9.436 
9.457 

13  14  23.0 
13  33  47.5 
13  52  58.7 

48.79 
48.24 
47.69 

2    7.35 
2  17.67 

2  27.48 

0.440 
0.419 
0.398 

Sunday  .  . 
Monday  . 
Tuesday  . 

2H 
21) 
30 

2  22  40.50 
2  26  28.27 
2  30  16.57 

9.479 
9.501 
9.524 

14  11  56.4 
14  30  40.0 
14  49    9.4 

47.11 
46.52 
45.92 

2  36.77 
2  45.53 
2  53.76 

0.376 
0.354 
0.332 

305 
TABLE  XXI. 

APRIL,  1878.—  Pages. 

AT  MEAN  NOON. 

i 

u 

* 

0 

£ 

-u 

•3 

>> 
a 
Q 

Day  of  the  Month. 

THE  SUN'S  EIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
subtracted 
from 

Apparent 
Right  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

added  to 
Mean  Time. 

Monday  .... 
Tuesday  .... 
Wednesday  . 

Thursday  .  .  . 
Friday  

1 
2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 

18 

19 
20 
21 

22 
23 
24 

25 
26 

27 

28 
29 
30 

h.    m.     s. 
0  42  46.63 
0  46  25.16 
0  50    3.83 

0  53  42.65 
0  57  21.63 
1    1     0.79 

1    4  40.14 
1     8  19.71 
1  11  59.50 

1  15  39.54 
1  19  19.83 
1  23    0.38 

1  26  41.22 
1  30  22.37 
1  34    3.84 

1  37  45.66 
1  41  27.84 
1  45  10.41 

1  48  53.39 
1  52  36.79 
1  56  20.63 

2    0    4.93 
2    3  49.69 
2    7  34.94 

2  11  20.67 
2  15    6.91 
2  18  53.65 

2  22  40.92 
2  26  28.71 
2  30  17.03 

N.  °4  36  13.4 
4  59  19.3 
5  22  19.9 

5  45  14.8 
6    8    3.6 
6  30  46.0 

6  53  21.7 
7  15  50.3 
7  38  11.3 

8    0  24.5 
8  22  29.5 
8  44  26.0 

9    6  13.6 
9  27  52.1 
9  49  21.1 

10  1.0  40.4 
10  31  49.6 
10  52  48.4 

11  13  36.7 
11  34  14.0 
11  54  40.0 

12  14  54.4 
12  34  56.9 
12  54  47.1 

13  14  24.7 
13  33  49.3 
13  53    0.7 

14  11  58.4 
14  30  42.2 
14  49  11.6 

16     l.S 
16    1.6 
16    1.3 

16    1.0 
16    0.7 
16    0.5 

16    0.2 
15  59.9 
15  59.7 

15  59.4 
15  59.1 
15  58.9 

15  58.6 
15  58.3 
15  58.1 

15  57.8 
15  57.6 
15  57,3 

15  57.0 
15  56.8 
15  56.5 

15  56.2 
15  56.0 
15  55.7 

15  55.5 
15  55.2 
15  55.0 

15  54.7 
15  54.5 
15  54.2 

m.     s. 
3  55.90 
3  37.88 
3  19.99 

3     2.25 
2  44.68 
2  27.29 

2  10.09 
1  53.10 
1  36.34 

1  19.82 
1     3.56 
0  47.56 

0  31.85 
0  16.44 
0     1.36 

Saturday  .... 
Sunday  

Monday  .... 
Tuesday  .... 

Wednesday  . 
Thursday  .  .  . 
Friday  

Saturday  .... 
Sunday  

Monday  

Tuesday  .... 
Wednesday  . 
Thursday  .  .  . 

Friday  

0  13.38 

0  27.76 
0  41.74 

0  55.32 
1     8.47 
1  21.18 

1  33.44 
1  45.23 
1  56.54 

2    7.36 
2  17.68 
2  27.49 

2  36.78 
2  45.55 
2  53.78 

Saturday  .  .  . 
Sunday  

Monday  .... 
Tuesday  .... 
Wednesday  . 

Thursday  .  .  . 
Friday  

Saturday  .... 
Sunday  

'  Monday  .... 
Tuesday  .... 

306 

TABLE  XXI. 

MAY,    1878.—  Page  1. 

AT  APPARENT  NOON. 

V 

9 

O 

Q 

c 

X 

M- 

z 
> 

c; 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
subtracted 
from 
Apparent 
Time. 

Var.  in 
1  hour. 

Apparent 
Right  Ascension 

Var.  in 
1  hour 

Apparent 
Declination. 

Var.  in 
1  hour 

Wednes'y 
Thursday 
Friday  .  .  . 

1 

9 

r 

h.  m.      s. 
2  34    5.42 
2  37  54.81 
2  41  44.76 

s. 
9.547 
9.570 
9.593 

m.       s. 

S. 

0.309 
0.286 
0.263 

N.15  7  24.1 
15  25  23.9 
15  43  8.5 

45.29 
44.67 
44.03 

3     1.45 
3    8.59 
3  15.19 

Saturday  . 
Sunday  .  . 
Monday  . 

4 

5 
6 

2  45  35.26 
2  49  26.31 
2  53  17.91 

9.616 
9.639 
9.662 

16  0  37.4 
16  17  50.3 
16  34  47.0 

43.37 
42.70 
42.02 

3  21.23 
3  26.72 
3  31.65 

0.240 
0.217 
0.194 

Tuesday  . 
Wednes'y 
Thursday 

7 

8 
c 

2  57  10.07 
3     1     2.79 
3    4  56.06 

9.685 
9.708 
9.731 

16  51  27.1 

17  7  50.3 
17  23  56.4 

41.32 
40.61 
39.89 

3  36.04 
3  39.87 
3  43.15 

0.171 
0.148 
0.125 

Friday.  .  . 
Saturday  . 
Sunday  .  . 

10 
11 
12 

3    8  49.88 
3  12  44.25 
3  16  39.17 

9.754 
9.777 
9.800 

17  39  44.9 
17  55  15.7 
18  10  28.3 

39.15 
38.40 
37.64 

3  45.87 
3  48.06 
3  49.69 

0.102 
0.080 
0.056 

Monday  . 
Tuesday  , 
Wednes'y 

13 
14 
15 

3  20  34.  G5 
3  24  30.70 
3  28  27.31 

9.824 
9.847 
9.870 

18  25  22.6 
18  39  58.4 
18  54  15.3 

36.88 
3610 
35.31 

3  50.76 
3  51.27 
3  51.22 

0.033 
0.010 
0.014 

Thursday 
Friday  .  .  . 
Saturday  . 

1C 
17 

18 

3  32  24.48 
3  36  22  23 
3  40  20.54 

9.894 
9.918 
9.941 

19  8  13.1 
19  21  51.6 
19  35  10.5 

34.51 
33.70 
32.87 

3  50.60 
3  49.41 
3  47.66 

0.038 
0.061 
0.085 

Sunday  .  . 
Monday  . 
Tuesday  . 

19 
20 
21 

3  44  19.42 
3  48  18.86 
3  52  18.86 

9.965 
9.988 
10.012 

19  48  9.5 
20  0  48.4 
20  13  7.0 

32.04 
31.20 
30.34 

3  45.35 
3  42.47 
3  39.04 

0.108 
0.131 
0.155 

Wednes'v 

22 

3  56  19.42 

10.035 

20  25  4.9 

29.48 

3  35.05 

0.178 

Thursday 
Friday  .  .  . 

23 
24 

4    0  20.52 
4    4  22.15 

10.057 
10.079 

20  36  42.0 
20  47  57.9 

28.60 
27.72 

3  30.52 
3  25.46 

0.200 
0.222 

Saturday  . 
Sunday  .  . 
Monday  . 

25 
27 

4    8  24.31 
4  12  26.98 
4  16  30.17 

10.101 
10.122 
10.143 

20  58  52.4 
21  9  25.3 
21  19  36.3 

26.82 
25.91 
25.00 

3  19.87 
3  13.76 
3    7.15 

0.244 
0.265 
0.286 

Tuesday  . 
Wedues'y 
Thursday 
Friday  .  .  . 

28 
29 
3, 
Jl 

4  20  33.86 
4  24  38.01 
4  28  42.62 
4  32  47.68 

10.163 

10.182 
10.201 
10.220 

21  29  25.3 
21  38  51.9 
21  47  56.1 
21  56  37.5 

24.08 
23.14 
22.20 
21.25 

3    0.05 
2  52.48 
2  44.45 
2  35.97 

0.306 
0.325 
0.344 
0.362 

307 
TABLE  XXI. 

MAY,   1878.—  Page  2, 

AT  MEAN  NOON. 

4 

0 

£ 

0 

3 

*o 
* 

n 

Day  of  the  Month. 

THE  SUM'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
added 
to 
Mean  Time. 

Apparent 
Right  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

"Wednesday 
Thursday  .  .  . 
Friday  

1 
2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 

18 

19 
20 
21 

22 
23 
24 

25 
20 
27 

28 
29 
30 
31 

h.    m.      s. 
2  34    5.90 
2  37  55.31 
2  41  45.28 

2  45  35.79 

2  49  26.8G 
2  53  18.48 

2  57  10.65 
3    1     3.38 
3    4  56.66 

3    8  50.49 
3  12  44.86 
3  16  39.79 

3  20  35.28 
3  24  31.33 
3  28  27.94 

3  32  25.11 
3  36  22.86 
3  40  21.17 

3  44  20.04 
3  48  19.48 
3  52  19.47 

3  56  20.02 
4    0  21.11 
4    4  22.73 

4    8  24.87 
4  12  27.53 
4  16  30.70 

4  20  34.36 
4  24  38.49 
4  28  43.09 
4  32  48.12 

N.15     i  26".  4 
15  25  26.3 
15  43  10.9 

16    0  39.8 
16  17  52.8 
16  34  49.5 

16  51  29.6 
17     7  52.8 
17  23  58.9 

17  39  47.4 
17  55  18.1 
18  10  30.7 

18  25-25.0 
18  40    0.7 
18  54  17.5 

19    8  15.3 
19  21  53.7 
19  35  12.5 

19  48  11.5 
20    0  50.4 
20  13    8.9 

20  25     6.7 
20  36  43.7 
20  47  59.5 

20  58  53.9 
21     9  26.7 
21  19  37.6 

21  29  26.5 
21  38  53.0 
2L  47  57.1 
21  56  38.5 

15  54~0 
15  53.7 
15  53.5 

15  53.3 
15  53.1 
15  52.8 

15  52.6 
15  52.4 
15  52.2 

15  52.0 
15  51.8 
15  51.6 

15  51.4 
15  51.2 
15  51.0 

15  50.8 
15  50.6 
15  50.4 

15  50.2 
15  50.0 
15  49.9 

15  49.7 
15  49.5 
15  49.3 

15  49.2 
15  49.0 
15  48.8 

15  48.7 
15  48.5 
15  48.4 
15  48.2 

m.      s. 
3    1.46 
3    8.61 
3  15.20 

3  21.24 
3  26.73 
3  31.67 

3  36.05 
3  39.88 
3  43.16 

3  45.88 
3  48.06 
3  49.69 

3  50.76 
3  51.27 
3  51.21 

3  50  60 
3  49.41 
3  47.66 

3  45.34 
3  42.46 
3  39.03 

3  35.04 
3  30  51 
3  25.44 

3  19.85 
3  13.75 
3    7.14 

3    0.04 
2  52.47 
2  44.43 
2  35.96 

Saturday  
Sunday  

Monday  

Tuesday  .... 
Wednesday  . 
Thursday  .  .  . 

Friday  .  . 

Saturday  .... 
Sunday  

Monday  .... 
Tuesday 
Wednesday  . 

Tluirsday  .  .  . 
Friday  

Saturday  .... 
Sunday  

Monday  .... 
Tuesday  .... 

Wednesday  . 
Thursday  .  .  . 
Fiiday  

Saturday  .... 
Sunday  

Monday  .... 

Tuesday  .... 
Wednesday  . 
Thui'sday  .  .  . 
Friday  

308 

TABLE  XXI. 

JUNE,   1878.—  Page  1. 

AT  APPARENT  NOON. 

1 
g 

c8 
P 

S 

c 

0 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time 
to  be 
subt.  from 

Var.  in 
1  hour. 

IE 

Apparent 
light  Ascension 

Var.  in 
1  hour. 

Apparent 
Declinati'on. 

Var.  in 

1  hour. 

added  to 
Apparent 
Time. 

Saturday  . 
Sunday  .  . 
Monday  . 

1 
2 
3 

h.    m.       s. 
4  36  53.16 
4  40  59.04 
4  45     5.30 

S. 
10.237 
10.253 
10.268 

N.2°2  4  56'  1 
22  12  51.5 
22  20  23.7 

20.29 
19.32 
18.35 

m.      s. 
2  27.07 
2  17.78 
2    8.10 

s. 
0.379 
0.395 
0.411 

Tuesday  . 
Wednes'y 
Thursday 

4 
5 

0 

4  49  11.92 
4  53  18.87 
4  57  26.13 

10.283 
10.296 
10.308 

22  27  32.4 
22  34  17.6 
22  40  39.1 

17.37 
16.39 
15.40 

1  58.07 
1  47.70 
1  37.03 

0.425 
0.438 
0.451 

Friday  .  .  . 
Saturday  . 

7 
8 

5     1  33.67 
5     5  41.48 

10.320 
10.331 

22  46  36.6 
22  52  10.1 

14.40 
13.40 

1  26.07 
1  14.85 

0.462 
0.473 

Sunday  .  . 

c 

5    9  49.54 

10.341 

22  57  19.6 

12.39 

1     3.38 

0.483 

Monday  . 
Tuesday  . 
Wedues'y 

10 
11 
12 

5  13  57.83 
5  18    6.33 
5  22  15.03 

10.350 
10.358 
10.366 

23  2  4.8 
23  6  25.7 
23  10  22.3 

11.38 
10.36 
9.35 

0  51.68 
0  39.77 
0  27.67 

0.492 
0.500 
0.508 

Thursday 
Friday  .  .  . 
Saturday  . 

13 
14 
15 

5  26  23.90 
5  30  32.92 
5  34  42.09 

10.373 
10.379 
10.385 

23  13  54.5 
23  17  2.1 
23  19  45.1 

8.33 
7.30 
6.28 

0  15.39 
0    2.96 

0.515 
0.521 
0.526 

0    9.62 

Sunday  .  . 
Monday  . 
Tuesday  . 

10 
17 

18 

5  38  51.38 
5  43    0.76 
5  47  10.23 

10.389 
10.393 
10.396 

23  22  3.5 
23  23  57.3 
23  25  26.4 

5.25 
4.23 
3.19 

0  22  31 
0  35.10 
0  47.97 

0531 
0.535 
0.537 

Wednes'y 
Thursday 
Friday  .  .  . 

19 
2( 
21 

5  51  19.75 
5  55  29.31 
5  59  38.88 

10.398 
10.399 
10.399 

23  26  30.6 
23  27  10.1 
23  27  24.7 

2.16 
1.13 
0.09 

1    0.90 
1  13.86 
1  26.84 

0.539 
0.540 
0.541 

Saturday 
Sunday  .  . 
Monday 

ir 

2, 

6    3  48.45 
6     7  57.98 
6  12    7.47 

10.398 
10.397 
10.394 

23  27  14.5 
23  26  39.5 
23  25  39.6 

0.94 

1.98 
3.01 

1  39  81 
1  52.76 
2    5.65 

0.540 
0.538 
0.535 

Tuesday 
Wednes'y 
Thursday 

25 
21 
•2" 

6  16  16.88 
6  20  26.18 
6  24  35.36 

10.390 
10.385 
10.379 

23  24  15.0 
23  22  25.6 
23  20  11.5 

4.04 
5.07 
6.10 

2  18.  4G 
2  31.1" 

2  43.  7G 

0.532 
0.527 
0.521 

Friday  .  . 
'  Saturday 

Sunday  . 

2S 
2! 
3( 

6  28  44.39 
6  32  53.25 
6  37     1.90 

10.373 
10.365 
10.356 

23  17  32.7 
23  14  29.4 
23  11  1.0 

7.13 

8.15 
9.17- 

2  56.20 
3     8.4f 
3  20.52 

0.515 

0.507 
0.498 

309 
TABLE  XXI. 

JUNE,   1878.—  Page  2, 

AT  MEAN  NOON. 

3 

• 

* 
<» 
£ 
-u 

"8 

i- 

Q 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
added  to 

Apparent 
Right  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

subtracted 
from 
Mean  Time. 

Saturday  .... 
Sunday  

1 
2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 
18 

19 
20 
21 

22 
23 
24 

25 
26 

27 

28 
29 
30 

h.    m.      s. 
4  36  53.57 
4  40  59.43 
4  45    5.67 

4  49  12.26 
4  53  19.18 
4  57  26.40 

5     1  33.92 
5    5  41.70 
5    9  49.73 

5  13  57.98 
5  18    6.45 
5  22  15.11 

5  26  23.94 
5  30  32.93 
5  34  42.06 

5  38  51.31 

5  43    0.66 
5  47  10.09 

5  51  19.57 
5  55  29.09 
5  59  38.63 

6    3  48.16 
6    7  57.66 
6  12     7.11 

6  16  16.48 
6  20  25.75 
6  24  34.89 

6  28  43.89 
6  32  52.71 
6  37     1.32 

N.22    i  56.9 
22  12  52.3 
22  20  24.4 

22  27  33.0 
22  34  18.1 
22  40  39.5 

22  46  37.0 
22  52  10.4 
22  57  19.8 

23    2    5.0 
23     6  25.9 
23  10  22.4 

23  13  54.5 
23  17    2.1 
23  19  45.1 

23  22    3.5 
23  23  57.3 
23  25  26.3 

23  26  30.6 
23  27  10.1 
23  27  24.7 

23  27  14.5 
23  26  39.5 
23  25  39.7 

23  24  15.1 
23  22  25.8 
23  20  11.8 

23  17  33.1 
23  14  29.8 
23  11     2.1 

15  48~1 
15  48.0 
15  47.9 

15  47.7 
15  47.6 
15  47.5 

15  47.4 
15  47.3 
15  47.2 

15  47.1 
15  47.0 
15  46.9 

15  46.8 
15  46.7 
15  46.6 

15  46.6 
15  46.5 
15  46.5 

15  46.4 
15  46.3 
15  46.3 

15  46.2 
15  46.2 
15  46.1 

15  46.1 
15  46.1 
15  46.0 

15  46.0 
15  46.0 
15  46.0 

m.     s. 
2  27.06 
2  17.76 
2    8.08 

1  58.05 
1  47.69 
1  37.02 

1  26.06 
1  14.84 
1    3.37 

0  51.68 
0  39.77 
0  27.67 

0  15.39 

0    2.96 

Monday  

Tuesday  .... 
Wednesday  . 
Thursday  .  .  . 

Friday.  . 

Saturday  .  .  . 
Sunday  

Monday  
Tuesday  .... 
Wednesday  . 

Thursday  .  .  . 
Friday  

Saturday  
Sunday  

0     9.62 

0  22.31 
0  35.10 
0  47.96 

1    0.89 
1  13.85 
1  26.83 

1  39.80 
1  52.74 
2    5.63 

2  18.44 
2  31.15 
2  43.74 

2  56.18 
3    8.44 
3  20.50 

Monday  
Tuesday  

Wednesday  . 
Thursday  .  .  . 
Friday  

Saturday  
Sunday  

Monday  .... 

Tuesday  .... 
Wednesday  . 
Thursday  .  .  . 

Friday  

Saturday  .... 
Sunday  

310 

TABLE  XXI. 

JULY,   1878.—  Page  1. 

AT  APPARENT  NOON. 

jj 

o 
o 

£ 

« 

HJ 

'o 

fr 

p 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
added 
to 
Apparent 
Time. 

Var.  in 
1  hour. 

Apparent 
Right  Ascension 

Var.  in 
1  hour. 

Apparent 
Declination. 

Var.  in 
1  hour 

Monday  . 
Tuesday  . 
Wednes'y 

1 
2 
3 

h.   m.      s. 
6  41  10.32 
6  45  18.47 
6  49  26.33 

s. 
10.345 
10.331 
10.321 

N.23  7  9'  4 
23  2  53.0 
22  58  12.4 

10.18 
11.19 
12.19 

m.      s. 
3  32.35 
3  43.91 
3  55.18 

S. 

0.487 
0.476 
0.463 

Thursday 

4 

6  53  33.88 

10.307 

22  53  7.7 

13.19 

4    6.14 

0.450 

Friday  .  .  . 
Saturday  . 

5 

G 

6  57  41.09 
7     1  47.94 

10.293 
10.278 

22  47  39.2 
22  41  46.9 

14.18 
15.17 

4  16.77 
4  27.03 

0.435 
0.420 

Sunday  .  . 
Monday  . 
Tuesday 

7 
8 
9 

7     5  54.41 
7  10    0.48 
7  14    6.14 

10.261 
10.244 
10.227 

22  35  31.0 
22  28  51.7 
22  21  49.3 

16.15 
17.12 

18.09 

4  36.91 
4  46.40 
4  55.48 

0.404 
0.387 
0.369 

Wednes'v 

10 

7  18  11.37 

10.209 

22  14  23.5 

19.05 

5    4.13 

0.351 

Thursday 
Friday.  .  . 

11 

12 

7  22  16.16 
7  26  20.50 

10.190 
10.171 

22  6  35.0 
21  58  23.7 

20.00 
20.94 

5  12.34 
5  20.10 

0.333 
0.314 

Saturday  . 
Sunday  . 
Monday  . 

13 
11 
15 

7  30  24.37 

7  34  27.77 
7  38  30.67 

10.151 
10.131 
10.110 

21  49  49.9 
21  40  53.7 
21  31  35.3 

21.87 
2280 
23.72 

5  27.39 
5  34.21 
5  40.54 

0.294 
0.274 
0.253 

Tuesday  . 
Wedues'y 
Thursday 

10 
17 
Ib 

7  42  33.07 
7  46  34.96 
7  50  36.34 

10.089 
10.068 
10.047 

21  21  55.0 
21  11  52.8 
21  1  29.1 

24.64 
25.54 
26.43 

5  46.37 
5  51.69 
5  56.49 

0.232 
0.211 
0.189 

Friday  .  .  . 
Saturday  . 
Sunday  .  . 

ID 
20 
21 

7  54  37.20 
7  58  37.52 
8    2  37.30 

10.025 
10.002 
9.979 

20  50  44.0 
20  39  37.7 
20  28  10.6 

27.32 

28.20 
29.06 

6    0.78 
6    4.53 
6    7.74 

0.167 
0.145 
0.122 

Monday  . 
Tuesday  . 
Wednes'y 

22 
23 
21 

8    6  36.53 
8  10  35.21 
8  14  33.33 

9.957 
9.933 
9.910 

20  16  22.7 
20  4  14.3 
19  51  45.7 

29.92 
30.77 
31.61 

6  10.41 
6  12.53 
6  14  09 

0.100 
0.077 
0.053 

Thursday 
Friday  .  .  . 
Saturday  . 

25 
2G 
27 

8  18  30.89 
8  22  27.87 
8  26  24.27 

9.886 
9.862 
9.838 

19  38  57.2 
19  25  49.0 
19  12  21.4 

32.43 
33.25 
34.05 

6  15.09 
6  15.51 
6  15.36 

0.030 
0.006 
0.019 

Sunday  .  . 
Monday  . 
Tuesday  . 
Wednes'y 

28 
2!) 
3 
31 

8  30  20.08 
8  34  15.30 
8  38    9.91 
8  42    3.90 

9.813 
9.788 
9.  762 
9.737 

18  58  34.6 
18  44  29.1 
18  30  5.1 
18  15  22.8 

34.84 
35.61 
36.38 
37.14 

6  14.61 
6  13.27 
6  11.33 

6     8.77 

0.044 
0.068 
0.094 
0.119 

311 
TABLE  XXI. 

JULY,   1878.—  Page  2. 

AT  MEAN  NOON. 

Day  of  the  Week. 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
subtracted 
from 
Mean  Time. 

Apparent 
Right  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

Monday  .... 
Tuesday  .... 
Wednesday  . 

Thursday  .  .  . 
Friday  

1 

2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 

18 

19 
20 
21 

22 
23 
24 

25 
26 
27 

28 
29 
30 
31 

h.    m.      s. 
6  41     9.71 
6  45  17.83 
6  49  25.66 

6  53  33.17 
6  57  40.35 
7    1  47.17 

7    5  53.61 
7    9  59.66 
7  14    5.30 

7  18  10.51 
7  22  15.28 
7  26  19.60 

7  30  23.45 
7  34  26.82 
7  38  29.71 

7  42  32.10 
7  46  33.98 
7  50  35.35 

7  54  36.19 
7  58  36.50 
8    2  36.28 

8    6  35.51 
8  10  34.18 
8  14  32.30 

8  18  29.86 
8  22  26.84 
8  26  23.25 

8  30  19.06 
8  34  14.28 
8  38    8.90 
8  42    2.90 

N.23    1  id'.O 
23    2  53.7 
22  58  13.2 

22  53    8.6 
22  47  40.2 
22  41  48.1 

22  35  32.3 
22  28  53.1 
22  21  50.7 

22  14  25.1 
22    6  36.7 
21  58  25.5 

21  49  51.8 
21  40  55.8 
21  31  37.6 

21  21  57.4 
21  11  55.3 
21    1  31.7 

20  50  46.7 
20  39  40.6 
20  28  13.5 

20  16  25.7 
20    4  17.5 

19  51  49.0 

19  39    0.6 
19  25  52.5 
19  12  24.9 

18  58  38.3 
18  44  32.8 
18  30    88 
18  15  26.6 

15  4G"0 
15  46.0 
15  46.0 

15  46.0 
15  46.0 
15  46.0 

15  46.0 
15  46.1 
15  46.1 

15  46.1 
15  46.2 
15  46.2 

15  46.3 
15  46.3 
15  46.4 

15  46.4 
15  46.5 
15  46.5 

15  46.6 
15  46.7 
15  46.7 

15  46.8 
15  46.9 
15  47.0 

15  47.1 
15  47.2 
15  47.3 

15  47.4 
15  47.5 
15  47.6 
15  47.7 

m.      s. 
3  32.32 
3  43.88 
3  55.15 

4    6.11 
4  16.73 
4  27.00 

4  36.88 
4  46.37 
4  55.45 

5    4.10 
5  12  31 
5  20.07 

5  27.37 
5  34.18 
5  40.51 

5  46  34 
5  51.66 
5  56.47 

6    0.76 
6    4.51 
6    7.73 

6  10.40 
6  12.52 
6  14.08 

6  15.08 
6  15.51 
6  15.36 

6  14.62 
6  18.28 
6  11.  ;U 
6    8.78 

Saturday  
Sunday  

Monday  .... 
Tuesday  .... 

Wednesday  . 
Thursday  .  .  . 
Friday  

Saturday  .... 
Sunday  
Monday  .... 

Tuesday  
Wednesday  . 
Thursday  .  .  . 

Friday  .  . 

Saturday  .... 
Sunday  

Monday  .... 
Tuesday  .... 
Wednesday 

Thursday  .  .  . 
Friday  

Saturday  
Sunday  

Monday  .... 
Tuesday  .... 
Wednesday  . 

312 

TABLE  XXI. 

AUGUST,   1878.—  Page  1, 

AT  APPARENT  NOON. 

J 

O> 
0> 

£ 

0 

"8 

£ 
ft 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time 
to  be 
added  to 

Var.  in 

1  hour. 

Apparent 
irlight  Ascension 

Var.  in 
1  hour. 

Apparent 
Declination. 

Var.  in 
1  hour. 

sitbt.  from 
Apparent 
Time. 

Thursday 
Friday  .  .  . 
Saturday  . 

1 
2 
3 

h.    m.       s. 
8  45  57.27 
8  49  50.02 
8  53  42.15 

S. 

9.711 
9.685 
9  659 

X.18     0  22  '6 
17  45    4.8 
17  29  29.8 

37.88 
38.60 
39.31 

m.       s. 
6     5.60 
6    1.80 
5  57.39 

8. 

0.145 
0.171 
0.197 

Sunday  .  . 
Monday  . 
Tuesday  . 

4 

5 
0 

8  57  33.66 
9    1  24.55 
9    5  14.83 

9.633 
9.608 
9.582 

17  13  37.8 
16  57  29.1 
16  41     4.1 

40.01 
40.70 
41.38 

5  52.36 
5  46.70 
5  40.44 

0.223 
0.248 
0.274 

Wednes'y 
Thursday 
Friday  .  .  . 

7 
8 

9 

9    9    4.49 
9  12  53.55 
9  16  42.01 

9.557 
9.532 
9.507 

16  24  23.0 
16     7  26.1 
15  50  13.8 

42.04 
42.69 
43.33 

5  33.57 
5  26.09 
5  18.02 

0.299 
0.324 
0.349 

Saturday  . 
Sunday  .  . 
Monday  . 

LO 

11 
12 

9  20  29.88 
9  24  17.16 
9  28    3.88 

9.482 
9.458 
9.435 

15  32  46.4 
15  15    4.0 
14  57     7.1 

43.95 
44.57 
45.17 

5    9.35 
5    0.11 
4  50.29 

0.373 

0.397 
0.421 

Tuesday  . 
Wednes'y 
Thursday 

13 
14 
15 

9  31  50.03 
9  35  35.63 
9  39  20.70 

9.411 

9.389 
9.367 

14  38  55.8 
14  20  30.6 
14    1  51.6 

45.76 
46.34 
46.90 

4  39.92 
4  29.00 
4  17.54 

0.444 
0.466 

0.488 

Friday.  .  . 
Saturday  . 
Sunday  .  . 

1(5 
17 
18 

9  43    5.25 

9  46  49.28 
9  50  32.82 

9.345 
9.324 
9.304 

13  42  59  2 
13  23  53.6 
13    4  35.2 

47.46 
48.00 
48.53 

4    5  56 
3  53.08 
3  40.10 

0510 
0.530 
0.551 

Monday  . 
Tuesday  . 
Wedues'y 

19 

20 
21 

9  54  15.88 
9  57  58.47 
10    1  40.60 

9.284 
9.265 
9.246 

12  45    4.1 
12  25  20.8 
12    5  25.7 

49.05 
49.55 
50.04 

3  26.64 
3  12.71 

2  58  33 

0.571 

0.590 
0.609 

Thursday 
Friday.  .  . 
Saturday  . 

22 
23 
24 

10    5  22.29 
10    9    3.55 
10  12  44.39 

9.228 
9.210 
9.193 

11  45  18.9 
11  25    0.8 
11    4  31.7 

50.52 
50.98 
51.43 

2  43  50 
2  28.25 
2  12.58 

0.627 
0.644 
0.661 

Sunday  .  . 
Monday  . 
Tuesday  . 

25 
26 
27 

10  16  24.82 
10  20    4.86 
10  23  44.51 

9.176 
9.160 
9.144 

10  43  52.0 
10  23     2.0 
10    2    2.1 

51.87 
52.29 
52.70 

1  56.50 
1  40.02 
1  23.16 

0.678 
0.695 
0.710 

Wednes'y 
Thursday 
Friday.  .  . 
Saturday. 

28 
29 
30 
31 

10  27  23.78 
10  31     2.69 
10  34  41.24 
10  38  19.46 

9.129 
9.114 

9.099 
9.086 

9  40  52.6 
9  19  33.8 
8  58     6.1 
8  36  30.0 

53.09 
53.47 
53.83 
54.18 

1    5.93 
0  48.33 
0  30.38 
0  12.09 

0.726 
0.741 
0.755 
0.769 

313 
TABLE  XXI. 

AUGUST,   1878.—  Page  2, 

AT  MEAN  NOON. 

O 
0 

"8 

Q 

*3 

d 

0 
« 

c8 

ft 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
subtracted 
from 

Apparent 
Right  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

added  to 
Mean  Time. 

Thursday  .  .  . 
Friday  .... 
Saturday  .... 

Sunday  .... 

1 

2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 

18 

19 
20 
21 

22 

23 
24 

25 
26 

27 

28 
29 
30 
31 

h.    m.     s. 
8  45  56.29 
8  49  49.05 
8  53  41.20 

8  57  32.72 
9    1  23.63 
9    5  13.92 

9    9    3.61 
9  12  52.69 
9  16  41.17 

9  20  29.06 
9  24  16.37 
9  28    3.12 

9  31  49.30 
9  35  34.93 
9  39  20.03 

9  43    4.61 
9  46  48.68 
9  50  32.25 

9  54  15.35 
9  57  57.97 
10    1  40.14 

10    5  21.87 
10    9    3.17 
10  12  44.05 

10  16  24.52 
10  20    4.60 
10  23  44.29 

10  27  23.61 
10  31     2.57 
10  34  41.17 
10  38  19.43 

N.18    0'  26.5 
17  45     8.7 
17  29  33.7 

17  13  41.7 
16  57  33.0 
16  41     8.0 

16  24  26.9 
16    7  30.0 
15  50  17.7 

15  32  50.1 
15  15    7.7 
14  57  10.7 

14  38  59.4 
14  20  34.0 
14    1  54.9 

13  43    2.4 
13  23  56.7 
13    4  38.1 

12  45    7.0 
12  25  23.5 
12    5  28.2 

11  45  21.2 
11  25     2.9 
11    4  33.6 

10  43  53.7 
10  23    3.5 
10    2    3.3 

9  40  53.5 
9  19  34.5 

8  58     6.6 
8  36  30.1 

15  47~9 
15  48.0 
15  48.1 

15  48.3 
15  48.4 
15  48.6 

15  48.7 
15  48.9 
15  49.0 

15  49.2 
15  49.4 
15  49.5 

15  49.7 
15  49.9 
15  50.1 

15  50.2 
15  50.4 
15  50.6 

15  50.8 
15  51.0 
15  51.2 

15  51.4 
15  51.6 
16.51.8 

15  52.0 
15  52.2 
15  52.4 

15  52.6 
15  52.8 
15  53.1 
15  53.3 

m.      s. 
6     5.61 
6     1.82 
5  57.41 

5  52.38 
5  46.73 
5  40.47 

5  33.60 
5  26.12 
5  18.04 

5    9.38 
5    0.14 
4  50.33 

4  39.95 
4  29.03 
4  17.58 

4    5.60 
3  53.11 
3  40.13 

3  26.67 
3  12.74 
2  58.36 

2  43.53 
2  28.27 
2  12.60 

1  56.52 
1  40.04 
1  23.18 

1    5.94 
0  48.34 
0  30.39 
0  12.10 

Monday  
Tuesday  .... 

Wednesday  . 
Thursday  .  .  . 
Friday  .  . 

Saturday  .... 
Sunday  

Monday  .... 

Tuesday  .... 
Wednesday  . 
Thursday  .  .  . 

Friday  

Saturday  .... 
Sunday  

Monday  .... 
Tuesday  .... 
Wednesday  . 

Thursday  .  .  . 
Friday.  . 

Saturday  .... 
Sunday  

Monday  

Tuesday  .... 

Wednesday  . 
Thursday  .  .  . 
Friday  

Saturday   .  . 

314 

TABLE  XXI. 

SEPTEMBER,   1878.—  Page  1. 

AT  APPARENT  NOON. 

^ 

V 

i 
• 

M 

*0 

>> 

cj 

« 

5 

<•• 
o 
"^ 

9 
>. 
es 

Q 

THE  SUN'S  EIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
subtracted 
from 
Apparent 
Time. 

Var.  in 
1  hour. 

Apparent 
Right  Ascension 

Var.  in 
1  hour. 

Apparent 
Declination. 

Var.  in 
1  hour. 

Sunday  .  . 
Monday  . 
Tuesday 

1 
2 
3 

h.  m.      s. 
10  41  57.35 
10  45  34.93 
10  49  12.22 

S. 

9.072 
9.060 
9.048 

N.  8  14  45"  6 
7  52  53.4 
7  30  53.6 

54.51 
54.83 
55.14 

m.      s. 
0    6.52 
0  25.44 
0  44.65 

S. 
0.782 
0.794 
0.806 

Wednes'v 

4 

10  52  49.23 

9.037 

7  8  46.7 

55.43 

1    4.14 

0.817 

Thursday 
Friday.  .  . 

6 

6 

10  56  25.98 
11     0     2.49 

9.026 
9.017 

6  46  32.9 
6  24  12.6 

55.71 
55.97 

1  23.89 
1  43.88 

0.828 
0.838 

Saturday  . 
Sunday  . 
Monday  . 

7 
8 
9 

11     3  38.78 
11     7  14.86 
11  10  50.76 

9.008 
9.000 
8.993 

6  1  46.1 
5  39  13.7 
5  16  35.6 

56.23 
56.47 
56.70 

2    4.10 
2  24.51 
2  45.11 

0.846 
0.854 
0.861 

Tuesday  . 
Wednes'y 
Thursday 

10 
11 

12 

11  14  26.50 
11  18    2.10 
11  21  37.59 

8.986 
8.981 
8.977 

4  53  52.2 
4  31  3.8 
4  8  10.7 

56.91 
57.11 
57.30 

3    5.86 
3  26.76 
3  47.76 

0.868 
0.873 
0.877 

Friday.  .  . 
Saturday  . 
Sunday  .  . 

13 
14 

15 

11  25  12.99 
11  28  48  32 
11  32  23.61 

8.974 
8.971 
8.970 

3  45  13.2 
3  22  11.5 
2  59  6.1 

57.48 
57  65 
57.80 

4    8.86 
4  30.03 
4*51.24 

0.881 
0.883 
0.884 

Monday  . 
Tuesday  . 
Wednes'y 

10 
17 

18 

11  35  58.87 
11  39  34  13 
11  43    9.41 

8.969 
8.970 
8.971 

2  35  57.2 
2  12  45.1 
1  49  30.2 

57.94 
5806 
58.17 

5  12.47 
5  33.70 
5  54.91 

0.885 
0.884 
0.883 

Thursday 
Friday  .  .  . 
Saturday  . 

19 
•20 
21 

11  46  44.74 
11  50  20.13 
11  53  55.61 

8.973 
8.976 
8.980 

1  26  12.8 

1  2  53.2 
0  39  31.7 

58.27 
58.36 
58.43 

6  16.08 
6  37.19 
6  58  21 

0.881 
0.878 
0.874 

Sunday  .  . 
Monday  . 
Tuesday  . 

22 
23 
24 

11  57  31.19 
12    1     6.89 
12    4  42.73 

8.985 
8.990 
8.997 

0  16  8.8 
0  7  15.3 
0  30  40.1 

58.48 
58.52 
58.54 

7  19.12 
7  39.92 
8    0.58 

0.869 
0.864 
0.858 

Wednes'y 
Thursday 
Friday  .  .  . 

25 
20 
27 

12    8  18.73 
12  11  54.89 
12  15  31.25 

9.003 
9.  OH 
9.019 

0  54  5.3 
1  17  30.5 
1  40  55.3 

58.55 
58.54 
58.52 

8  21.08 
8  41.41 
9     1.55 

0.851 
0.843 
0.835 

Saturday  . 
Sunday  .  . 
Monday  . 

28 
2!) 
3u 

12  19    7.82 
12  22  44.61 
12  26  21.65 

9.028 
9.038 
9.049 

2  4  19.4 
2  27  42.4 
2  51  3.9 

58.48 
58.43 
58.36 

9  21.48 
9  41.18 
10     0.64 

0.826 
0.816 

0.8U6 

315 
TABLE  XXI. 

SEPTEMBER,  1878.—  Page  2. 

AT  MEAN  NOON. 

i 

1 

i 

IM 

O 

>» 

A 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
added 
to 
Mean  Time. 

Apparent 
Right  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

Sunday  

1 

2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 
18 

19. 
20 
21 

22 
23 
24 

25 
26 
27 

28 
29 
30 

h.    m.      s. 
10  41  57.37 
10  45  35.00 
10  49  12.33 

10  52  49.39 
10  56  26.19 
11    0    2.75 

11     3  39.09 
11    7  15.22 
11  10  51.17 

11  14  26.97 
11  18    2.62 
11  21  38.16 

11  25  13.61 
11  28  48.99 
11  32  24.33 

11  35  59.64 
11  39  34.96 
11  43  10.30 

11  46  45.68 
11  50  21.12 
11  53  56.65 

11  57  32.29 
12    1    8.04 
12    4  43.93 

12    8  19.98 
12  11  56.20 
12  15  32.61 

12  19    9.23 
12  22  46.07 
12  26'  23.16 

N.°8  14  45'.  5 
7  52  53.0 
7  30  52.9 

7     8  45.7 
6  46  31.6 
6  24  11.0 

6    1  44.2 
5  39  11.4 
5  16  33.0 

4  53  49.2 
4  31     0.5 
4    8    7.0 

3  45    9.2 
3  22    7.2 
2  59    1.4 

2  35  52.2 
2  12  39.8 
1  49  24.5 

1  26    6.7 
1     2  46.7 
0  39  24.9 

N.  0  16    1.6 
S.   0    7  22.8 
0  30  47.9 

0  54  13.5 
1  17  39.0 
1  41    4.2 

2    4  28.6 
2  27  51.8 
2  51  13.6 

15  53  '5 
15  53.8 
15  540 

15  54.2 
15  54.5 
15  54.7 

15  55.0 
15  55.2 
15  55.5 

15  55.7 
15  56.0 
15  56.3 

15  56.5 
15  56.8 
15  57.0 

15  57.3 
15  57.5 
15  57.8 

15  58.0 
15  58.3 
15  58.6 

15  58.8 
15  59.1 
15  59.4 

15  59.6 
15  59.9 
16    0.2 

16    0.5 
16    0.7 
16    1.0 

m.      s. 
0    6.52 
0  25.44 
0  34.66 

1     4.16 
1  23.91 
1  43.91 

2    4.13 
2  24.55 
2  45.15 

3    5.91 
3  26  81 
3  47.82 

4    8.92 
4  30.09 
4  51.31 

5  12  55 
5  33  79 
5  55.00 

6  16.18 
6  37.29 
6  58.31 

7  19.23 
7  40.03 
8    0  69 

8  21.19 
8  41.53 
9    1.68 

9  21.61 
9  41.31 
10    0.77 

Monday  .... 
Tuesday  .... 

Wednesday  . 
Thursday  .  .  . 
Friday  

Saturday  
Sunday    .... 

Monday  .... 

Tuesday  .... 
Wednesday  . 
Thursday  .  .  . 

Friday  .  . 

Saturday  .... 
Sunday  

Monday  
Tuesday  .... 
Wednesday 

Thursday  .  .  . 
Friday  

Saturday  
Sunday  

Monday  
Tuesday  .... 

Wednesday  . 
Thursday  .  .  . 
Friday  

Saturday  
Sunday  

Monday  

316 

TABLE  XXI. 

OCTOBEK,  1878.—  Page  1, 

AT  APPARENT  NOON. 

jjj 

o 

0 

* 

2 

+3 

"o 
>> 

e3 

ft 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time 
to  be 
subtracted 
from 
Apparent 
Time. 

Var.  in 
1  hour. 

Apparent 
Right  Ascension 

Var.   in 
1  hour. 

Apparent 
Declination. 

Var.  in 
1  hour. 

Tuesday  . 
Wednes'y 
Thursday 

1 
2 
3 

h.    m.       s. 
12  29  58.95 
12  33  36.52 
12  37  14.39 

s. 
9.060 
9.072 
9.084 

S.  °3  14  23''  5 
3  37  40.8 
4    0  55.6 

58.27 
58.17 
58.0G 

m.      s. 
10  19.85 
10  38.78 
10  57.41 

S. 

0.795 
0.783 
0.770 

Friday.  .  . 
Saturday  . 
Sunday  .  . 

4 
5 
G 

12  40  52.57 
12  44  31.09 
12  48    9.96 

9.098 
9.112 
9.127 

4  24    7.5 
4  47  16.0 
5  10  20.9 

57.93 

57.78 
57.62 

11  15.73 
11  33.72 
11  51.35 

0.756 
0.742 
0.727 

Monday  . 
Tuesday  . 
Wednes'y 

7 
8 
9 

12  51  49.21 
12  55  28.86 
12  59    8.93 

9.144 
9.161 
9.179 

5  33  21.8 
5  56  18.4 
6  19  10.3 

57.45 
57.26 
57.06 

12    8.61 
12  25.47 
12  41.91 

0.711 

0.694 
0.676 

Thursday 
Friday  .  .  . 
Saturday  . 

10 
11 

12 

13     2  49.45 
13    6  30.43 
13  10  11.91 

9.198 
9.218 
9.239 

6  41  57.2 
7    4  38.7 
7  27  14.5 

56.84 
56.61 
56.36 

12  57.90 
13  13.43 
13  28.46 

0.657 
0.637 
0.616 

Sunday  .  . 
Monday  . 
Tuesday  . 

13 
14 

15 

13  13  53.90 
13  17  36.43 
13  21  19.51 

9.261 
9.284 
9.307 

7  49  44.2 
8  12    7.5 
8  34  24.0 

56.10 
55.83 
55.54 

13  42.99 
13  56.98 
14  10.41 

0.594 
0.571 
0.548 

Wednes'y 
Thursday 
Friday.  .  . 

1G 
17 

18 

13  25    3.16 
13  28  47.42 
13  32  32.29 

9.331 
9.357 
9.383 

8  56  33  4 
9  18  35.2 
9  40  29.2 

55.23 
54.91 
54.57 

14  23.27 
14  35.54 
14  47.19 

0524 

0.498 
0.472 

Saturday  . 
Sunday  .  . 
Monday  . 

19 
20 
21 

13  36  17.79 
13  40    3.94 
13  43  50.75 

9.409 
9.437 
9.465 

10     2  14.8 
10  23  51.8 
10  45  19.6 

54.26 
53.85 
53.46 

14  58.22 
15    8.60 
15  18.31 

0.446 
0.419 
0.390 

Tuesday  . 
Wednes'y 
Thursday 

22 
23 
24 

13  47  38.24 
13  51  26.43 
13  55  15.33 

9.493 
9.523 
9.552 

11     6  37.9 
11  27  46.3 
11  48  44.3 

53.06 
52.63 
52.19 

15  27  34 
15  35.69 
15  43.33 

0.362 
0.333 
0.303 

Friday.  .  . 
Saturday. 
Sunday  .  . 

25 
2G 
27 

13  59    4.94 
U    2  55.29 
14    6  46.37 

9.582 
9.613 
9.644 

12    9  31.5 
12  30    7.5 

12  50  31.9 

51.73 
51.26 
50.76 

15  50.24 
15  56.44 
16    1.90 

0.274 
0.243 
0.212 

Monday  . 
Tuesday  . 
Wednes'y 
Thursday 

28 
29 
30 
3] 

14  10  38.20 
14  14  30.78 
14  18  24.11 
14  22  18.21 

9.675 
9.706 
9.738 
9.770 

13  10  44.2 
13  30  44.0 
13  50  30.9 
14  10    4.G 

50.25 
49.72 
49.18 
48.62 

16    6.61 
16  10.58 
1.6  13.78 
16  16.23 

0.181 
0.149 
0.118 
0.086 

317 
TABLE  XXI. 

OCTOBEK,   1878.—  Page  2. 

AT  MEAN  NOON. 

x 
u 

0 

£ 
<u 

5 

*o 
>t 

& 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
added 
to 
Mean  Time. 

Apparent 
Right  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

Tuesday  .... 
Wednesday  . 
Thursday  .  .  . 

Friday  

1 

2 
3 

4 
5 

6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 

18 

19 
20 
21 

22 
23 
24 

25 
26 

27 

28 
29 
30 
31 

h.    m.     s. 
12  30    0.51 
12  33  38.13 
12  37  16.05 

12  40  54.28 
12  44  32.85 
12  48  11.77 

12  51  51.06 
12  55  30.76 
12  59  10.87 

13     2  51.44 
13     6  32.47 
13  10  13.99 

13  13  56.02 
13  17  38.58 
13  21  21.70 

13  25    5.40 
13  28  49.69 
13  32  34.60 

13  36  20.13 
13  40    6.32 
13  43  53.17 

13  47  40.69 
13  51  28.91 
13  55  17.83 

13  59    7.47 

14    2  57.84 
14    6  48.95 

14  10  40.80 
14  14  33.40 
14  18  26.75 
14  22  20.86 

S.  °3  U  33.5 
3  37  51.2 
4    1     6.2 

4  24  18.3 
4  47  27.1 
5  10  32.3 

5  33  33.4 
5  56  30.2 
6  19  22.4 

6  42    9.5 
7    4  51.2 
7  27  27.1 

7  49  57.0 
8  12  20.5 
8  34  37.1 

8  56  46.6 
9  18  48.6 
9  40  42.6 

10     2  28.3 
10  24    5.3 
10  45  33.2 

11     6  51.6 
11  28    0.0 
11  48  57.9 

12    9  45.1 
12  30  21.1 
12  50  45.4 

13  10  57.6 
13  30  57.4 

13  50  44.2 
14  10  17.7 

16     £3 
16    1.6 
16     1.9 

16    2.1 
16    2.4 

16    2.7 

16    3.0 
16    3.3 
16    3.6 

16    3.8 
16    4.1 
16    4.4 

16    4.7 
16    4.9 
16    5.2 

16    5.5 
16    5.7 
16    6.0 

16    6.3 
16    6.5 
16    6.8 

16    7.0 
16    7.3 
16    7.6 

16    7.8 
16    8.1 
16    8.4 

'16    8.6 
16    8.9 
16    9.1 
16    9.4 

m.      8. 
10  19.98 
10  38.92 
10  57.55 

11  15.87 
11  33.86 
11  51.50 

12    8.76 
12  25.61 
12  42.05 

12  58.04 
13  13.57 
13  28.60 

13  43.12 
13  57.11 
14  10.54 

14  23.40 
14  35.66 
14  47.31 

14  58  33 
15    8.70 
15  18.41 

15  27.44 
15  35.77 
15  43.40 

15  50.31 
15  56.50 
16     1  .  95 

16    6.66 
16  10.62  1 
16  13  b-2 
16  16.26 

Saturday  
Sunday    .... 

Monday  .... 
Tuesday  .... 
Wednesday  . 

Thursday  .  .  . 
Friday  .  . 

Saturday  
Sunday  

Monday  

Tuesday  .... 

Wednesday  . 
Thursday  .  .  . 
Friday  ...... 

Saturday  
Sunday  

Monday  .... 

Tuesday  
Wednesday  . 
Thursday  .  .  . 

Friday  

Saturday  .... 
Sunday  .... 

Monday  .... 
Tuesday  .... 
Wednesday  . 
Thursday  .  .  . 

318 

TABLE  XXI. 

NOVEMBER,  1878.—  Page  1. 

AT  APPARENT  NOON. 

4 

V 

* 

0 

53 

*o 

& 

B 

3 
£• 

s 

> 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of"  Time, 
to  be 
subtracted 
from 
Apparent 
Time. 

Var.  in 
1  hour. 

Apparent 
Right  Ascensioi 

Var.  in 
1  hour. 

Apparent 
Declination. 

Var.  in 
1  hour 

Friday.  .  . 
Saturday  . 
Sunday  .  . 

I 

n 

4 

h.  m.      s. 
14  26  13.09 
14  30    8.74 
14  34    5.19 

S. 

9.803 
9.835 
9.869 

S.14  29  24"  5 
14  48  30.3 
15  7  21.5 

48.04 
47.44 
46.83 

m.       s. 
16  17.91 
16  18.81 
16  18.92 

S. 

0.054 
0.021 
0.012 

Monday  . 
Tuesday  . 
Wednes'y 

4 

c 

6 

14  38    2.43 
11  42    0.49 
14  45  59.3G 

9.902 
9.936 
9.970 

15  25  57.9 
15  44  18.9 
16  2  24.2 

46.20 
45.55 
44.89 

16  18.23 
16  16.74 
16  14.43 

0.045 
0.079 
0.114 

Thursday 
Friday  .  .  . 
Saturday  . 

7 

8 
<j 

14  49  59.06 
14  53  59.59 
14  58    0.97 

10.005 
10.040 
10.075 

16  20  13.4 
16  37  46.2 
16  55  2.1 

44.21 
43.51 

42.80 

16  11.29 
16    7.33 
16    2.52 

0.148 
0.183 
0.218 

Sunday  .  . 
Monday  . 
Tuesday  . 

10 
11 
12 

15     2    3.19 
15     6    6.27 
15  10  10.21 

10.110 
10.146 
10.182 

17  12  0.8 
17  28  41.8 
17  45  4.9 

42.08 
41.34 
40.58 

15  56.86 
15  50.36 
15  43.00 

0.253 
0.289 
0.325 

"Wednes'y 
Thursday 
Friday  .  .  . 

13 
14 
15 

15  14  15.00 
15  18  20.66 
15  22  27.18 

10.218 
10.254 
10.290 

18  1  9.5 
18  16  55.3 
18  32  22.0 

39.80 
3901 
38.21 

15  34.78 
15  25.71 
15  15.77 

0.360 
0.396 
0.432 

Saturday  . 
Sunday  .  . 
Monday  . 

1G 
17 

Ib 

15  26  34.57 
15  30  42.81 
15  34  51.91 

10.326 
10.361 
10.397 

18  47  29.2 
19  2  16.3 
19  16  43.1 

37.38 
3654 
35.68 

15    4.97 
14  53.32 
14  40.81 

0.468 
0.503 
0.539 

Tuesday  . 
Wednes'y 
Thursday 

11) 

20 
21 

15  39    1.85 
15  43  12.64 
15  47  24.27 

10.432 
10.467 
10.502 

19  30  49.1 
19  44  33.9 
19  57  57.2 

34.81 
33.92 
33.01 

14  27.46 
14  13.27 
13  58.24 

0.574 
0.609 
0.643 

Friday.  .  . 
Saturday  . 
Sunday  .  . 

22 

23 
24 

15  51  36.72 
15  55  49.97 
16    0    4.01 

10.535 
10.569 
10.601 

20  10  58.6 
20  23  37.8 
20  35  54.3 

32.10 
31.16 
30.21 

13  42.40 
13  25.75 
13    8.31 

0.677 
0.710  i 
0.743 

Monday  . 
Tuesday  . 

25 
2(i 

16    4  18.82 
16    8  34.38 

10.633 
10.664 

20  47  47.7 
20  59  17.9 

29.24 
28.26 

12  50.10 
12  31.15 

0.774 

0.805  ! 

Wednes'y 

27 

16  12  50.67 

10.694 

21  10  24.4 

27.27 

12  11.47 

0.835 

Thursday 
Friday  .  .  . 
Saturday  . 

2s 
2i) 
JJ 

16  17     7.67 
16  21  25.34 
16  25  43.68 

10.722 
10.750 
10.777 

21  21  6.8 
21  31  25.0 
21  41  18.5 

26.26 
25.24 
24.21 

11  51.09 
11  30.03 
11     8.31 

0.863 
0.891 
0.918 

319 
TABLE  XXI. 

NOVEMBER,   1878.—  Page  2, 

AT  MEAN  NOON. 

J 

S 

0 

* 

0 

*3 

kM 

O 

>, 

ci 

fi 

Day  of  the  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
added 
to 
Mean  Time. 

Apparent 
light  Ascension 

Apparent 
Declination. 

Semi- 
diameter. 

i  Friday.  ..... 

1 

2 
3 

4 
5 
G 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 

18 

19 
20 
21 

22 

23 
24 

25 

2G 
27 

28 
29 
30 

h.    m.      s. 
14  26  15.75 
14  30  11.42 
14  34    7.87 

14  38    5.12 
14  42    3.18 
14  46    2.06 

14  50    1.76 
14  54    2.29 
14  58    3.66 

15    2    5.88 
15    6    8.95 
15  10  12.88 

15  14  17.66 
15  18  23.30 
15  22  29.80 

15  26  37.16 
15  30  45.38 
15  34  54.45 

15  39    4.36 
15  43  15.12 
15  47  26.71 

15  51  39.12 
15  55  52.33 
16     0     6.33 

16    4  21.10 
16    8  36.61 
16  12  52.85 

16  17     9.79 
16  21  27.40 
16  25  45.68 

S.  14  29'  37".  5 
14  48  43.1 
15     7  34.2 

15  26  10.4 
15  44  31.2 
16    2  36.3 

16  20  25.3 
16  37  57.9 
16  55  13.5 

17  12  11.9 
17  28  52.7 
17  45  15.5 

18    1  19.8 
18  17     5.4 
18  32  31.7 

18  47  38.5 
19     2  25.3 
19  16  51.8 

19  30  57.5 
19  44  42.0 
19  58    4.9 

20  11     6.0 
20  23  44.8 
20  36    0.9 

20  47  54.0 
20  59  23.8 
21  10  29.9 

21  21  12.0 
21  31  29.8 
21  41  23.0 

16     9~7 
16     9.9 
16  10.2 

16  10.4 
16  1D.6 
16  10.9 

16  11.1 
16  11.3 
16  11.6 

16  11.8 
16  12.0 
16  12.3 

16  12.5 
16  12.7 
16  12.9 

16  13.1 
16  13.3 
16  13.5 

16  13.7 
16  13.9 
16  14.1 

16  14.3 
16  14.4 
16  14.6 

16  14.8 
16  15.0 
16  15.1 

16  15.3 
16  15.5 
16  15.6 

m.      s. 
16  17.92 
16  18.81 
16  18.92 

16  18.22. 
16  16.71 
16  14.39 

16  11.25 

16     7.28 
16     2.46 

15  56.80 
15  50  28 
15  42.91 

15  34.69 
15  25.60 
15  15.66 

15    4  85 
14  53.19 
14  40.68 

14  27.32 
14  13.12 
13  58.09 

13  42.24 
13  25.59 
13     8  15 

12  49.94 
12  30.98 
12  11.30 

11  50.92 
11  29.86 
11     8.14 

Saturday  .... 

i  Monday  .... 
Tuesday  .... 
Wednesday 

Thursday  .  .  . 
Friday  

Saturday  
Sunday  

Monday  
Tuesday  .... 

Wednesday  . 
Thursday  .  .  . 
Friday  

Saturday  .... 
Sunday    .... 

Monday  .... 

Tuesday  .... 
Wednesday 
Thursday  .  . 

Friday  .  . 

Saturday  .  .  . 
Sunday  .... 

Monday  .... 
Tuesday  .  .  . 
Wednesday 

Thursday  .  . 
Friday   

Saturday   .  . 

320 

TABLE  XXI. 

DECEMBER,  1878.—  Page  1, 

AT  APPARENT  NOON. 

•j 

« 

* 

o 
^ 

"o 

£ 

p 

e  Month. 

THE  SUN'S  RIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time 
to  be 
snbt  from 

Var.  in 
1  hour. 

**H 
O 

ce 

Apparent 
Right  Ascension 

Var.  in 
1  hour. 

Apparent 
Declination. 

Var.  in 
1  hour. 

added  to 
Apparent 
Time. 

Sunday  .  . 
Monday  . 
Tuesday  . 

1 
2 
3 

h.    m.       S. 
16  30     2.66 
16  34  22.27 
16  38  42.47 

S. 
10.804 
10.829 
10.854 

S.2°l  50  47  'l 
21  59  50.4 
'22    8  28.4 

23.16 
22.11 
21.05 

m.      s. 
10  45.95 
10  22.96 
9  59.38 

S. 

0.944 
0.970 
0.994 

Wednes'y 
Thursday 
Friday  .  .  . 

4 
5 
G 

16  43    3.25 
16  47  24.59 
16  51  46.46 

10.878 
10.900 
10.922 

22  16  40.7 
22  24  27.0 
22  31  47.0 

19.97 
18.88 
17.79 

9  35.23 
9  10.52 
8  45.27 

1.018 
1.041 
1.063 

Saturday  . 
Sunday  .  . 
Monday  . 

7 
8 
9 

16  56    8.84 
17    0  31.71 
17    4  55.04 

10.943 
10.963 
10.981 

22  38  40.7 
2245    7.7 
22  51     8.0 

16.68 
15.57 
14.45 

8  19.52 
7  53.28 
7  26.58 

1.083 
1.103 
1.122 

Tuesday  . 
Wednes'y 
Thursday 

10 
11 
12 

17     9  18.81 
17  13  42.99 
17  18    7.55 

10.999 
11.013 
11.031 

22  56  41.2 
23     1  47.3 
23    6  26.0 

13.32 
12.18 
11.04 

6  59.44 
6  31.90 
6    3.98 

1.139 
1.155 
1.171 

Friday.  .  . 
Saturday. 
Sunday  .  . 

13 

U 
15 

17  22  32.46 
17  26  57.71 
17  31  23.25 

11.045 
11.058 
11.070 

23  10  37.2 
23  14  20.8 
23  17  36.6 

9.89 
8.74 

7.58 

5  35.70 
5    7.09 
4  38.19 

1.185 
1.198 
1.210 

Monday  . 
Tuesday  . 
Wednes'y 

1C 
17 

18 

17  35  49.06 
17  40  15.11 
17  44  41.36 

11.080 
11.090 
11.098 

23  20  24  4 
23  22  44.1 
23  24  35.7 

6.41 
5.24 
4.06 

4    9  02 
3  39.61 
3    9.99 

1  220 
1.230 
1.238 

Thursday 
Friday  .  .  . 
Saturday  . 

19 
20 
21 

17  49    7.78 
17  53  34.35 
17  58    1.01 

11.104 
11.109 
11.112 

23  25  59.1 
23  26  54.1 
23  27  20.8 

2.88 
1.70 
0.52 

2  40.21 
2  10.29 
1  40.26 

1.244 
1.249 
1.252 

Sunday  .  . 
Monday  . 
Tuesday  . 

Wednes'y 
Thursday 
Friday  .  .  . 

22 
23 
24 

25 
20 
27 

18    2  27.74 
18    6  54.49 
18  11  21.21 

18  15  47.87 
18  20  14.43 
18  24  40.84 

11.114 
11.114 
11.112 

11.109 
11.104 
11.097 

23  27  19.2 
23  26  49.2 
23  25  50.9 

23  24  24.3 
23  22  29  4 
23  20    6.3 

0.66 
1.84 
3.02 

4.20 
5.37 
6.55 

1  10.18 
0  40.07 
0     9.99 

1.254 
1.254 
1.252 

1.249 
1.244 
1.237 

0  20.03 
0  49.95 
1  19.73 

Saturday  . 
Sunday  .  . 
Monday  . 
Tuesday  . 

28 
29 
30 

31 

18  29    7.08 
18  33  33.11 
18  37  58.88 
18  42  24.38 

11.089 
11.079 
11.068 
11.056 

23  17  15.1 
23  13  55.8 
23  10    8.6 
23    5  53.6 

7.72 
8.89 
10.05 
11.20 

1  49.32 
2  18.71 
2  47.85 
3  16.71 

1.229 
1.219 
1.208 
1.196 

321 
TABLE  XXI. 

DECEMBER,  1878.—  Page  2. 

AT  MEAN  NOON. 

jj 

9 

£ 

« 
5 
•« 

t 

Day  of  the  Month. 

THE  SUN'S  EIGHT  ASCENSION  AND 
DECLINATION. 

Equation 
of  Time, 
to  be 
added  to 

Apparent 
Right  Ascensioi 

Apparent 
Declination. 

Semi- 
diameter. 

subt.  J'rom 
Mean  Time. 

Sunday  

1 
2 
3 

4 
5 
6 

7 
8 
9 

10 
11 
12 

13 
14 
15 

16 
17 

18 

19 
20 
21 

22 
23 
24 

25 
2G 

27 

28 
29 
30 
31 

h.    m.     s. 
16  30    4.60 
16  34  24.14 
16  38  44.28 

16  43    4.99 
16  47  26.25 
16  51^48.05 

16  56  10.36 
17    0  36.15 
17    4  56.41 

17    9  20.09 
17  13  44.19 
17  18    8.66 

17  22  33.49 
17  26  58.65 
17  31  24.10 

17  35  49.82 
17  40  15.78 
17  44  41.94 

17  49    8.28 
17  53  34.75 
17  58     1.32 

18    2  27.95 
18    6  54.61 
18  11  21.24 

18  15  47.81 
18  20  14.28 
18  24  40.60 

18  29     6.75 
18  33  32.68 
18  37  58.37 
18  42  23.78 

S.21  50'  5l'.2 
21  59  54.2 
22    8  31.9 

22  16  43.9 
22  24  29.8 
22  31  49.6 

22  38  43.0 
22  45    9.8 
22  51     9.8 

22  56  42.8 
23     1  48.7 
23     6  27.2 

23  10  38.2 
23  14  21.5 
23  17  37.1 

23  20  24.8 
23  22  44.4 
23  24  35.9 

23  25  59.2 
23  26  54.2 
23  27  20.9 

23  27  19.2 
23  26  49.2 
23  25  50.9 

23  24  24.3 
23  22  29.5 
23  20    6.5 

23  17  15.3 
23  13  56.2 
23  10    9.1 
23    5  54.2 

16  15~8 
16  15.9 
16  16.1 

16  16.3 
16  16.4 
16  16.5 

16  16.6 
16  16.8 
16  16.9 

16  17.0 
16  17.1 
16  17.2 

16  17.3 
16  17.4 
16  17.5 

16  17.5 
16  17.6 
16  17.7 

16  17.7 
16  17.8 
16  17.9 

16  17.9 
16  18.0 
16  18.0 

16  18.1 
16  18.1 
16  18.1 

16  18.2 

16  18.2 
16  18.2 
16  18.2 

m.      s. 
10  45.78 
10  22.80 
9  59.22 

9  35.07 
9  10.36 
8  45.12 

8  19.37 
7  53.13 
7  26.44 
\- 
6  59(.31 
6  31V78 
6    3.86 

5  35.59 
5     6.99 
4  38.09 

4    8.93 
3  39.53 
3     9.93 

2  40.15 
2  10.24 
1  40.23 

1  10.15 
0  40.06 
0     9.98 

Monday  

Tuesday  .... 

"Wednesday  . 
Thursday  .  .  . 
Friday  

Saturday  .... 
Sunday  

Monday  .... 

Tuesday  
Wednesday  . 
Thursday  .  .  . 

Friday  

Saturday  .... 
Sunday  

Monday  .... 
Tuesday  .... 
Wednesday  . 

Thursday  .  .  . 
Friday  

Saturday  .... 
Sunday  

Monday  .... 
Tuesday  .... 

Wednesday. 
Thursday  .  .  . 
Friday  

0  20.03 
0  49.93 
1  19.70 

1  49.29 
2  18.66 
2  47.79 
3  16.64 

Saturday  
Sunday  

Monday  
Tuesday  .... 

322     ,                                  TABLE  XXII. 

LATITUDES    AND   LONGITUDES 
Of  the  Principal  Ports,  Capes,  and  Lights  in  the  World. 

EAST  COAST  OF  UNITED  STATES  OF  AMERICA. 

Qnoddy-head  Light.  . 
Mt.  Desert-rock    "   . 
Martinicus  Island  Lt. 
Portland  Li"ht  

LAT. 

LONG. 

Philadelphia  (St.  H.) 
Cape  Charles  

LAT. 

LONG. 

44  49  N 
43  58 
43  47 
43  37 

42  38 
42  31 
42  20 
42  21 
42  02 
41  16 
41  35 
41  29 
41  13 
41   19 
41  04 
40  43 
40  28 
40  24 
38  56 
38  47 

ISL 

10  ION 
11  20 
12  00 
13  03 
14  27 
15  38 
16  30 
18  29 
18  28 

] 

19  12  N 
17  29 
19  49 
9  34 
10  26 
10  39 
10  28 
10  30 
6  49 
5  48 
4  56 
1  10 

•\ 

33  02  S 
12  03 
12  04 
2  13 

8  57  N 

EAST 
43  24  N 
44  39 
45  19 
45  57 
45  42 

6°6  58  W 
68  08 
68  51 
70  12 

70  34 
70  54 
70  53 
71  04 
70  03  . 
70  04 
70  54 
71  18 
71  34 
72  05 
71  51 
74  00 
74  00 
73  59 
74  57 
75  05 

LNDS   IN  THI 
61    00  W 

60  27 
61  49 
59  37 
60  55 
61  26 
61  29 
66  07 
69  52 

}AST  COAST 
96  09  W 
88  12 
90  33 
79  40 
75  38 
71  45 
68  07 
67  01 
58  11 
55  00 
52  13 
50  00 

VEST  COAST 
71  41  W 
77  06 
77  13 
79  53 
79  31 

COAST  OF 
65  36  W 
63  55 
60  55 
59  48 
61  29 

39  67  N 
37  07 
36  55 
37  32 
38  53 
39  18 
35  15 
34  37 
33  52 
33  13 
32  42 
32  01 
32  05 
28  28 
25  40 
24  33 
30  21 
30  14 
29  57 
29  20 

18  33  N 
19  46 
17  58 
19  58 
20  20 
23  09 
23  03 
25  51 
32  22 

1  28  S 
8  04 
5  28 
8  21 
13  01 
22  03 
23  01 
22  56 
34  53 
34  36 
55  59 

16  55  N 
37  48 
49  36 
70  29 

46  39  N 
47  34 
46  49 
59  49 

75  09  W 
75  58 
76  00 
77  26 
77  00 
76  37 
75  31 
76  31 
78  00 
79  11 
79  52 
80  51 
81  05 
80  34 
80  09 
81  48 
87  17 
88  00 
90  00 
94  45 

72  16W 
72  11 
76  46 
75  52 
77  11 
82  22 
81  40 
77  11 
64  38 

48  29  W 
34  52 
35  17 
34  57 
38  32 
41  00 
41  59 
43  09     . 
56  13 
58  22 
67  16 

99  48  W 
122  26 
126  35 
161  42 

53  05  W 
52  43 
71  16 
43  54 

Cape  Henry  Light.  .  . 
Richmond 

Cape  Ann  (Thatcher's 
Island)  Light.  .... 

Washington  City  .... 
Baltimore  

Salem  (City  Hall)  .  .  . 
Boston  L.  H  

Cape  Hatteras  

Cape  Lookout  Light  . 
Cape  Fear           '  ' 
Georgetown         " 
Charleston           " 
Tybee                   " 
Savannah  

Boston  (State  House) 
Capo  Cod  Li^ht  

Nantucket  harbor  Lt. 
Xc  w  Bedford  L.  H.  . 
Newport  Spire  

Block  Island  Light  .  . 
New  London  L.  II  .. 
Montauk  Point  L.  H. 
New  York  (City  Hall) 
Sandy  Hook  Light  .  . 
Neversink  Light  
Cape  May  Light  .... 
Cape  Henlopen  L.  H. 

Trinidad  (Pt.  Galiote) 
Tobago  (N.E.  Point) 
Grenada(S.W.  Point) 
Barbadoes  (S.  Point) 
Martinico            " 
Dominica  (N.  Point). 
Guadeloupe  (NE.Pt.) 
Porto  Rico  (St.  A.  Bt.) 
St.  Domingo  Light  .  . 

Vera  Cruz  

Cape  Carnaveral  
Cape  Florida  Light  .  . 
Key  West 
Pensacola           " 
Mobile  Point    " 
New  Orleans  

Galveston  (entrance)  . 

:  WEST  INDIES. 
Port  au  Prince  

Cape  Hayti  City  .... 
Kingston  

St.  Jago  de  Cuba  Lt. 
Manzanillo  

Havana  (the  Moro).  . 
Matanzas  

Hole-in-the-wall  Lt.  . 
Georgetown  

OF  AMERICA. 
Para  

Balize         .  .        

Pernambuco  

Campeche  

Cape  St.  Roque  

Porto  Bello  

Cape  St.  Angustin  .  . 
Bahia,  St.  Antonio  Lt. 
Cape  St.  Thomas  
Cape  Frio  

Cartagena  

Maracaybo  

Porto  Cabello 

Caraccas  

Rio  Janeiro  

Georgetown  Light  .  .  . 
Paramaribo  

Monte  Video  

iBuenos  Ayres  

Cayenne  

Cape  Horn  

River  Amazon  

OF  AMEBICA. 
Acapulco  

Valparaiso  

Lima  

San  Francisco  

Callao  

Nootka  

Guayaquil   

Icy  Cape  

Panama  

NORTH  AMERICA. 
Cape  Race  

Cape  Sable      .     ... 

Halifax  

St.  Johns  

Cape  Canso  '  .  . 

Quebec  

Cape  Breton  

Cape  Farewell  

Gut  of  Canso  

323 
TABLE  XXII. 

LATITUDES   AND    LONGITUDES 
Of  the  Principal  Ports,  Capes,  and  Lights  in  the  \Vorld. 

ENGLAND,  SCOTLAND,  AND  IRELAND. 

Lizard  Point  ....... 

LAT. 

LONG. 

Glasgow  

LAT. 

LONG. 

49  58  N 
50  22 
50  47 
51  C8 
51  31 
52  37 
53  45 
55  46 
56  00 
55  57 
57  09 
58  40 

FBO 
36  07  N 
36  32 
36  59 
37  03 
38  42 
41  09 
43  22 
43  30 
43  30 
43  15 
43  29 
44  50 
45  35 
45  56 
46  09 
47  13 
48  23 

SotTND,  THE 

57  38  N 
59  55 
57  42 
55  41 
56  02 
56  10 
59  21 
53  52 

36  07  N 
36  43 
37  36 
38  20 
39  28 
41  09 
41  23 
43  18 
43  07 
44  24 
43  46 
43  32 
41  54 
40  50 
43  38 

5  12  W 
4  10 
1  06 
1  19  E 
0  06  W 
1  44  E 
0  20  W 
1  59 
2  29 
3  12 
2  08 
3  08 

M   GlBEALTA 
5    21  W 

6  18 
5  58 
9  00 
9  09 
8  37 
8  24 
8  13 
3  47 
2  54 
1  29 
0  34 
1  10 
0  58 
1  09 
1  33 
4  29 

BALTIC,  AST 
7  02  E 
10  43 
11  55 
12  34 
12  37 
15  36 
18  04 
10  42 

THE  MEDI 
5  21  W 
4  26 
1  01 
0  26 
0  24 
1  18E 
2  11 
5  22 
5  56 
8  53 
11  16 
10  18 
12  27 
14  16 
13  30 

55  52  N 
54  54 
53  25 
51  27 
51  26 
52  40 
55  00 
54  35 
53  23 
51  48 
51  29 

48  29  N 
49  38 
48  50 
49  29 
50  44 
50  58 
51  03 
51  14 
51  13 
51  27 
51  54 
52  22 
53  22 
53  05 
53  33 
57  43 

AND  BOTHN 

54  22  N 
54  43 
56  57 
54  25 
59  26 
59  59 
59  56 
65  51 

45  26  N 
45  39 
42  38 
37  54 
37  58 
40  39 
41  01 
38  26 
36  11 
30  03 
31  12 
32  54 
36  47 
36  47 
35  47 

4  16\V 
2  56 
3  00 
2  35 
9  29 
8  39 
7  19 
5  57 
6  20 
8  15 
9  22 

5  03  W 
1  37 
2  20  E 
0  06 
1  37 
1  51 
2  22 
2  55 
4  24 
3  35 
4  29 
4  53 
7  12 
8  49 
9  58 
10  37 

IA. 

18  41  E 
20  30 
24  C6 
13  28 
24  45 
29  47 
30  19 
24  14 

12  21  E 
13  46 
18  07 
22  52 
23  44 
22  57 
28  59 
27  07 
37  10 
31  18 
29  53 
13  11 
10  06 
3  04 
5  50  W 

Plymouth  

Carlisle  

Portsmouth  

Liverpool  

Dover     

Bristol  

London  

Cape  Clear  Light.  .  .  . 
Limerick  

Yarmouth  

Hull  

Londonderry  

Berwick  Li^ht.  .  .    . 

Belfast  ".  

Dunbar.  

Dublin  

Edinburgh  

Cork  

Aberdeen   ... 

Baltimore  

Duncansby  Head  .... 
Gibraltar  

R  TO  THE   SCAW. 

Ushant  Light  

Cadiz  Light  

Cherbourg  

Seville  

Paris  

Cape  St.  Vincent  Lt  . 
Lisbon  

Havre  de  Grace  

Boulogne  

Oporto  Li^ht  

Calais  

Corunna    "     

Dunkirk  

Ferrol  

Ostend  

Santander  Li^ht  

Antwerp  

Bilbao         ' 

Flushing     ^ 

Bavonnc  

Rotterdam  

Bordeaux  

Amsterdam  

Cordouau  Light         > 

Embden  . 

Rochefort  

Bremen.  ...       

Ilochelle  Light  

Hamburgh  

Nantes  .•  

Scaw  Light  

Brest  

D  THE  GTTLFS  OF  FINLAND 
Dantzig  

CATTEGAT  AND 
The  Naze  Li^ht  

Christiana  

Konigsberg  

Gothenburf'h  

Rica  .  . 

Copenhagen  

Bergen  (Isl'd  Rugen) 
Revel  

Elsineur  

Carlscrona  

Cronstadt.             .... 

Stockholm  

Petersburg  

Lubeck  

Tornea  

Gibraltar  

TERRANEAN. 

Venice  

Alala^a,         ... 

Trieste  

Cartha^ena  

Ra°nsa  

Alicante  

Corinth  

Valencia  

Athens  

Terra  ^ona         

Salonica  

Barcelona  

Constantinople  

Marseilles  

Smyrna.  

Toulon  

Genoa  

Cairo  

Florence           .  ..... 

Alexandria  

Leghorn  

Tripoli  

Rome             

Tunis  

Naples         

Algiers  

Ancona  LiMit  

Tangier  

TABLE  XXII. 

LATITUDES   AND   LONGITUDES 
Of  the  Principal  Ports,  Capes,  and  Lights  in  the  World. 


324 


WEST  COAST  OF  AFRICA. 


CapeSpartel. 
Mogador. 

Senegal 

Cape  Verde . . 


LAT. 


35  48  N 
31  31 
16  01 
14  44 


LONG. 


5  54  W 
9  46 

16  32 

17  32 


Sierra  Leone  Cape. . 

Capetown 

Cape  of  Good  Hope . 
Cape  Lagullas 


LAT. 


ISLANDS  IN  IHE  ATLANTIC  OCEAN. 


Fayal,  S.E.  point 

Funchal . . 


Santa  Cruz(Teneriffe) 
"  (St.  Anthony) 

Cape  Lagullas 

Mozambique 

Suez 

Mocha 

Bassora 

Surat 

Bombay 

Goa 

Mangalore 

Cape  Comorin 

Ceylon  (Columbo  Lt. ) 

Pondicherry 

Madras . . 


38  30  N 
32  38 

28  28 
17  02 


28  42  W 
16  55 
16  16 
25  15 


Porto  Praya 

Ascension 

St.    Helena  ( James- 
town ) 


FROM  CAPE  OF 


34  508 
15  03 

29  59  N 
13  20 

30  30 
21  11 
18  54 
15  28 

12  51 
8  05 
6  56 

11  56 

13  04 


ISLANDS  IN  THE 


Madagascar — 

Cape  St.  Mary . . 

Cape  Amber 
Mauritius  (Pt.  Louis) 
Sumatra  (Bencoolen) 

Java  (Batavia) 

Banca  (South  Point) . 
Singapore  (East  Pt. ) . 

Borneo  (Road) 

Celebes  (Macassar).. 
Amboyna  (Ft.  Viet.) 
Formosa  (S.  Cape)  . 


25  39  S 
11  58 

20  10 
3  48 
6  08 
3  08 

1  22  N 
5  00 
5  09  S 
3  41 

21  56  N 


45 
49 
57 
102 
106 
106 
104 
115 
119 
128 
120 


GOOD 

01  E 

48 

34 

12 

00 

47 

52 

52 

49 

30 

49 

50 

16 

INDIAN  AND  PACIFIC  OCEANS. 

[Niphon  (Yeddo) 

Jesso  (Matzumay). . . 
Australia — 

Cape  York 

N.W.  Cape 

Sydney 

Botany  Bay 

Melbourne 

Sandwich  Islands — 

Owhyhee(N.Pt.) 
"        (E.  Pt.) 

Honolulu 


HOPE  TO  KAMISKATKA. 

Masulipatam 

Ballasore 

Calcutta 

Pegu 

Point  Romania 

Siam 

Hong  Kong 

Canton 

Shanghai 

Nankin 

Pekin 

St.  Peter  and  St.  Paul 
North  Cape 


07  E 

19 

30 

19 

50 

28 

00 

00 

23 

10 

56 


8  30  N 

33  56  S 

34  22 

34  50 

14  54N 
7  56  S 

15  55 

16  09  N 

21  30 

22  34 

18  00 
1  23 

14  55 

22  15 

23  07 

31  12 

32  02 
39  54 
53  00 
68  56 

35  40  N 
41  32 

10  44  S 
21  50 

33  52 

34  02 
37  49 

20  23  N 

19  34 

21  19 


LONG. 


13  18  W 
18  29  E 
18  30 
20  01 

23  30  W 

14  25 

5  45 

81  08  E 

87  10 

88  20 
96  52 

104  16 
100  00 
114  22 

113  14 
121  28 
118  49 
116  29 
158  44 
179  47  W 

140  00  E 
140  04 

142  33 

114  04 
151  14 
151  13 
144  58 

155  54 W 
154  54 
157  52 


COAST  OF  CALIFORNIA. 


St.  Diego,  Point  Loma 

St.  Catalina  Island. 

Santa  Cruz  Island,  W.  end * 

Point  Conception 

Mount  Buchon 

Point  Pinos 

Monterey  Fort 

Farallones  Rocks  peak 

San  Francisco  Fort,  S.  side  entrance 

Mt.  Bolbones,  3765  ft,  10  leag.  inland 

Cape  Mendocino 

Cape  Perpetiia 

Pt.  Adam  entrance,  Columbo  River 

Cape  Disappointment 

Astoria  City 

Pacific  City 

Gray's  Harbor,  N.  Head 

Cape  Flattery  S.  side  ent,  of  Straits  of  Juan  de  Fuca . 


LAT. 


32  38. 8 N 

33  28 

34  10 

34  31 

35  18 

36  38.5 

36  36.4 

37  42 
37  48.5 
37  52.9 
40  29 
44  12 
46  12 
16  16 
46  10 

46  20 

47  0 

48  9 


LONG. 


117  14.7 

118  38 

119  47 

120  30 

120  50 

121  55 

121  53 

122  59 

122  28.5 
121  54.5 
124  32 
124  17 
124  1 
124  5 

123  49 

124  3 
124  7 
124  46 


TESTIMONIALS. 


From  a  long  list  of  subscribers  we  select  the  following  names  as 
evidencing  that  our  "  GUIDE  "  has  won  the  patronage  of  the  best 
nautical  men : 

YV.  B.  Seabury,  Commanding  Steamship  Alaska,  P.  M.  S.  S.  Co. 

W.  H.  McLean,  First  Officer 

T.  E.  Thompson,  Second  Officer  "  "          " 

James  E.  Hunter,  Third  Officer  "  " 

D.  E.  Friele,  Commanding  Steamship  China,  P.  M.  S.  S.  Co. 

Thos.  Golding,  First  Officer  "          "         " 

C.  Basset,  Second  Officer  "          "         " 
I.  M.  Dow,  Third  Officer  "          "         " 
H.  C.  Dearborn,  Commanding  Steamship  City  of  Sydney. 

F.  H.  Johnson,  First  Officer  "  " 
WiUiam  Danol,  Second  Officer                      "             " 
A.  H.  Panzes,  Third  Officer 

J.  Metcalfe,  Commanding  Steamship  Belgic,  0.  0.  S.  S.  Co. 
Louis  Meyer,  First  Officer  "  "         " 

Daniel  Joyce,  Second  Officer  "          "          " 

G.  A.  Williams,  Fourth  Officer  "  "          " 

A.  G.  Jones,  Commanding  Steamship  Salvador,  P.  M.  S.  S.  Co. 

D.  Clark,  First  Officer 

M.  Connolly,  Commanding  Steamship  Granada,  P.  M.  S.  S.  Co. 

F.  W.  Hart,  First  Officer  "          « 

G.  Foster,  Second  Officer  "  " 

C.  T.  Rode,  Third  Officer 

D.  C.  Griffiths,  First  Officer  Steamship  Dakota,  P.  M.  S.  S.  Co. 
W.  Lascombe,  Second  Officer  "  "  " 

D.  Berry,  Third  Officer 

L.  B.  Walls,  First  Officer  Steamship  City  of  Tokio,  P.  M.  S.  S.  Co. 

J.  H.  Powell,  Second  Officer  "  •'          "  " 

J.  Luke,  Third  Officer  "  "          "          " 

D.  S.  Austin,  Commanding  Steamship  Wilmington,  P.  M.  S.  S.  Co. 

A.  N.  M.  Tnlloh,  First  Officer  Steamship  Australia,  P.  M.  S.  S.  Co. 

Francis  Connor,  Commanding  Steamship  Oregon,  Oregon  S.  S.  Co. 

W.  H.  Kidley,  Commanding  Steamship  Gaelic,  O.  &  O.  Line. 

H.  Davison,  First  Office*  "          " 

T.  Suafton,  Second  Officer 

J.  M.  Cavarly,  Commanding  Steamship  Georgia. 

Wm.  CargiLl,  Commanding  P.  M.  S.  Australia. 

Robert  It.  Searle,  Commanding  Steamship  Colima,  P.  M.  S.  S.  Co. 

Thos.  Chapman,  First  Officer  "          "  " 

Thos.  P.  Deering,  Second  Officer  "          "  " 

W.  Ward,  Third  Officer  "          "  " 

G.  G.  Berry,  Commanding  Steamship  China,  P.  M.  S.  S.  Co. 

J.  T.  Mulcohm,  First  Officer  Steamship  Los  Angeles,  P.  M.  S.  S.  Co. 


TESTIMONIALS. 

This  work,  the  first  of  its  kind  published  within  the  last  half-century,  seems, 
upon  even  cursory  glance,  admirably  calculated  to  effect  the  professed  object, 
viz.,  to  enable  the  navigator  to  find  at  any  time,  quickly  and  accurately,  his 
position  at  sea.  The  text-matter  is  exceedingly  clear  and  concise.  The  rules  and 
instructions,  throughout,  though  based  on  theory,  are  altogether  practical,  and  will 
in  no  wise  repel  the  non-scientific  seafarer  from  attaining  (as  far  as  can  be  done  from 
a  book),  a  trustworthy  knowledge  of  what  he  most  needs.  Only  a  man  who 
knows  by  experience  the  sailor's  wants,  could  have  written  this  book,  which, 
from  the  arrangement  of  its  matter  as  well  as  from  its  numerous  original  prob- 
lems— all  carefully  worked  out — and  valuable  practical  suggestions,  will  AVC  think, 
make  it  prized  wherever  it  finds  its  way.  We  certainly  think  that  all  naviga- 
tors, no  matter  what  their  attainments,  but  especially  those  who  have  yet  to  ad- 
vance in  their  profession,  will  find  it  advantageous  to  make  themselves  acquainted 
with  the  contents  of  this  work.  Its  typographical  execution  is  admirable,  and 
reflects  great  credit  on  the  publishers. — Alta  California,  May  20,  1878. 


This  book,  prepared  by  Captain  E.  McNevin,  appears,  after  a  careful  survey 
of  its  pages,  to  be  all  that  it  claims  on  its  title  page.  It  gives  the  rules  for  solv- 
ing all  necessary  nautical  problems  in  the  simplest  and  most  practical  manner, 
and  enables  the  seaman  to  find,  without  other  aid  than  that  of  an  ordinary  edu- 
cation, his  position  at  sea.  It  attracts  from  the  first,  beginning  with  the  matter 
that  a  sailor  should  first  know,  viz.,  the  compass  and  a  table  of  the  angles  which 
its  points  and  quarter-points  make  with  the  meridian.  The  book  is  interspersed 
with  practical  and  original  suggestions  that  cannot  fail  to  be  appreciated  by  sea- 
men. The  method  of  finding  simultaneously,  latitude  and  longitude  by  double 
altitudes  has  not,  we  believe,  heretofore  been  published  in  any  American  work . 
The  same  good  judgment  is  observable  in  the  arrangement  of  the  the  tables  as 
of  the  text.  The  first  gives  the  logarithmic  lines,  tangents,  etc.,  for  the  points 
and  quarter-points  of  the  compass,  and  the  second  the  logarithms  of  the  natural 
numbers.  The  typographical  appearance  of  the  tables  is  excellent,  the  columns 
being  so  well  spaced  and  the  figures  so  distinct  that  they  can  be  used  with  facil- 
ity and  without  danger  of  error — an  important  point  for  both  student  and  navi- 
gator. A  great  deal  has  been  written  about  the  deviation  of  the  compass;  but 
we  venture  to  say  that  the  few  paragraphs  of  this  book  on  the  subject  will  be  all 
that  the  student  need  ever  seek  to  know,  either  as  to  its  theory  or  use.  We  pre- 
dict for  this  book,  which  must  have  cost  its  author  much  time  and  thought,  a 
large  patronage. — Morning  Call,  June  7,  1878. 


MARINE   DRUG   COMPANY, 

JAMESJ3URTIS 

DRUGGIST, 

CORNER   MARKET   AND   SPEAR   STS. 

SAN    FRANCISCO. 

Particular  attention  paid  to  furnishing  and  refitting  Ship's  Medicine  Chests 

-WiZtTES    .A-lsTX)    LI  QUOINS. 


MARINE  DRUG  STORE. 


N.  S.  THOMPSON 

g  DRUGGIST,  $ 

COR.  STEUART  AND  MARKET  STS. 

Particular  Attention  paid  to  replenishing  Ship's  Chests  ivitJi  Pi:re  Medicine 

A  Cood  Assortment  of  Medicine  Chests  always  on  hand,  at  Reasonable  f 'rial's. 


SAN   FRANCISCO  CORDAGE  CO. 

ESTABLISHED  1856. 
MANUFACTURERS  OF  ALL  SIZES  OF 

CORDAGE  AND  HAY  ROPE 

A  full  assortment  constantly  on  hand,  and  extra  sizes  and  lergths  made  st  short  notice. 

TTJBTSS  cfc  OO. 

6n   AND  613  FRONT  ST.  SAN  FRANCISCO,  CAL. 

Rubber  Goods  for  Steamboat  Use! 


HOSE,  PACKING,  VALVES,  GASKETS,  ETC. 

WE  MAKE  VALVES  AND  GASKETS  TO  ORDER, 
Thus  saving  the  waste  which  occurs  by  cutting  them  from  the  sheet. 

ALSO,     AM.     KINDS     OK 

RUBBER  CLOTHING,  INCLUDING  SOU-WESTERS,  LEGGGINS 

HIV.,    KIT. 

Factory  and  Warerooms;   •!  501  Market  Street'  cor'  First'  San  Francisco, 
I  327  Broadway,  New  York. 

The  Gutta  Percha  and  Ruhhcr  Manufacturing  Company, 

JOHN   \V.  TAYLOR,  M AXAC.HR, 


I.  L.  MERRELL  &  CO. 

WIRE-BOUND 

Utilized  Asbestos 


AND 


STEATITE  OR  SOAP  STONE 


BOILEK  COVEKING 


AND 


ROOFINQ   MATERIAL. 

(Patented  November  i6th,  1875.) 

Office  and   Factory,  314  Townsencl  St. 

SAN    FRANCISCO,   CALIFORNIA. 


This  is  the  best  non-conductor  of  heat  in  use.     For  covering  Steam  Boilers  and  Pipes 

it  has  no  equal.     It  has  the  highest  endorsement  for  durability,  lightness, 

elasticity,  ease  of  application,  and  all  desirable  qualities. 

It  effects  a  LARGE  SA  VI NG  OF  FUEL,  Itut*  a*  lomj  a*  the  iron  on  <'•/<«•/,  it 
is  applied ,  and  is  reasonable  in  cost. 

SZEZESTIE)     IFOIR, 


STEATITE  FELTING. 


WE  REFER  TO  THE  FOLLOWING: 


Bay  Soap  and  Candle  Works,          San  Francisco 

Mission  Woolen  Mills, 

Chemical  Works, 

Nicholas  Goetjen  Jelly  Factory, 

P.  M.  S.  S.  Milieu  Griffith, 

"  Colima, 

"  City  of  New  York, 

"  City  of  Sydney,  " 

"  City  of  San  Francisco, 

"  City  of  Panama, 

Neustadter  Bros.  Shirt  Factory, 
Steam  Tug  Jos.  H.  Redmond, 
Frear  Stone  Company. 
Steamer  Centennial, 
"         Coquille, 
"         Hope, 
Steam  Tug  Columbia, 
Lick  House, 
Steam  Tug  Monarch 
S.'F.  Gold  and  Silver  Refinery, 
Coffee  and  Spice  Mills, 
Cal.  Wine  Cooperage  and  Mill  Co. 
St'r  Rahboni,  Black  Diamond  Coal  Co. 
Steam  Tug  Continental, 
North  Beach  Dry  Dock  Works, 
Pioneer  Woolen  Mills, 
Steam  Tug  Lookout, 


California  Cutlery  Company,       .    San  Francisco 

Bay  View  Sugar  Refinery, 

Price  &  Lee's  Wool  Bleaching  Mill 

State  Harbor  Dredgers, 

Tug  Anasha, 

Fire  Commissioners'  Tug  Gov.  Irwin, 

Sacramento  Coffee  and  Spice  Mills, 

M.  C.  Hawley's  Agricultural  Warehouse  ' 

Mrs.  Johnson's  Building, 

P.M.  S.  S.  Belgic, 

Steamer  Washington, 

"         Harriett, 

"         Reform, 
Occidental  Hotel, 

-y  Mine, 
Virginia 
C  &  C.  Shaft, 
Stockton  Steamer  Centennial. 

"  "         City  of  Stockton. 

"  "         Alice  Garratt. 

Sacramento  Sawing  &  Planing  Mills,  Sacr.imento 
Sacramento  Flouring  Mills, 
Pioneer  Box  Factory 
Phoenix  Flouring  Mills, 
H.  S.  Crocker  &  Co. 
R.  K.  Barnes  &  Co. 
Brooklyn  Jute  Works,  Brooklyn 


WIRE     BOUND 


Gould  &  Curry  Mine, 
Consolidated  Virginia  Mine, 


Nevada 


BOILER   COVERING 

That  our  customers  may  understand 
our  true  position  in  the  suits  recently 
brought  against  us  by  the  U.  S.  Salaman- 
der Felting  Co.,  for.alleged  infringement 
of  their  patents,  we  beg  to  say  that  the 
charge  is  absurd  for  the  simple  reason 
that  our  interest  lay  in  carefully  avoiding 
the  use  of  any  of  their  material,  our  own 
patented  one  being  much  superior. 
The  move  against  us  is  merely  an  adver- 
tising dodge  and  a  futile  attempt  to 
injure  o\ir  business  by  deceiving  the 
public.  They  had  the  effrontery  of  noti- 
fying our  customers  not  to  pay  us  for 
work  done,  just  as  if  we  were  not  responsible  to  our  patrons  for  all  our  acts. 
We  hope  our  friends  will  stand  by  us,  and  we  assure  them  that  the 
Salamander  Felting  Company  will  be  glad  to  get  off  by  paying  the  costs  of 
suit.  Our  opinion  is  that  they  never  intend  to  allow  the  case  to  come  to 
trial,  knowing  full  well  that  we  have  never  used  their  material.  Our 
success  in  business  has  driven  them  to  their  wits'  end  and  their  only 
resource  is  to  commence  suit  to  frighten  away  from  us  the  patronage  of 
the  timid  and  ignorant. 

I.  L.  MERRELL  &  CO. 

Office  and  Factory,  314  Townsend  Street. 


C.  B.  JENNINGS  JNO.  S.  CARR 

The  undersigned  having  formed  a  partnership  under  the  firm  name  of 

JENNINGS.    CARR    &   CO. 

for  the  purpose  of  conducting  the  Wholesale  Grocery  Business, 
have  purchased  the  stock  and  good  will  of  FORDHAM  &  JEXNIXGS,  and  will 
continue  the  same  at  the  old  stand, 

Nos.  600  .  AND  602  FRONT  STREET, 

and  desire  to  call  your  attention  to  their  large  and  well  selected  stock  of 

GROCERIES. 

We  are  able  to  offer  inducements  such  as  can  be  surpassed  by  no 
house  in  the  trade,  and  respectfully  solicit  your  orders. 

Vessels  supplied  with  the  best  quality  of  goods  on  the  most  reason- 
able terms. 

We  refer,  by  permission,  to  the  author  of  this  work. 

JENNINGS,  CARR  &  CO. 

San  Francisco,  May  8th,  1878. 

ALEX.  MACKAY, 

No.  1110  Market  Street,  and  No.  11  Turk  Street, 


IMPORTER    AND    DEALER    IN 


Tapestry  1  Ingrain  Carpeting 

OIL   CLOTHS,  RUGS,  MATS, 

LACE  CURTAINS,  WINDOW  SHADES,  ETC. 
MANUFACTURER  OF  COCOA  MATTING  AND  RAG  CARPET. 

&.  W.    SMITil, 

UPHOLSTERER  WITH  ALEX.  MACKAY. 

Funiture,  and 


Spring  Mattresses,  Bedding,  Curtains,  Draperies,  Parlor  Furniture,  ahd  all  kinds 
of  Upholstery  Work  done  in  the  Best  Style,  and  at  Moderate  Prices. 

Particular  Attention  paid  to  Upholstering  &  Furnishing  Steamers  &  Vessels 
CARPETS  CLEANED  BY  STEAM  BEATING  MACHINE,  AND  RELAID. 

REFERS   TO 

Oregon  Steamship  Company.  H.  F.  Williams,  Agent  Pacific  Mail  Steamship  Co. 

California  Transportation  Company.  Western  Development  Company. 

Orders  by  Postal  Cards  Promptly  Attended  to. 


YOU   CAN   SEE   HOW   IT   IS   YOURSELF 


THAT 


SPECTACLES  AND  EYE  GLASSES 

Are  sold  Cheaper  at  Houseworth's  than  anywhere  else. 


His  Optical  Parlors  being 
on  the  first  floor  up  stairs, 
his  rent  is  cheaper  than 
any  other  dealer  in  the 
same  goods.  You  can  save 
twenty-five  per  cent,  by 
purchasing  of  him.  He 
has  been  established  in  San 
Francisco  since  1851.  The 
most  prominent  Oculists 
send  their  patients  to  him 
with  prescriptions  for 
Glasses  that  require  great 
care  and  skill  in  fitting. 

Houseworth's  Optical 
Parlors  are  at  12  Mont- 
gomery Street,  up -stairs, 
San  Francisco. 

HOUSEWORTH, 

THE  LEADING 

PHOTOGRAPHER 

HAS  RECEIVED  THE 

Higest  Prize  Medals 

At  Paris,  Vienna.Centennial 
and  San  Francisco,  for  the 
finest  photographs  in  the 
world. 

All  the  prominent  Cele- 
brities, who  visit  this  coast, 
have  their  Portraits  taken 
at  his  studio  to  insure  a 
perfect  likeness.  He  invites 
all  who  appreciate  artistic 
Photography  to  visit  his 
parlors  and  inspect  his 
large  collection  of  portraits, 
copies  of  fine  paintings,  and 
views  and  curiosities  of 
Calfornia. 

HOUSEWORTH, 

ARTIST  PHOTOGRAPHER, 

12  Montgomery  Street, 

SAN  FRANCISCO. 


HENRY  BRUGGEMANN, 


Late   with  J.  EISENBERG, 


Merchant  Tailor 

No.  526  Montgomery  Street, 

Near   corner  of  Clay,  SAN   FRANCISCO,  CAL. 


I  keep  in  stock  an  elegant  assortment  of  NOVELTIES, 
both  Foreign  and  Domestic,  Including 

FRENCH  COATINGS  1 CASSIMERES 

and   all    that   appertains   to    a   full   line    of 

CLOTHING  GOODS. 

I  make  a  Specialty  of  Military 

OFFICERS1 !  MARINERS'  OUTFITS, 

and  am  convinced  that  it  will  be  advantageous  for  all  to 
call  on  us. 

Masters  of  Ships  can  be  supplied  with 
Outfits  for  Seamen. 

Se  Habla  Espanol. 

Man  Spricht  Deutsch. 

On  Parle  Fran^ais. 


ASBESTOS  COATING 

FOR 

STEAM  BOILERS,  PIPES,  ETC. 

UNITED    STATES    AND    FOREIGN 

Salamander  Felting  Company 

PACIFIC     BRANCH. 

(Patents  issued  Sept.  4,  1869;   Oct.  5,  1869;   Oct.  4,  1870;    May  9,  1871.) 

SEWARD    COLE, 


MANAGER. 


OFFICE, 


No.  317  California  Street,  S.  F. 

FACTORY, 

Berry  Street,  between  4th  and  5th,  S.  F. 

IT  SAVES  FUEL,  SAVES  LABOR  AND  IS  REASONABLE  IN  COST. 

This  is  the  best  non-conductor  of  heat  in  use.  For  covering  Steam 
Boilers  and  Pipes  it  has  no  equal.  It  has  the  highest  endorsements  for 
durability,  lightness,  elasticity,  ease  of  application,  and  all  desirable 
qualities.  It  has  been  adopted  by  the  several  Departments  of  (Government 
of  the  United  States,  and  is  in  general  use  in  the  Atlantic  States. 

SEND    FOR    CIRCULAR. 


PAINTER  &  CO. 


SAN  FRANCISCO  I  CALIFORNIA 


510-512  CLAY  STREET, 


SAN    FRANCISCO,    CALIFORNIA. 


Printers'  Furnishing  Warehouse 


4 

This  Old  Established  Foundry  having  a  Large  Stock  and 
1  Complete  Assortment  of  the  Modern  Faces  of 

BOOK,  NEWS,  JOB  AND  ORNAMENTAL  TYPE 

IS    PREPARED    TO     FILL    ALL    ORDERS     PROMPTLY. 


PRINTING  MATERIAL 

OF  EVERY  DESCRIPTION,  INCLUDING 

POWER,  HANDIJOB  PRESSES 

OF  THE  POPULAR  MANUFACTURERS. 


ELECTROTYITNG  AND  STEREOTYPING. 

Capt.  McNevinY'PRACTiCAL  NAVIGATION'^  printed  from  Stereotype  Plates 
made  by  Painter  &  Co. 


Milton 


COUNSELLOR  AT  LAW 


AND 


Rooms  18,  19  and  20 

UNITED    STATES   COURT    BUILDING, 


NORTH-EAST  CORNER 


Washington  and  Battery  Streets, 


SAN  FRANCISCO,  CALIFORNIA. 


ATKINSON'S  WINE  HOUSE 


JAMES  ATKINSON, 


Importer  and  Dealer  in 


]  Fine  Wines!  Liquors, 

|     1021  Market  Street, 

ABOVE  SIXTH, 

SAN  FRANCISCO,  CAL. 


&  Ships  Supplied  at  Lowest  Rates. 


BASS'  PALE  ALE   IN  PI  NFS   AND   HALF-PINTS. 
French  Wines  of  all  Descriptions,  California  Wines,  Etc. 


SINGER 

•• 

Sewing  Machine 

Nearly  Three  Million  in  Use. 
EVERY     MACHINE     WARRANTED     PERFECT. 


The  Singer  Manufacturing  Co. 

118  SUTTER  STREET, 

San  Francisco,  Cal. 

J.  HOLLAND, 

GROCERIES 

HAMS  AND  BACON, 

EGGS,  BUTTER  AND  CHEESE, 
PERFUMERY  AND   TOILET  ARTICLES 

FINE  WINES  FOR  FAMILY  USE. 

SOUTH-WEST 

Cor.  Folsom  and  Fremont  Streets, 

SAN  FRANCISCO,  CALIFORNIA. 
GOODS  DELIVERED. 


3   1158  00473   1542 


40 
405 


•-•-•**»  **•  »  J      Of      ^CIII  I  (Jf  f  llci 

REGIONAL  LIBRARY  FACILITY 
Avenue,  Los  Angeles,  CA  90024-1388 
Return  this  material  to  the  library 
from  which  it  was  borrowed. 


M  DATE  RECEIVED 


UCLA  ACCESS  SERVICES 

Interlibrary  Loan 

1 1630  Universitv)  Research  Library 

Box  951 575 

Los  Angeles,  CAJ90C95-1575 


VK 

?55 

M23C 


OCT  1  8  1999 

SEL  CHEMISTF 


DUE2WK8FR 


